# Difference between revisions of "Math 411: Numerical Methods"

From MathWiki

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# Numerical solution of initial-value problems | # Numerical solution of initial-value problems | ||

− | #* Euler's method | + | #* Taylor methods |

+ | #** Euler's method | ||

#* Runge-Kutta methods | #* Runge-Kutta methods | ||

#** Runge-Kutta-Fehlberg method | #** Runge-Kutta-Fehlberg method |

## Revision as of 14:11, 31 December 2009

## Contents

## Catalog Information

### Title

Numerical Methods.

### (Credit Hours:Lecture Hours:Lab Hours)

(3:3:0)

### Offered

W

### Prerequisite

### Description

Iterative solvers for linear systems, eigenvalue, eigenvector approximations, numerical solutions to nonlinear systems, numerical techniques for initial and boundary value problems, elementary solvers for PDEs.

## Desired Learning Outcomes

### Prerequisites

### Minimal learning outcomes

[Draft of 12/31/2009]

- Numerical solution of initial-value problems
- Taylor methods
- Euler's method

- Runge-Kutta methods
- Runge-Kutta-Fehlberg method

- Multi-step methods
- Extrapolation methods
- Stability
- Stiff differential equations

- Taylor methods
- Numerical solution of boundary-value problems
- Numerical solution of nonlinear systems of equations
- Approximation theory
- Least-squares approximation
- Orthogonal polynomials
- Chebyshev polynomials

- Rational function approximation
- Trigonometric polynomial approximation
- Fast Fourier transforms

- Numerical computation of eigenvalues and eigenvectors
- Power Method

- Partial differential equations