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Difference between revisions of "MMS: Programming and Numerical Analysis"

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'''Contents'''
 
'''Contents'''
  
Root finding and solutions to non-linear equations
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1. Root finding and solutions to non-linear equations [[Media:Class1.pdf]]
  
Numerical approximation Rn
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2. Numerical approximation Rn
1. Interpolation
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2. Polynomial approximation for exact reconstruction
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3. Minimal squares for linear systems
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Solution to linear algebraic equations I
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1. Basics on linear systems
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2. Gauss elimination and back substitution
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3. LU decomposition
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4. Gauss-Seidel method and iterative methods
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Solution to linear algebraic equations II
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1. Eigenvalue problems
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2. Singular Value Decomposition
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3. Sparse linear systems
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Numerical derivation and integration
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Numerical solution to ODEs
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3. Solution to linear algebraic equations I
1. Introduction to ODEs
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2. Eulers, Taylor, Runge-Kutta, and multistep methods
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4. Solution to linear algebraic equations II
3. Stability and Solution of Sets of ODEs
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Numerical solution to PDEs I
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5. Numerical derivation and integration
1. Introduction to PDEs
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2. Classification of PDEs (Elliptic, Hyperbolic, Parabolic)
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6. Numerical solution to ODEs
3. Solution to initial value PDEs
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Numerical solution to PDEs II
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7. Numerical solution to PDEs I
1. Solution to boundary value PDEs
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 +
8. Numerical solution to PDEs II

Revision as of 19:43, 1 February 2014

Contents

1. Root finding and solutions to non-linear equations Media:Class1.pdf

2. Numerical approximation Rn

3. Solution to linear algebraic equations I

4. Solution to linear algebraic equations II

5. Numerical derivation and integration

6. Numerical solution to ODEs

7. Numerical solution to PDEs I

8. Numerical solution to PDEs II