# CS450 Calendar

Note: Some calendar entries are clickable and link to entries below.
Examlet 4 (Dec. 13, 2018 - Dec. 20, 2018)

As you may have seen in our class policies, our "examlets" and "finals" will take place in a computer-based testing facility ("CBTF") in Grainger Library.

You must schedule your test appointment with the Computer-Based Testing Facility at this link. This examlet is now available for scheduling.

Find out more about the testing facility, such as:

• where it is
• when to show up
• what to bring (and not to bring)

The exam will be 3 hours in length, and it will cover all chapters.

Final Exam Study Guide

Examlet 3 Study Guide

Examlet 2 Study Guide

Examlet 1 Study Guide

Lecture 28 (Dec. 10, 2018, 3:30 p.m. - Dec. 10, 2018, 4:45 p.m.)
• Collocation methods
• Weighted residual methods
• Galerkin method and weak form
• ODE BVP eigenvalue problems
• Classification of PDEs
• Ccharacteristic curves

Activity: Solving the 1D Poisson Equation

Quiz 24: Discretization of ODEs using Basis Functions and Basics of PDEs

Lecture 27 (Dec. 5, 2018, 3:30 p.m. - Dec. 5, 2018, 4:45 p.m.)

Lecture Notes

• Existence of solutions to ODE BVPs
• Green's functions and conditioning
• Shooting and multiple shooting methods
• Finite difference methods
• Collocation methods
• Weighted residual methods

Quiz 23: Numerical Solutions to ODE BVPs

Lecture 26 (Dec. 3, 2018, 3:30 p.m. - Dec. 3, 2018, 4:45 p.m.)

Lecture Notes

• Stability of ODEs and methods
• Local and global error, order of accuracy
• Stability regions for forward and backward Euler
• Runge Kutta methods
• Multistep methods

Activity: Backward Euler Method

Quiz 22: Numerical Solutions to ODEs

Examlet 3 (Nov. 29, 2018, 9 a.m. - Dec. 1, 2018, 10 p.m.)

As you may have seen in our class policies, our "examlets" and "finals" will take place in a computer-based testing facility ("CBTF") in Grainger Library.

You must schedule your test appointment with the Computer-Based Testing Facility at this link. This examlet is now available for scheduling.

Find out more about the testing facility, such as:

• where it is
• when to show up
• what to bring (and not to bring)

The exam will be 50 minutes in length, and it will cover the material of the first seven chapters.

Examlet 3 Study Guide

Examlet 2 Study Guide

Examlet 1 Study Guide

Lecture 25 (Nov. 28, 2018, 3:30 p.m. - Nov. 28, 2018, 4:45 p.m.)
• Numerical differentiation
• Extrapolation
• Types of ODEs
• Stability of ODEs
• ODEs existence and uniqueness of solutions
• Forward Euler method and stability

Activity: Richardson Extrapolation

Lecture 24 (Nov. 26, 2018, 3:30 p.m. - Nov. 26, 2018, 4:45 p.m.)

Lecture Notes

• Error in midpoint and trapezoid rules
• Error estimation for Newton-Cotes
• Error and conditioning of quadrature rules
• Basics of Monte Carlo and integral equations

Quiz 21: Composite and Gaussian Quadrature

Lecture 23 (Nov. 14, 2018, 3:30 p.m. - Nov. 14, 2018, 4:45 p.m.)

Lecture Notes

• Method of undetermined coefficients

Lecture 22 (Nov. 12, 2018, 3:30 p.m. - Nov. 12, 2018, 4:45 p.m.)

Lecture Notes

• Chebyshev/orthogonal interpolation
• Piecewise interpolation
• B-splines

Activity: Chebyshev Interpolation

Quiz 19: Orthogonal and Piecewise Interpolation

Lecture 21 (Nov. 7, 2018, 3:30 p.m. - Nov. 7, 2018, 4:45 p.m.)

Lecture Notes

• Introduction to interpolation
• Vandermonde systems and conditioning
• Polynomial bases
• Chebyshev nodes

Activity: Monomial Interpolation

Quiz 18: Basics of Interpolation

Lecture 20 (Nov. 5, 2018, 3:30 p.m. - Nov. 5, 2018, 4:45 p.m.)

Lecture Notes

• Nonlinear least squares and Gauss-Newton
• Constrained optimization optimality
• Active set methods
• Penalty and barrier methods

Quiz 17: Multidimensional Unconstrained Optimization Algorithms

Lecture 19 (Oct. 31, 2018, 3:30 p.m. - Oct. 31, 2018, 4:45 p.m.)

Lecture Notes

• Golden section search
• Steepest descent
• Convergence of steepest descent and extrapolation methods
• Newton's method for multidimensional unconstrained optimization

Quiz 16: Multidimensional Unconstrained Optimization Algorithms

Lecture 18 (Oct. 29, 2018, 3:30 p.m. - Oct. 29, 2018, 4:45 p.m.)

Lecture Notes

• Numerical optimization introduction
• Conditions of optimal solutions
• Golden section search
• Newton's method and quasi-Newton methods for 1D problems
• Safeguarding techniques
• Steepest descent

Quiz 15: Optimization Problems and Algorithms for 1D Optimization

Lecture 17 (Oct. 24, 2018, 3:30 p.m. - Oct. 24, 2018, 4:45 p.m.)

Lecture Notes

• Secant method
• Convergence of fixed point iteration and Newton's method for multidimensional nonlinear solve
• Broyden's method
• Safeguarding techniques

Activity: Broyden's Method

Quiz 14: Cost and Robustness of Methods for Solving Nonlinear Equations

Lecture 16 (Oct. 22, 2018, 3:30 p.m. - Oct. 22, 2018, 4:45 p.m.)

Lecture Notes

• Introduction to nonlinear function solve problems
• Existence, uniqueness, and conditioning of roots
• Multiplicity of roots and conditioning
• Convergence rates
• Bisection algorithms
• Fixed-point functions and convergence
• Newton's method

Activity: Newton's Method for 2-by-2 System of Equations

Quiz 13: Basic Methods for Solving Nonlinear Equations

Examlet 2 (Oct. 18, 2018, 9 a.m. - Oct. 20, 2018, 10 p.m.)

As you may have seen in our class policies, our "examlets" and "finals" will take place in a computer-based testing facility ("CBTF") in Grainger Library.

You must schedule your test appointment with the Computer-Based Testing Facility at this link. This examlet is now available for scheduling.

Find out more about the testing facility, such as:

• where it is
• when to show up
• what to bring (and not to bring)

The exam will be 50 minutes in length, and it will cover the material of the first four chapters.

Examlet 2 Study Guide

Examlet 1 Study Guide

Lecture 15 (Oct. 17, 2018, 3:30 p.m. - Oct. 17, 2018, 4:45 p.m.)

Lecture Notes

• Divide and conquer for tridiagonal eigenproblem
• Krylov subspace methods
• Ritz values and vectors

Activity: Orthogonal Iteration

Lecture 14 (Oct. 15, 2018, 3:30 p.m. - Oct. 15, 2018, 4:45 p.m.)

Lecture Notes

• Review orthogonal iteration and QR iteration
• Divide and conquer for tridiagonal eigenproblem
• Krylov subspace methods
• Ritz values and vectors

Quiz 12: Tridiagonal Eigenproblems and Krylov Subspace Methods

Lecture 13 (Oct. 10, 2018, 3:30 p.m. - Oct. 10, 2018, 4:45 p.m.)
Lecture 12 (Oct. 8, 2018, 3:30 p.m. - Oct. 8, 2018, 4:45 p.m.)

Lecture Notes

• Similarity and matrix types
• Canonical forms: Schur and Jordan forms
• Obtaining eigenvalues from triangular matrices
• Conditioning and sensitivity of eigenvalue decomposition and eigenpairs
• Convergence of power iteration
• Deflation

Quiz 10: Canonical Forms for Eigenvalue Problems and Deflation

Activity: Calculating Eigenpairs of Triangular Matrix

Lecture 11 (Oct. 3, 2018, 3:30 p.m. - Oct. 3, 2018, 4:45 p.m.)

Lecture Notes

• Eigenvalues and similarity
• Eigenvalue decomposition
• Power iteration, inverse iteration, Rayleigh-Quotient iteration
• Conditioning, Gershgorin theorem

Quiz 9: Conditioning and Basic Algorithms for Eigenvalue Problems

Activity: Rayleigh Quotient Iteration

Lecture 10 (Oct. 1, 2018, 3:30 p.m. - Oct. 1, 2018, 4:45 p.m.)
• Review lecture for eigenvalue problems

Activity: Inverse Iteration with a Shift

Lecture 9 (Sept. 26, 2018, 3:30 p.m. - Sept. 26, 2018, 4:45 p.m.)

Lecture Notes

• Householder QR
• Givens QR
• Rank-deficient least squares
• Truncated SVD and Eckart-Young-Mirsky theorem
• Tykhonov regularization
• QR with column pivoting

Quiz 8: Least Squares Algorithms and Rank-Deficiency

Activity: Rank Deficient Least Squares Problems

Lecture 8 (Sept. 24, 2018, 3:30 p.m. - Sept. 24, 2018, 4:45 p.m.)
• Review lecture for least squares

Activity: Householder QR

Examlet 1 (Sept. 20, 2018, 9 a.m. - Sept. 23, 2018, 10 p.m.)

As you may have seen in our class policies, our "examlets" and "finals" will take place in a computer-based testing facility ("CBTF") in Grainger Library.

You must schedule your test appointment with the Computer-Based Testing Facility at this link. This examlet is now available for scheduling.

Find out more about the testing facility, such as:

• where it is
• when to show up
• what to bring (and not to bring)

The exam will be 50 minutes in length, and it will cover the material of the first two chapters.

Examlet 1 Study Guide

Lecture 7 (Sept. 19, 2018, 3:30 p.m. - Sept. 19, 2018, 4:45 p.m.)

Lecture Notes

• Linear least squares motivation and introduction
• Conditioning of linear least squares
• QR factorization
• Normal equations and Cholesky QR
• Gram-Schmidt methods
• Householder QR

Quiz 7: Least Squares and QR Factorization

Lecture 6 (Sept. 17, 2018, 3:30 p.m. - Sept. 17, 2018, 4:45 p.m.)

Lecture Notes

• Pivoting in LU
• Multiplier growth and stability
• Cholesky and other specialized factorizations
• Sherman-Morrison-Woodbury formula

Quiz 6: Stability and Matrix Structure in Solving Linear Systems

Activity: Sherman-Morrison-Woodbury Formula

Lecture 5 (Sept. 12, 2018, 3:30 p.m. - Sept. 12, 2018, 4:45 p.m.)

Lecture Notes

• Solving triangular systems of equations
• LU factorization existence
• LU with partial pivoting
• Error in LU factorization

Quiz 5: Gaussian Elimination

Lecture 4 (Sept. 10, 2018, 3:30 p.m. - Sept. 10, 2018, 4:45 p.m.)

Lecture Notes

• Orthogonal matrices
• Singular values and conditioning
• Peturbation analysis of linear systems

Quiz 4: Matrix Conditioning and Error in Linear Systems

Activity: Singular Value Decomposition and Norms

Lecture 3 (Sept. 5, 2018, 3:30 p.m. - Sept. 5, 2018, 4:45 p.m.)

Lecture Notes

• Error in floating point arithmetic
• Vector and matrix norms
• Matrix condition number

Quiz 3: Floating Point, Matrix Norms, and Matrix Condition Number

Lecture 2 (Aug. 29, 2018, 3:30 p.m. - Aug. 29, 2018, 4:45 p.m.)

Lecture Notes

• Floating point representation
• Floating point arithmetic
• Roundoff error analysis

Quiz 2: Error, Conditioning, and Floating Point

Activity: Cancellation in Standard Deviation Computation"

Lecture 1 (Aug. 27, 2018, 3:30 p.m. - Aug. 27, 2018, 4:45 p.m.)

Lecture Notes