Math 4401 Numerical Methods
| # | Topic | Reading | Resources |
|---|---|---|---|
| 1 | Course Introduction | 1.1, 1.2, 1.3 | Mathematica | Proof of Taylor`s Theorem |
| 2 | Mathematica Lab | Mathematica | Mathematica Quick Reference | |
| 3 | Rootfinding | 2.1, 2.2 | Mathematica |
| 4 | Newton Methods | 2.3, 2.4 | Mathematica | Roots of Unity | article |
| 5 | Accelerating Convergence | 2.5, 2.6 | Mathematica | article |
| 6 | Padé Approximants | 8.4 & Handout | Mathematica | application | algebraic approximants |
| 7 | Lagrangian Interpolation | 3.1, 3.2 | Mathematica |
| 8 | Hermite Interpolation | 3.3 | Mathematica |
| 9 | Cubic Splines | 3.4 | Mathematica | application |
| 10 | Numerical Differentiation | 4.1, 4.2 | Mathematica |
| 11 | Composite Quadrature | 4.3, 4.4 | Mathematica |
| 12 | Romberg Integration | 4.5, 4.6 | Mathematica |
| 13 | Gaussian Quadrature | 4.7 | Mathematica | Maxwell Velocity Distribution
Orthogonal Polynomials |
| 14 | Monte Carlo Integration | Handout | Mathematica | Quasi Random Sequences
Monte Carlo Methods in Chemistry | Sobol Sequences |
| 15 | Least Squares | 8.1, 8.2 | Mathematica | Gram-Schmidt Orthonormalization |
| 16 | Chebyshev Approximation | 8.3 | Mathematica |
| 17 | Initial Value Problems | 5.1, 5.2, 5.3 | Mathematica |
| 18 | Runge-Kutta | 5.4, 5.5 | Mathematica
Derivation of Runge Kutta Methods | article |
| 19 | Predictor-Corrector | 5.6, 5.7 | Mathematica | application |
| 20 | Dynamical Systems | 5.9, Handout | Mathematica | application | Pursuit Problems |
| 21 | Gaussian Elimination Linear Systems; Matrix Inversion, Determinants, Matrix Factorization |
6.1, 6.2, 6.3, 6.4, 6.5 | Mathematica |
| 22 | Norms | 7.1, 7.2 | Mathematica | article (logarithmic matrix norms) |
| 23 | Iterative Matrix Methods | 7.3, 7.4 | Mathematica | sparse matrix collection |
| 24 | Eigenvalues | 9.1, 9.2, 9.3, 9.4 | Mathematica | article |
| 25 | Newton's Method for Systems | 10.2 | Mathematica |