MMS: Programming and Numerical Analysis
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Root finding and solutions to non-linear equations
1. Taylor series for analytical functions 2. Bisection 3. Fixed point iteration. 4. Newton's method and roots of polynomials.
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
