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Numerical Analysis (CS 450) Fall 2019

What	Where
Time/place	MW 3:30pm--4:45pm 1320 DCL / Catalog
Class URL	https://relate.cs.illinois.edu/course/cs450-f19/ or https://bit.ly.cs450-f19
Instructor	Luke Olson
Quick Links	Discuss on Piazza »Calendar »Echo 360 Video»

Course Outline

Introduction

Demo: Catastrophic Cancellation

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    <a href="repocur:demos/upload/error_and_fp/Conditioning of Evaluating tan.html">Demo: Conditioning of Evaluating tan</a>
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        <a href="repocur:demos/upload/error_and_fp/Conditioning of Evaluating tan.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/error_and_fp/Density of Floating Point Numbers.html">Demo: Density of Floating Point Numbers</a>
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        <a href="repocur:demos/upload/error_and_fp/Density of Floating Point Numbers.py">Download Python script</a>
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        <a href="repocur:demos/upload/error_and_fp/Density of Floating Point Numbers.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/error_and_fp/Floating Point and the Series for the Exponential Function.html">Demo: Floating Point and the Series for the Exponential Function</a>
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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>
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        <a href="repocur:demos/upload/error_and_fp/Floating Point and the Series for the Exponential Function.py">Download Python script</a>
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        <a href="repocur:demos/upload/error_and_fp/Floating Point and the Series for the Exponential Function.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/error_and_fp/Floating Point vs Program Logic.html">Demo: Floating Point vs Program Logic</a>
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    <a href="repocur:demos/upload/error_and_fp/Floating point and the Harmonic Series.html">Demo: Floating point and the Harmonic Series</a>
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    <a href="repocur:demos/upload/error_and_fp/Picking apart a floating point number.html">Demo: Picking apart a floating point number</a>
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        <a href="repocur:demos/upload/error_and_fp/Picking apart a floating point number.py">Download Python script</a>
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    <a href="repocur:demos/upload/error_and_fp/Polynomial Evaluation Floating Point.html">Demo: Polynomial Evaluation Floating Point</a>
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        <a href="repocur:demos/upload/error_and_fp/Polynomial Evaluation Floating Point.py">Download Python script</a>
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    <a href="repocur:demos/upload/error_and_fp/Truncation vs Rounding.html">Demo: Truncation vs Rounding</a>
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    <a href="repocur:demos/upload/error_and_fp/Vector Norms.html">Demo: Vector Norms</a>
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        <a href="repocur:demos/upload/error_and_fp/Vector Norms.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/error_and_fp/Writing Testable Numerics Code.html">Demo: Writing Testable Numerics Code</a>
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Systems of Linear Equations

Demo: Coding back-substitution

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    <a href="repocur:demos/upload/linear_systems/Complexity of Mat-Mat multiplication and LU.html">Demo: Complexity of Mat-Mat multiplication and LU</a>
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        <a href="repocur:demos/upload/linear_systems/Complexity of Mat-Mat multiplication and LU.py">Download Python script</a>
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        <a href="repocur:demos/upload/linear_systems/Complexity of Mat-Mat multiplication and LU.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/linear_systems/Condition number visualized.html">Demo: Condition number visualized</a>
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        <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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    <a href="repocur:demos/upload/linear_systems/Conditioning of 2x2 Matrices.html">Demo: Conditioning of 2x2 Matrices</a>
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    <a href="repocur:demos/upload/linear_systems/Elimination Matrices I.html">Demo: Elimination Matrices I</a>
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    <a href="repocur:demos/upload/linear_systems/Elimination Matrices II.html">Demo: Elimination Matrices II</a>
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        <a href="repocur:demos/upload/linear_systems/Elimination Matrices II.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/linear_systems/LU factorization.html">Demo: LU factorization</a>
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        <a href="repocur:demos/upload/linear_systems/LU factorization.py">Download Python script</a>
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        <a href="repocur:demos/upload/linear_systems/LU factorization.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/linear_systems/LU with Partial Pivoting.html">Demo: LU with Partial Pivoting</a>
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    <a href="repocur:demos/upload/linear_systems/Matrix norms.html">Demo: Matrix norms</a>
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        <a href="repocur:demos/upload/linear_systems/Matrix norms.ipynb">Download Jupyter notebook</a>
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    <a href="repocur:demos/upload/linear_systems/Sherman-Morrison.html">Demo: Sherman-Morrison</a>
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    <a href="repocur:demos/upload/linear_systems/Vanilla Gaussian Elimination.html">Demo: Vanilla Gaussian Elimination</a>
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Linear Least Squares

Demo: 3x3 Givens demo

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    <a href="repocur:demos/upload/linear_least_squares/3x3 Householder demo.html">Demo: 3x3 Householder demo</a>
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    <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt and Modified Gram-Schmidt.html">Demo: Gram-Schmidt and Modified Gram-Schmidt</a>
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    <a href="repocur:demos/upload/linear_least_squares/Gram-Schmidt--The Movie.html">Demo: Gram-Schmidt--The Movie</a>
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    <a href="repocur:demos/upload/linear_least_squares/Image compression.html">Demo: Image compression</a>
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    <a href="repocur:demos/upload/linear_least_squares/Interactive Polynomial Fit.html">Demo: Interactive Polynomial Fit</a>
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    <a href="repocur:demos/upload/linear_least_squares/Issues with the normal equations.html">Demo: Issues with the normal equations</a>
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    <a href="repocur:demos/upload/linear_least_squares/Keeping track of coefficients in Gram-Schmidt.html">Demo: Keeping track of coefficients in Gram-Schmidt</a>
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    <a href="repocur:demos/upload/linear_least_squares/Normal equations vs Pseudoinverse.html">Demo: Normal equations vs Pseudoinverse</a>
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    <a href="repocur:demos/upload/linear_least_squares/Polynomial fitting with the normal equations.html">Demo: Polynomial fitting with the normal equations</a>
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    <a href="repocur:demos/upload/linear_least_squares/Relative cost of matrix factorizations.html">Demo: Relative cost of matrix factorizations</a>
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Eigenvalue Problems

Demo: Arnoldi Iteration with Complex Eigenvalues

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    <a href="repocur:demos/upload/eigenvalue/Arnoldi Iteration.html">Demo: Arnoldi Iteration</a>
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    <a href="repocur:demos/upload/eigenvalue/Bauer-Fike Eigenvalue Sensitivity Bound.html">Demo: Bauer-Fike Eigenvalue Sensitivity Bound</a>
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    <a href="repocur:demos/upload/eigenvalue/Computing the SVD.html">Demo: Computing the SVD</a>
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    <a href="repocur:demos/upload/eigenvalue/Householder Similarity Transforms.html">Demo: Householder Similarity Transforms</a>
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    <a href="repocur:demos/upload/eigenvalue/Orthogonal Iteration.html">Demo: Orthogonal Iteration</a>
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    <a href="repocur:demos/upload/eigenvalue/Power iteration and its Variants.html">Demo: Power iteration and its Variants</a>
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    <a href="repocur:demos/upload/eigenvalue/Rounding in characteristic polynomial using SymPy.html">Demo: Rounding in characteristic polynomial using SymPy</a>
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Nonlinear Equations

Demo: Bisection Method

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    <a href="repocur:demos/upload/nonlinear/Convergence of Newton's Method.html">Demo: Convergence of Newton's Method</a>
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    <a href="repocur:demos/upload/nonlinear/Convergence of the Secant Method.html">Demo: Convergence of the Secant Method</a>
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    <a href="repocur:demos/upload/nonlinear/Fixed point iteration.html">Demo: Fixed point iteration</a>
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    <a href="repocur:demos/upload/nonlinear/Newton's Method.html">Demo: Newton's Method</a>
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    <a href="repocur:demos/upload/nonlinear/Newton's method in n dimensions.html">Demo: Newton's method in n dimensions</a>
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    <a href="repocur:demos/upload/nonlinear/Rates of Convergence.html">Demo: Rates of Convergence</a>
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    <a href="repocur:demos/upload/nonlinear/Secant Method.html">Demo: Secant Method</a>
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    <a href="repocur:demos/upload/nonlinear/Three quadratic functions.html">Demo: Three quadratic functions</a>
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Optimization

Demo: Conjugate Gradient Method

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    <a href="repocur:demos/upload/optimization/Conjugate Gradient Parallel Tangents as Krylov Subspace Method.html">Demo: Conjugate Gradient Parallel Tangents as Krylov Subspace Method</a>
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    <a href="repocur:demos/upload/optimization/Gauss-Newton.html">Demo: Gauss-Newton</a>
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    <a href="repocur:demos/upload/optimization/Golden Section Proportions.html">Demo: Golden Section Proportions</a>
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    <a href="repocur:demos/upload/optimization/Nelder-Mead Method.html">Demo: Nelder-Mead Method</a>
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    <a href="repocur:demos/upload/optimization/Newton's Method in 1D.html">Demo: Newton's Method in 1D</a>
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    <a href="repocur:demos/upload/optimization/Newton's Method in n dimensions.html">Demo: Newton's Method in n dimensions</a>
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    <a href="repocur:demos/upload/optimization/Sequential Quadratic Programming.html">Demo: Sequential Quadratic Programming</a>
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    <a href="repocur:demos/upload/optimization/Steepest Descent.html">Demo: Steepest Descent</a>
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Interpolation

Demo: Chebyshev interpolation

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    <a href="repocur:demos/upload/interpolation/Choice of Nodes for Polynomial Interpolation.html">Demo: Choice of Nodes for Polynomial Interpolation</a>
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    <a href="repocur:demos/upload/interpolation/Composite Gauss Interpolation Error.html">Demo: Composite Gauss Interpolation Error</a>
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        <a href="repocur:demos/upload/interpolation/Composite Gauss Interpolation Error.py">Download Python script</a>
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      <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="repocur:demos/upload/interpolation/Interpolation Error.html">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>
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      <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="repocur:demos/upload/interpolation/Interpolation with Radial Basis Functions.html">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-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="repocur:demos/upload/interpolation/Jump with Chebyshev Nodes.html">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-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="repocur:demos/upload/interpolation/Monomial interpolation.html">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-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="repocur:demos/upload/interpolation/Orthogonal Polynomials.html">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>
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      <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>
</ul>

Numerical Integration and Differentiation

Demo: Accuracy of Newton-Cotes

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        <a href="repocur:demos/upload/quadrature_and_diff/Accuracy of Newton-Cotes.py">Download Python script</a>
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      <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="repocur:demos/upload/quadrature_and_diff/Finite Differences vs Noise.html">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-terminal"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Finite Differences vs Noise.py">Download Python script</a>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Finite Differences vs Noise.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/quadrature_and_diff/Floating point vs Finite Differences.html">Demo: Floating point vs Finite Differences</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Floating point vs Finite Differences.html">View on the web</a>
      </li>
      <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>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Floating point vs Finite Differences.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/quadrature_and_diff/Gaussian quadrature weight finder.html">Demo: Gaussian quadrature weight finder</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Gaussian quadrature weight finder.html">View on the web</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="repocur:demos/upload/quadrature_and_diff/Newton-Cotes weight finder.html">Demo: Newton-Cotes weight finder</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Newton-Cotes weight finder.html">View on the web</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="repocur:demos/upload/quadrature_and_diff/Richardson with Finite Differences.html">Demo: Richardson with Finite Differences</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Richardson with Finite Differences.html">View on the web</a>
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      <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="repocur:demos/upload/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.html">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>
      </li>
      <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>
      </li>
      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/quadrature_and_diff/Taking Derivatives with Vandermonde Matrices.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

Initial Value Problems for ODEs

Demo: Backward Euler stability

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        <a href="repocur:demos/upload/ivp_odes/Backward Euler stability.py">Download Python script</a>
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        <a href="repocur:demos/upload/ivp_odes/Backward Euler stability.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/ivp_odes/Dissipation in Runge-Kutta Methods.html">Demo: Dissipation in Runge-Kutta Methods</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/ivp_odes/Dissipation in Runge-Kutta Methods.html">View on the web</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>
      </li>
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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>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/ivp_odes/Forward Euler stability.html">Demo: Forward Euler stability</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/ivp_odes/Forward Euler stability.html">View on the web</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="repocur:demos/upload/ivp_odes/Stability regions.html">Demo: Stability regions</a>
    <ul>
      <li data-jstree='{"icon": "fa fa-newspaper-o"}'>
        <a href="repocur:demos/upload/ivp_odes/Stability regions.html">View on the web</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="repocur:demos/upload/ivp_odes/Stiffness.html">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="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

Demo: Finite differences

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        <a href="repocur:demos/upload/bvp_odes/Finite differences.py">Download Python script</a>
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        <a href="repocur:demos/upload/bvp_odes/Finite differences.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/bvp_odes/Shooting method.html">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="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>
      </li>
    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/bvp_odes/Sparse matrices.html">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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      <li data-jstree='{"icon": "fa fa-terminal"}'>
        <a href="repocur:demos/upload/bvp_odes/Sparse matrices.py">Download Python script</a>
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      <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

Demo: Jacobi vs Conjugate Gradient

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        <a href="repocur:demos/upload/pdes/Jacobi vs Conjugate Gradient.py">Download Python script</a>
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        <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="repocur:demos/upload/pdes/Sparse Matrix Factorizations and Fill-In.html">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>
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      <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="repocur:demos/upload/pdes/Stationary Iterative Methods.html">Demo: Stationary Iterative Methods</a>
    <ul>
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        <a href="repocur:demos/upload/pdes/Stationary Iterative Methods.html">View on the web</a>
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        <a href="repocur:demos/upload/pdes/Stationary Iterative Methods.py">Download Python script</a>
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      <li data-jstree='{"icon": "fa fa-download"}'>
        <a href="repocur:demos/upload/pdes/Stationary Iterative Methods.ipynb">Download Jupyter notebook</a>
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    </ul>
  </li>
  <li data-jstree='{"icon": "fa fa-keyboard-o"}'>
    <a href="repocur:demos/upload/pdes/Time-dependent PDEs.html">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>
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      <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

Demo: Fast Fourier Transform

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        <a href="repocur:demos/upload/fft/Fast Fourier Transform.py">Download Python script</a>
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        <a href="repocur:demos/upload/fft/Fast Fourier Transform.ipynb">Download Jupyter notebook</a>
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    </ul>
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</ul>

Additional Topics

Demo: An Introduction to Sympy

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        <a href="repocur:demos/upload/misc/An Introduction to Sympy.py">Download Python script</a>
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        <a href="repocur:demos/upload/misc/An Introduction to Sympy.ipynb">Download Jupyter notebook</a>
      </li>
    </ul>
  </li>
</ul>

Team

Luke Olson

Luke Olson

(Instructor)

Email: lukeo@illinois.edu

Alexey Voronin

Alexey Voronin

(Teaching Assistant)

Email: voronin2@illinois.edu

Office: 0209 Siebel

Office Hours: Wednesday 1.30-2.30 pm Friday 2.30-3.30 pm

Ping-Hsuan Tsai

Ping-Hsuan Tsai

(Teaching Assistant)

Email: pht2@illinois.edu

Office: 0209 Siebel

Office Hours: Tuesday and Friday 9-10 am

Isuru Fernando

Isuru Fernando

(Teaching Assistant)

Email: idf2@illinois.edu

Office: 0209 Siebel

Office Hours: Wednesday and Friday 12.30-1.30 pm

Malachi Phillips

Malachi Phillips

(Teaching Assistant)

Email: malachi2@illinois.edu

Office: 0207 Siebel

Office Hours: Monday 2-3 pm, Thursday 3-4pm

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 relate 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 »

Python Help

(see section 1 of the outline for more)

Python tutorial
Facts and myths about Python names and values
Learn Python the hard way
Project Euler (Lots of practice problems)
From Python to Numpy

Python workshop material

Video: Located on Echo 360 along with the other class recordings
Tutorial material
Scipy lecture notes
CSE workshop training material

Numpy Help

(see section 1 of the outline for more)

Introduction to Python for Science
The SciPy lectures
The Numpy MedKit by Stéfan van der Walt
The Numpy User Guide by Travis Oliphant
Numpy/Scipy documentation
More in this reddit thread
Spyder (a Python IDE, like Matlab) is installed in the virtual machine. (Applications Menu > Development > Spyder)
An introduction to Numpy and SciPy

Grading Policies

View policies »