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

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## Revision as of 08:34, 18 February 2010

## 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

The formal prerequisites reflect the fact that incoming students should have basic knowledge of ordinary differential equations and have had a first course in numerical methods. Indirectly, the prerequisites ensure that students have had multivariable calculus.

### Minimal learning outcomes

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

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

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

- Taylor methods
- Numerical solution of boundary-value problems
- Shooting methods
- Finite-difference methods
- Rayleigh-Ritz method

- Numerical solution of nonlinear systems of equations
- Newton's method
- Quasi-Newton methods
- Steepest-descent methods

- 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
- Finite-difference methods
- For elliptic equations
- For parabolic equations
- For hyperbolic equations

- Introduction to finite-element methods

- Finite-difference methods

### Additional topics

If time permits, students could be given an introduction to finite element methods.

### Courses for which this course is prerequisite

None.