645:572 Computational Mathematics II / 640:497 Advanced Computational Mathematics -
Spring
2021
Course Outline (Tentative):
- Matrices and Systems of Linear Equations
- Introduction
- Gaussian Elimination
- Pivoting Strategy
- Triangular Factorization
- Inverses and Determinants
- Cholesky Factorization
- Error Analysis, Norms and Condition Numbers
- Iterative Improvement
- Iterative Methods
- Newton's Method
- Fixed-Point Iteration
- Iteration/Relaxation Methods
- Jacobi
- Gauss-Seidel
- Successive Overelaxation (SOR)
- Gradient and Conjugate Gradient Methods
- Matrix Eigenvalue Problem
- Introduction
- Power Method
- Deflation
- Inverse Power Method
- QR Method
- Ordinary Differential Equations (ODEs)
- Initial Value Problems (IVPs)
- One-step and Multi-step Methods
- Stability
- Boundary Value Problems (BVPs)
- Shooting Methods
- Finite Difference Methods
- Finite Element Methods