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MMS: Programming and Numerical Analysis

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Contents

Root finding and solutions to non-linear equations

Numerical approximation Rn

1. Interpolation 2. Polynomial approximation for exact reconstruction 3. Minimal squares for linear systems

Solution to linear algebraic equations I

1. Basics on linear systems 2. Gauss elimination and back substitution 3. LU decomposition 4. Gauss-Seidel method and iterative methods

Solution to linear algebraic equations II

1. Eigenvalue problems 2. Singular Value Decomposition 3. Sparse linear systems

Numerical derivation and integration
Numerical solution to ODEs

1. Introduction to ODEs 2. Eulers, Taylor, Runge-Kutta, and multistep methods 3. Stability and Solution of Sets of ODEs

Numerical solution to PDEs I

1. Introduction to PDEs 2. Classification of PDEs (Elliptic, Hyperbolic, Parabolic) 3. Solution to initial value PDEs

Numerical solution to PDEs II

1. Solution to boundary value PDEs