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

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