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Numerical Analysis (CS 450) Fall 2021

What Where
Time/place Tue/Thu 11:00am--12:15pm 0027/1025 Campus Instructional Facility / Catalog
Class URL https://bit.ly/cs450-f21
Class recordings Illinois Mediaspace
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Quizzes

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Homework

4-Credit Hour Assignment

Exams

Please find information on our upcoming exams in the corresponding section of the class calendar. Reserve your time slots in the testing facility as soon as possible--otherwise your preferred times may no longer be available.

Course Outline

  • Introduction to Scientific Computing
    • Notes
    • Notes (unfilled, with empty boxes)
    • About the Class
    • Errors, Conditioning, Accuracy, Stability
    • In-Class Activity: Forward/Backward Error
    • Floating Point
    • In-Class Activity: Floating Point
    • Demo: Catastrophic Cancellation 
        </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Conditioning of Evaluating tan.ipynb">Demo: Conditioning of Evaluating tan</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/error_and_fp/Conditioning of Evaluating tan.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Conditioning of Evaluating tan.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Conditioning of Evaluating tan.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Conditioning of Evaluating tan.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Conditioning of Evaluating tan.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Density of Floating Point Numbers.ipynb">Demo: Density of Floating Point Numbers</a>
    <ul>
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        <a href="repocur:demos/upload/error_and_fp/Density of Floating Point Numbers.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Density of Floating Point Numbers.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Density of Floating Point Numbers.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Density of Floating Point Numbers.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Density of Floating Point Numbers.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Floating Point and the Series for the Exponential Function.ipynb">Demo: Floating Point and the Series for the Exponential Function</a>
    <ul>
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        <a href="repocur:demos/upload/error_and_fp/Floating Point and the Series for the Exponential Function.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Floating Point and the Series for the Exponential Function.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Floating Point and the Series for the Exponential Function.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating Point and the Series for the Exponential Function.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating Point and the Series for the Exponential Function.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Floating Point vs Program Logic.ipynb">Demo: Floating Point vs Program Logic</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating Point vs Program Logic.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Floating Point vs Program Logic.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Floating Point vs Program Logic.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating Point vs Program Logic.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating Point vs Program Logic.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Floating point and the Harmonic Series.ipynb">Demo: Floating point and the Harmonic Series</a>
    <ul>
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        <a href="repocur:demos/upload/error_and_fp/Floating point and the Harmonic Series.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Floating point and the Harmonic Series.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Floating point and the Harmonic Series.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating point and the Harmonic Series.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Floating point and the Harmonic Series.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Picking apart a floating point number.ipynb">Demo: Picking apart a floating point number</a>
    <ul>
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        <a href="repocur:demos/upload/error_and_fp/Picking apart a floating point number.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Picking apart a floating point number.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Picking apart a floating point number.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Picking apart a floating point number.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Picking apart a floating point number.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Truncation vs Rounding.ipynb">Demo: Truncation vs Rounding</a>
    <ul>
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        <a href="repocur:demos/upload/error_and_fp/Truncation vs Rounding.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Truncation vs Rounding.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Truncation vs Rounding.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Truncation vs Rounding.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Truncation vs Rounding.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Vector Norms.ipynb">Demo: Vector Norms</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/error_and_fp/Vector Norms.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Vector Norms.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Vector Norms.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Vector Norms.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Vector Norms.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Writing Testable Numerics Code.ipynb">Demo: Writing Testable Numerics Code</a>
    <ul>
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        <a href="repocur:demos/upload/error_and_fp/Writing Testable Numerics Code.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/error_and_fp/Writing Testable Numerics Code.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/error_and_fp/Writing Testable Numerics Code.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/error_and_fp/Writing Testable Numerics Code.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/error_and_fp/Writing Testable Numerics Code.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

    • Systems of Linear Equations
      • Theory: Conditioning 
        •   <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-conditioning/start/">In-Class Activity: Matrix Norms and Conditioning</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Methods to Solve Systems
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    LU: Application and Implementation
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-lu/start/">In-Class Activity: LU</a>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Coding back-substitution.ipynb">Demo: Coding back-substitution</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/Coding back-substitution.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Coding back-substitution.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Coding back-substitution.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Coding back-substitution.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/Coding back-substitution.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Complexity of Mat-Mat multiplication and LU.ipynb">Demo: Complexity of Mat-Mat multiplication and LU</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/Complexity of Mat-Mat multiplication and LU.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Complexity of Mat-Mat multiplication and LU.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Complexity of Mat-Mat multiplication and LU.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Complexity of Mat-Mat multiplication and LU.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/Complexity of Mat-Mat multiplication and LU.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Condition number visualized.ipynb">Demo: Condition number visualized</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/Condition number visualized.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Condition number visualized.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Condition number visualized.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Condition number visualized.py">Download Python script</a>
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        <a href="repocur:demos/upload/linear_systems/Condition number visualized.ipynb">Download Jupyter notebook</a>
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    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Conditioning of 2x2 Matrices.ipynb">Demo: Conditioning of 2x2 Matrices</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/Conditioning of 2x2 Matrices.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Conditioning of 2x2 Matrices.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Conditioning of 2x2 Matrices.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Conditioning of 2x2 Matrices.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/Conditioning of 2x2 Matrices.ipynb">Download Jupyter notebook</a>
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    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/LU Factorization with Partial Pivoting.ipynb">Demo: LU Factorization with Partial Pivoting</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/LU Factorization with Partial Pivoting.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/LU Factorization with Partial Pivoting.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/LU Factorization with Partial Pivoting.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/LU Factorization with Partial Pivoting.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/LU Factorization with Partial Pivoting.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/LU Factorization.ipynb">Demo: LU Factorization</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/LU Factorization.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/LU Factorization.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/LU Factorization.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/LU Factorization.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/LU Factorization.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Matrix norms.ipynb">Demo: Matrix norms</a>
    <ul>
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        <a href="repocur:demos/upload/linear_systems/Matrix norms.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Matrix norms.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Matrix norms.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Matrix norms.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/Matrix norms.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Sherman-Morrison.ipynb">Demo: Sherman-Morrison</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_systems/Sherman-Morrison.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Sherman-Morrison.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Sherman-Morrison.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Sherman-Morrison.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/Sherman-Morrison.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Vanilla Gaussian Elimination.ipynb">Demo: Vanilla Gaussian Elimination</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_systems/Vanilla Gaussian Elimination.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_systems/Vanilla Gaussian Elimination.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_systems/Vanilla Gaussian Elimination.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_systems/Vanilla Gaussian Elimination.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_systems/Vanilla Gaussian Elimination.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

      • Linear Least Squares
        • Introduction 
          •   <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-least-squares/start/">In-Class Activity: Least Squares</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Sensitivity and Conditioning
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Solving Least Squares
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-qr/start/">In-Class Activity: QR</a>
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-hh-givens-svd/start/">In-Class Activity: Householder, Givens, SVD</a>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/3x3 Givens demo.ipynb">Demo: 3x3 Givens demo</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/3x3 Givens demo.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/3x3 Givens demo.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/3x3 Givens demo.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/3x3 Givens demo.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/3x3 Givens demo.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/3x3 Householder demo.ipynb">Demo: 3x3 Householder demo</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/3x3 Householder demo.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/3x3 Householder demo.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/3x3 Householder demo.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/3x3 Householder demo.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/3x3 Householder demo.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.ipynb">Demo: Gram-Schmidt and Modified Gram-Schmidt</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Gram-Schmidt--The Movie.ipynb">Demo: Gram-Schmidt--The Movie</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt--The Movie.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Gram-Schmidt--The Movie.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Gram-Schmidt--The Movie.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt--The Movie.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt--The Movie.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Image compression.ipynb">Demo: Image compression</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Image compression.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Image compression.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Image compression.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Image compression.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Image compression.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Interactive Polynomial Fit.ipynb">Demo: Interactive Polynomial Fit</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Interactive Polynomial Fit.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Interactive Polynomial Fit.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Interactive Polynomial Fit.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Interactive Polynomial Fit.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Interactive Polynomial Fit.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Issues with the normal equations.ipynb">Demo: Issues with the normal equations</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Issues with the normal equations.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Issues with the normal equations.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Issues with the normal equations.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Issues with the normal equations.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Issues with the normal equations.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.ipynb">Demo: Keeping track of coefficients in Gram-Schmidt</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Normal equations vs Pseudoinverse.ipynb">Demo: Normal equations vs Pseudoinverse</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Normal equations vs Pseudoinverse.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Normal equations vs Pseudoinverse.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Normal equations vs Pseudoinverse.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Normal equations vs Pseudoinverse.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Normal equations vs Pseudoinverse.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Polynomial fitting with the normal equations.ipynb">Demo: Polynomial fitting with the normal equations</a>
    <ul>
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        <a href="repocur:demos/upload/linear_least_squares/Polynomial fitting with the normal equations.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Polynomial fitting with the normal equations.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Polynomial fitting with the normal equations.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Polynomial fitting with the normal equations.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Polynomial fitting with the normal equations.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Relative cost of matrix factorizations.ipynb">Demo: Relative cost of matrix factorizations</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/linear_least_squares/Relative cost of matrix factorizations.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/linear_least_squares/Relative cost of matrix factorizations.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/linear_least_squares/Relative cost of matrix factorizations.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/linear_least_squares/Relative cost of matrix factorizations.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/linear_least_squares/Relative cost of matrix factorizations.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

        • Eigenvalue Problems
          • Properties and Transformations 
            •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    Sensitivity
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Computing Eigenvalues
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-eigenvalues/start/">In-Class Activity: Eigenvalues</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Krylov Space Methods
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Arnoldi Iteration.ipynb">Demo: Arnoldi Iteration</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/eigenvalue/Arnoldi Iteration.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Arnoldi Iteration.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Arnoldi Iteration.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Arnoldi Iteration.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/eigenvalue/Arnoldi Iteration.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.ipynb">Demo: Bauer-Fike Eigenvalue Sensitivity Bound</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Computing the SVD.ipynb">Demo: Computing the SVD</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/eigenvalue/Computing the SVD.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Computing the SVD.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Computing the SVD.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Computing the SVD.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/eigenvalue/Computing the SVD.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Exploring the Numerical Range.ipynb">Demo: Exploring the Numerical Range</a>
    <ul>
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        <a href="repocur:demos/upload/eigenvalue/Exploring the Numerical Range.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Exploring the Numerical Range.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Exploring the Numerical Range.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Exploring the Numerical Range.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/eigenvalue/Exploring the Numerical Range.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Householder Similarity Transforms.ipynb">Demo: Householder Similarity Transforms</a>
    <ul>
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        <a href="repocur:demos/upload/eigenvalue/Householder Similarity Transforms.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Householder Similarity Transforms.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Householder Similarity Transforms.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Householder Similarity Transforms.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/eigenvalue/Householder Similarity Transforms.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Orthogonal Iteration.ipynb">Demo: Orthogonal Iteration</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/eigenvalue/Orthogonal Iteration.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Orthogonal Iteration.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Orthogonal Iteration.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Orthogonal Iteration.py">Download Python script</a>
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        <a href="repocur:demos/upload/eigenvalue/Orthogonal Iteration.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Power iteration and its Variants.ipynb">Demo: Power iteration and its Variants</a>
    <ul>
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        <a href="repocur:demos/upload/eigenvalue/Power iteration and its Variants.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Power iteration and its Variants.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Power iteration and its Variants.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/eigenvalue/Power iteration and its Variants.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/eigenvalue/Power iteration and its Variants.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Rounding in characteristic polynomial using SymPy.ipynb">Demo: Rounding in characteristic polynomial using SymPy</a>
    <ul>
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        <a href="repocur:demos/upload/eigenvalue/Rounding in characteristic polynomial using SymPy.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/eigenvalue/Rounding in characteristic polynomial using SymPy.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/eigenvalue/Rounding in characteristic polynomial using SymPy.ipynb">Run interactively with cleared input</a>
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        <a href="repocur:demos/upload/eigenvalue/Rounding in characteristic polynomial using SymPy.py">Download Python script</a>
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        <a href="repocur:demos/upload/eigenvalue/Rounding in characteristic polynomial using SymPy.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
</ul>

          • Nonlinear Equations
            • Introduction 
              •   <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-krylov-nonlinear/start/">In-Class Activity: Krylov and Nonlinear Equations</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Iterative Procedures
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Methods in One Dimension
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-nonlinear/start/">In-Class Activity: Nonlinear Equations</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Methods in $n$  Dimensions (``Systems of Equations'')
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Bisection Method.ipynb">Demo: Bisection Method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Bisection Method.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Bisection Method.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Bisection Method.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Bisection Method.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Bisection Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Convergence of Newton's Method.ipynb">Demo: Convergence of Newton's Method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Convergence of Newton's Method.html">View on the web</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Convergence of Newton's Method.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Convergence of Newton's Method.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Convergence of Newton's Method.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Convergence of Newton's Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Convergence of the Secant Method.ipynb">Demo: Convergence of the Secant Method</a>
    <ul>
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        <a href="repocur:demos/upload/nonlinear/Convergence of the Secant Method.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Convergence of the Secant Method.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Convergence of the Secant Method.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Convergence of the Secant Method.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Convergence of the Secant Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Fixed point iteration.ipynb">Demo: Fixed point iteration</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Fixed point iteration.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Fixed point iteration.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Fixed point iteration.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Fixed point iteration.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Fixed point iteration.ipynb">Download Jupyter notebook</a>
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    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Newton's Method.ipynb">Demo: Newton's Method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Newton's Method.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Newton's Method.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Newton's Method.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Newton's Method.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Newton's Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Newton's method in n dimensions.ipynb">Demo: Newton's method in n dimensions</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Newton's method in n dimensions.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Newton's method in n dimensions.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Newton's method in n dimensions.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Newton's method in n dimensions.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Newton's method in n dimensions.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Rates of Convergence.ipynb">Demo: Rates of Convergence</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Rates of Convergence.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Rates of Convergence.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Rates of Convergence.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Rates of Convergence.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Rates of Convergence.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Secant Method.ipynb">Demo: Secant Method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Secant Method.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Secant Method.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Secant Method.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Secant Method.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Secant Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Three quadratic functions.ipynb">Demo: Three quadratic functions</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/nonlinear/Three quadratic functions.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/nonlinear/Three quadratic functions.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/nonlinear/Three quadratic functions.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/nonlinear/Three quadratic functions.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/nonlinear/Three quadratic functions.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

            • Optimization
              • Introduction 
                •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    Methods for unconstrained opt. in one dimension
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-optimization-theory/start/">In-Class Activity: Optimization Theory</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Methods for unconstrained opt. in $n$  dimensions
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-optimization-methods/start/">In-Class Activity: Optimization Methods</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Nonlinear Least Squares
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Constrained Optimization
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Conjugate Gradient Method.ipynb">Demo: Conjugate Gradient Method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Conjugate Gradient Method.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Conjugate Gradient Method.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Conjugate Gradient Method.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Conjugate Gradient Method.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Conjugate Gradient Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Gauss-Newton.ipynb">Demo: Gauss-Newton</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Gauss-Newton.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Gauss-Newton.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Gauss-Newton.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Gauss-Newton.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Gauss-Newton.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Golden Section Proportions.ipynb">Demo: Golden Section Proportions</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Golden Section Proportions.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Golden Section Proportions.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Golden Section Proportions.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Golden Section Proportions.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Golden Section Proportions.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Nelder-Mead Method.ipynb">Demo: Nelder-Mead Method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Nelder-Mead Method.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Nelder-Mead Method.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Nelder-Mead Method.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Nelder-Mead Method.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Nelder-Mead Method.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Newton's Method in 1D.ipynb">Demo: Newton's Method in 1D</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Newton's Method in 1D.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Newton's Method in 1D.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Newton's Method in 1D.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Newton's Method in 1D.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Newton's Method in 1D.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Newton's Method in n dimensions.ipynb">Demo: Newton's Method in n dimensions</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Newton's Method in n dimensions.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Newton's Method in n dimensions.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Newton's Method in n dimensions.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Newton's Method in n dimensions.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Newton's Method in n dimensions.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Sequential Quadratic Programming.ipynb">Demo: Sequential Quadratic Programming</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Sequential Quadratic Programming.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Sequential Quadratic Programming.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Sequential Quadratic Programming.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Sequential Quadratic Programming.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Sequential Quadratic Programming.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Steepest Descent.ipynb">Demo: Steepest Descent</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/optimization/Steepest Descent.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/optimization/Steepest Descent.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/optimization/Steepest Descent.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/optimization/Steepest Descent.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/optimization/Steepest Descent.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

              • Interpolation
                • Introduction 
                  •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    Methods
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-interpolation/start/">In-Class Activity: Interpolation</a>
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Error Estimation
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Piecewise interpolation, Splines
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Chebyshev interpolation.ipynb">Demo: Chebyshev interpolation</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Chebyshev interpolation.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Chebyshev interpolation.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Chebyshev interpolation.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Chebyshev interpolation.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Chebyshev interpolation.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Choice of Nodes for Polynomial Interpolation.ipynb">Demo: Choice of Nodes for Polynomial Interpolation</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Choice of Nodes for Polynomial Interpolation.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Choice of Nodes for Polynomial Interpolation.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Choice of Nodes for Polynomial Interpolation.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Choice of Nodes for Polynomial Interpolation.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Choice of Nodes for Polynomial Interpolation.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Composite Gauss Interpolation Error.ipynb">Demo: Composite Gauss Interpolation Error</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Composite Gauss Interpolation Error.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Composite Gauss Interpolation Error.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Composite Gauss Interpolation Error.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Composite Gauss Interpolation Error.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Composite Gauss Interpolation Error.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Interpolation Error.ipynb">Demo: Interpolation Error</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Interpolation Error.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Interpolation Error.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Interpolation Error.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Interpolation Error.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Interpolation Error.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Interpolation with Radial Basis Functions.ipynb">Demo: Interpolation with Radial Basis Functions</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Interpolation with Radial Basis Functions.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Interpolation with Radial Basis Functions.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Interpolation with Radial Basis Functions.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Interpolation with Radial Basis Functions.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Interpolation with Radial Basis Functions.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Jump with Chebyshev Nodes.ipynb">Demo: Jump with Chebyshev Nodes</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Jump with Chebyshev Nodes.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Jump with Chebyshev Nodes.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Jump with Chebyshev Nodes.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Jump with Chebyshev Nodes.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Jump with Chebyshev Nodes.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Monomial interpolation.ipynb">Demo: Monomial interpolation</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Monomial interpolation.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Monomial interpolation.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Monomial interpolation.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Monomial interpolation.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Monomial interpolation.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Orthogonal Polynomials.ipynb">Demo: Orthogonal Polynomials</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Orthogonal Polynomials.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Orthogonal Polynomials.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Orthogonal Polynomials.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Orthogonal Polynomials.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Orthogonal Polynomials.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Playing with Barycentric Interpolation.ipynb">Demo: Playing with Barycentric Interpolation</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/interpolation/Playing with Barycentric Interpolation.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/interpolation/Playing with Barycentric Interpolation.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/interpolation/Playing with Barycentric Interpolation.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/interpolation/Playing with Barycentric Interpolation.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/interpolation/Playing with Barycentric Interpolation.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

                • Numerical Integration and Differentiation
                  • Numerical Integration 
                    •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    Quadrature Methods
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Accuracy and Stability
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Gaussian Quadrature
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Composite Quadrature
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Numerical Differentiation
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Richardson Extrapolation
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-quadrature/start/">In-Class Activity: Differentiation and Quadrature</a>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Accuracy of Newton-Cotes.ipynb">Demo: Accuracy of Newton-Cotes</a>
    <ul>
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        <a href="repocur:demos/upload/quadrature_and_diff/Accuracy of Newton-Cotes.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Accuracy of Newton-Cotes.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Accuracy of Newton-Cotes.ipynb">Run interactively with cleared input</a>
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        <a href="repocur:demos/upload/quadrature_and_diff/Accuracy of Newton-Cotes.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Accuracy of Newton-Cotes.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Finite Differences vs Noise.ipynb">Demo: Finite Differences vs Noise</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Finite Differences vs Noise.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Finite Differences vs Noise.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Finite Differences vs Noise.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Finite Differences vs Noise.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Finite Differences vs Noise.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Floating point vs Finite Differences.ipynb">Demo: Floating point vs Finite Differences</a>
    <ul>
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        <a href="repocur:demos/upload/quadrature_and_diff/Floating point vs Finite Differences.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Floating point vs Finite Differences.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Floating point vs Finite Differences.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Floating point vs Finite Differences.py">Download Python script</a>
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        <a href="repocur:demos/upload/quadrature_and_diff/Floating point vs Finite Differences.ipynb">Download Jupyter notebook</a>
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    </ul>
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    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Gaussian quadrature weight finder.ipynb">Demo: Gaussian quadrature weight finder</a>
    <ul>
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        <a href="repocur:demos/upload/quadrature_and_diff/Gaussian quadrature weight finder.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Gaussian quadrature weight finder.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Gaussian quadrature weight finder.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Gaussian quadrature weight finder.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Gaussian quadrature weight finder.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Newton-Cotes weight finder.ipynb">Demo: Newton-Cotes weight finder</a>
    <ul>
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        <a href="repocur:demos/upload/quadrature_and_diff/Newton-Cotes weight finder.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Newton-Cotes weight finder.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Newton-Cotes weight finder.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Newton-Cotes weight finder.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Newton-Cotes weight finder.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Richardson with Finite Differences.ipynb">Demo: Richardson with Finite Differences</a>
    <ul>
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        <a href="repocur:demos/upload/quadrature_and_diff/Richardson with Finite Differences.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Richardson with Finite Differences.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Richardson with Finite Differences.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Richardson with Finite Differences.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Richardson with Finite Differences.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.ipynb">Demo: Taking Derivatives with Vandermonde Matrices</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.py">Download Python script</a>
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        <a href="repocur:demos/upload/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
</ul>

                  • Initial Value Problems for ODEs
                    • Existence, Uniqueness, Conditioning 
                      •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    Numerical Methods (I)
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Accuracy and Stability
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Stiffness
  </li>
  <li data-jstree='{"icon": "fa fa-file-o"}'>
    Numerical Methods (II)
  </li>
  <li data-jstree='{"icon": "fa fa-user"}'>
    <a href="https://relate.cs.illinois.edu/course/cs450-f21/flow/inclass-ivp/start/">In-Class Activity: Initial Value Problems</a>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Backward Euler stability.ipynb">Demo: Backward Euler stability</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/ivp_odes/Backward Euler stability.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/ivp_odes/Backward Euler stability.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Backward Euler stability.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/ivp_odes/Backward Euler stability.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/ivp_odes/Backward Euler stability.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Dissipation in Runge-Kutta Methods.ipynb">Demo: Dissipation in Runge-Kutta Methods</a>
    <ul>
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        <a href="repocur:demos/upload/ivp_odes/Dissipation in Runge-Kutta Methods.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/ivp_odes/Dissipation in Runge-Kutta Methods.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Dissipation in Runge-Kutta Methods.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/ivp_odes/Dissipation in Runge-Kutta Methods.py">Download Python script</a>
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        <a href="repocur:demos/upload/ivp_odes/Dissipation in Runge-Kutta Methods.ipynb">Download Jupyter notebook</a>
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    </ul>
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  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Forward Euler stability.ipynb">Demo: Forward Euler stability</a>
    <ul>
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        <a href="repocur:demos/upload/ivp_odes/Forward Euler stability.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/ivp_odes/Forward Euler stability.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Forward Euler stability.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/ivp_odes/Forward Euler stability.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/ivp_odes/Forward Euler stability.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Predator-Prey System.ipynb">Demo: Predator-Prey System</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/ivp_odes/Predator-Prey System.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/ivp_odes/Predator-Prey System.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Predator-Prey System.ipynb">Run interactively with cleared input</a>
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        <a href="repocur:demos/upload/ivp_odes/Predator-Prey System.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/ivp_odes/Predator-Prey System.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Stability regions.ipynb">Demo: Stability regions</a>
    <ul>
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        <a href="repocur:demos/upload/ivp_odes/Stability regions.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/ivp_odes/Stability regions.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Stability regions.ipynb">Run interactively with cleared input</a>
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        <a href="repocur:demos/upload/ivp_odes/Stability regions.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/ivp_odes/Stability regions.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Stiffness.ipynb">Demo: Stiffness</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/ivp_odes/Stiffness.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/ivp_odes/Stiffness.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/ivp_odes/Stiffness.ipynb">Run interactively with cleared input</a>
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        <a href="repocur:demos/upload/ivp_odes/Stiffness.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/ivp_odes/Stiffness.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

                    • Boundary Value Problems for ODEs
                      • Existence, Uniqueness, Conditioning 
                        •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    Numerical Methods
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/bvp_odes/Finite differences.ipynb">Demo: Finite differences</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/bvp_odes/Finite differences.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/bvp_odes/Finite differences.ipynb">Run interactively</a>
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      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/bvp_odes/Finite differences.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/bvp_odes/Finite differences.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/bvp_odes/Finite differences.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/bvp_odes/Shooting method.ipynb">Demo: Shooting method</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/bvp_odes/Shooting method.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/bvp_odes/Shooting method.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/bvp_odes/Shooting method.ipynb">Run interactively with cleared input</a>
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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/bvp_odes/Shooting method.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/bvp_odes/Shooting method.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/bvp_odes/Sparse matrices.ipynb">Demo: Sparse matrices</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/bvp_odes/Sparse matrices.html">View on the web</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/bvp_odes/Sparse matrices.ipynb">Run interactively</a>
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        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/bvp_odes/Sparse matrices.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/bvp_odes/Sparse matrices.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/bvp_odes/Sparse matrices.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

                      • Partial Differential Equations and Sparse Linear Algebra
                        • Sparse Linear Algebra 
                          •   <li data-jstree='{"icon": "fa fa-file-o"}'>
    PDEs
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Jacobi vs Conjugate Gradient.ipynb">Demo: Jacobi vs Conjugate Gradient</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/pdes/Jacobi vs Conjugate Gradient.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/pdes/Jacobi vs Conjugate Gradient.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Jacobi vs Conjugate Gradient.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/pdes/Jacobi vs Conjugate Gradient.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/pdes/Jacobi vs Conjugate Gradient.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Sparse Matrix Factorizations and Fill-In.ipynb">Demo: Sparse Matrix Factorizations and Fill-In</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/pdes/Sparse Matrix Factorizations and Fill-In.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/pdes/Sparse Matrix Factorizations and Fill-In.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Sparse Matrix Factorizations and Fill-In.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/pdes/Sparse Matrix Factorizations and Fill-In.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/pdes/Sparse Matrix Factorizations and Fill-In.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Stationary Iterative Methods.ipynb">Demo: Stationary Iterative Methods</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/pdes/Stationary Iterative Methods.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/pdes/Stationary Iterative Methods.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Stationary Iterative Methods.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/pdes/Stationary Iterative Methods.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/pdes/Stationary Iterative Methods.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Time-dependent PDEs.ipynb">Demo: Time-dependent PDEs</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/pdes/Time-dependent PDEs.html">View on the web</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/pdes/Time-dependent PDEs.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/pdes/Time-dependent PDEs.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/pdes/Time-dependent PDEs.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/pdes/Time-dependent PDEs.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

                        • Fast Fourier Transform
                        • Additional Topics
                          • Demo: An Introduction to Sympy
                            • View on the web 
                              •       <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=demos/misc/An Introduction to Sympy.ipynb">Run interactively</a>
      </li>
      <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
        <a href="https://mybinder.org/v2/gh/inducer/numerics-notes/main?filepath=cleared-demos/misc/An Introduction to Sympy.ipynb">Run interactively with cleared input</a>
      </li>
      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/misc/An Introduction to Sympy.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/misc/An Introduction to Sympy.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

Class scribbles (click to view)

**CAUTION!** These scribbled PDFs are an *unedited* reflection of what I wrote during class. They need to be viewed in the context of the class discussion that led to them. See the lecture videos for that. If you would like actual, self-contained class notes, look in the outline above. These scribbles are provided here to provide a record of our class discussion, to be used in perhaps the following ways: * as a way to cross-check your own notes * to look up a formula that you know was shown in a certain class * to remind yourself of what exactly was covered on a given day By continuing to read them, you acknowledge that these files are provided as supplementary material on an as-is basis.

Team

Andreas Kloeckner

Andreas Kloeckner

(Instructor)

Email: andreask@illinois.edu

Office: 4318 Siebel

Xiaoyu Wei

Xiaoyu Wei

(Instructor)

Email: xywei@illinois.edu

Office: 4215 Siebel

Nathanael Assefa

Nathanael Assefa

(TA)

Email: nassefa2@illinois.edu

Office: 0207 Siebel

Navjot Singh

Navjot Singh

(TA)

Email: navjot2@illinois.edu

Office: 0207 Siebel

Lukas Spies

Lukas Spies

(TA)

Email: lspies@illinois.edu

Office: 0207 Siebel

Mina Sun

Mina Sun

(TA)

Email: ms65@illinois.edu

Office: 0207 Siebel

Textbook

Scientific Computing: An Introductory Survey

Scientific Computing: An Introductory Survey / E-Book (accessible free of charge from campus network/VPN)

Michael T. Heath, Revised Second Edition, Society for Industrial and Applied Mathematics

Resource site

Also see our class Piazza forum for a discount code for purchasing the book from SIAM.

Computing

We will be using Python with the libraries numpy, scipy and matplotlib for in-class work and assignments. No other languages are permitted. Python has a very gentle learning curve, so you should feel at home even if you've never done any work in Python.

Running Code on your Own Computer

While running code in this online system should technically suffice to do your work for this class, you may find it useful to also install Python on your own computer.

The recommended and perhaps one of the easier ways of doing so involves downloading the Anaconda Python distribution. Note that this is a commercial product (even if it is free of charge), and this is not intended as an endorsement of the company or the product. Note that we cannot promise to provide technical support for this installation.

Download Anaconda Python »

Another way to obtain a Python installation is through a virtual machine image:

Download Virtual Machine »

Grading Policies

View policies »

Python Help

(see section 1 of the outline for more)

Python workshop material

Numpy Help

(see section 1 of the outline for more)