CS450 Calendar
Note: Some calendar entries are clickable and link to entries below.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.
- 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
- Existence of solutions to ODE BVPs
- Green's functions and conditioning
- Shooting and multiple shooting methods
- Finite difference methods
- Collocation methods
- Weighted residual methods
- Stability of ODEs and methods
- Local and global error, order of accuracy
- Stability regions for forward and backward Euler
- Runge Kutta methods
- Multistep methods
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.
- Numerical differentiation
- Extrapolation
- Types of ODEs
- Stability of ODEs
- ODEs existence and uniqueness of solutions
- Forward Euler method and stability
- Error in midpoint and trapezoid rules
- Error estimation for Newton-Cotes
- Error and conditioning of quadrature rules
- Gaussian quadrature
- Progressive quadrature rules
- Composite quadrature rules
- Basics of Monte Carlo and integral equations
- Numerical integration/quadrature
- Newton-Cotes quadrature rules
- Method of undetermined coefficients
- Gaussian quadrature
- Chebyshev/orthogonal interpolation
- Piecewise interpolation
- B-splines
- Introduction to interpolation
- Vandermonde systems and conditioning
- Polynomial bases
- Chebyshev nodes
- Nonlinear least squares and Gauss-Newton
- Constrained optimization optimality
- Sequential quadratic programming
- Active set methods
- Penalty and barrier methods
Quiz 17: Multidimensional Unconstrained Optimization Algorithms
- Golden section search
- Steepest descent
- Convergence of steepest descent and extrapolation methods
- Conjugate gradient
- Newton's method for multidimensional unconstrained optimization
Quiz 16: Multidimensional Unconstrained Optimization Algorithms
- 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
- Secant method
- Convergence of fixed point iteration and Newton's method for multidimensional nonlinear solve
- Broyden's method
- Safeguarding techniques
Quiz 14: Cost and Robustness of Methods for Solving Nonlinear Equations
- 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
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.
- Divide and conquer for tridiagonal eigenproblem
- Krylov subspace methods
- Ritz values and vectors
- 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
- Deflation
- Simultaneous and Orthogonal Iteration
- QR Iteration
Quiz 11: Schur Decomposition and QR Iteration
- 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
- Eigenvalues and similarity
- Eigenvalue decomposition
- Power iteration, inverse iteration, Rayleigh-Quotient iteration
- Conditioning, Gershgorin theorem
Quiz 9: Conditioning and Basic Algorithms for Eigenvalue Problems
- Review lecture for eigenvalue problems
- Householder QR
- Givens QR
- Rank-deficient least squares
- Truncated SVD and Eckart-Young-Mirsky theorem
- Tykhonov regularization
- QR with column pivoting
- Review lecture for least squares
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.
- Linear least squares motivation and introduction
- Conditioning of linear least squares
- QR factorization
- Normal equations and Cholesky QR
- Gram-Schmidt methods
- Householder QR
- 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
- Solving triangular systems of equations
- LU factorization existence
- LU with partial pivoting
- Error in LU factorization
- Orthogonal matrices
- Singular values and conditioning
- Peturbation analysis of linear systems
- Error in floating point arithmetic
- Vector and matrix norms
- Matrix condition number
Quiz 3: Floating Point, Matrix Norms, and Matrix Condition Number
- Floating point representation
- Floating point arithmetic
- Roundoff error analysis
- Course administration
- Motivation
- Applications
- Error
- Posedness
- Conditioning