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Math 300

Spring 2006

Overview of Numerical Methods

Lecturer:

Pavel Grinfeld

Korman 275

Tel: 215.895.1291



pg@math.drexel.edu

Lectures:

MTWF, 2pm-2:50pm, Korman 247

Website:



Textbook:

None. Class Notes

Suggested Reading:

Introduction to Linear Algebra by Gilbert Strang

Introduction to Applied Mathematics by Gilbert Strang

(for Laplace's equation and FFT)

Numerical Recipes in C by William H. Press

(available online and )

Grading:

Midterm 1: 40

Midterm 2: 40

Homework: 20%

Summary

The course focuses on applications and its primary goal is to highlight the essential concepts in numerical methods: convergence, stability, and efficiency. The course will also include an introduction to MATLAB which will be a major component of the course. The main topics include numerical integration, optimization, the FFT and spectral methods, and finite differences.

Topics

1. Introduction

Introduction to Matlab

Vectorization

Convergence

Richardson extrapolation

2. Numerical Integration

Computation of definite integrals in 1D.

Gaussian integration in 1D

Gaussian integration in 2D (squares and triangles)

Integration of singularities

Definite integration as an ODE solver

3. Finite differences

Introduction to finite differences

Solution of Laplace’s equation in 1D

Solution of Laplace’s equation in 2D

Possoin’s equation

4. IEEE floating point

5. Spectral methods

Review of Complex numbers.

Introduction to the discrete Fourier transform

Introduction to the FFT

Implementation details of the FFT

Solution of the Laplace equation on the circle

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