Difference between revisions of "MMS: Programming and Numerical Analysis"
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(Created page with " Root �nding 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 polynom...") |
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| − | Root | + | Root finding and solutions to non-linear equations |
1. Taylor series for analytical functions | 1. Taylor series for analytical functions | ||
2. Bisection | 2. Bisection | ||
3. Fixed point iteration. | 3. Fixed point iteration. | ||
| − | 4. | + | 4. Newton's method and roots of polynomials. |
Numerical approximation Rn | Numerical approximation Rn | ||
1. Interpolation | 1. Interpolation | ||
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Numerical solution to PDEs I | Numerical solution to PDEs I | ||
1. Introduction to PDEs | 1. Introduction to PDEs | ||
| − | 2. | + | 2. Classification of PDEs (Elliptic, Hyperbolic, Parabolic) |
3. Solution to initial value PDEs | 3. Solution to initial value PDEs | ||
Numerical solution to PDEs II | Numerical solution to PDEs II | ||
1. Solution to boundary value PDEs | 1. Solution to boundary value PDEs | ||
Revision as of 06:48, 1 February 2014
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
