Topics
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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