Course Description for Math 151B: Numerical Analysis

Textbook: Numerical Analysis, by Burden and Faires

Many problems in science are described by differential equations. Very few of these equations can actually be solved analyticaly. Thus, the numerical solution to these equations is very important. The first half of this course will deal with the numerical solution to ordinary differential equations (ODE's). We will discuss several numerical algorithms that are typically used for the solution of ODE's. In particular, we will discuss accuracy, stability, and convergence behaviour of the different methods. The material covered will be most of section 5 of the textbook. In the second half of the course, we will discuss the numerical solutions to linear systems of equations. This will involve iterative solutions of linear equations. These will be selected sections of chapter 7 of the textbook. We will also discuss approximation theory (chapter 8). In particular, we will discuss least square approximations.

General Outline

Weeks 1-5:

• Introduction and course overview
• Chapter 5: ODEs: Initial Value Problems

Week 6:

• Midterm: Monday, May 10, during class
• Chapter 11: ODEs: boundary value problems

Week 7,8:

• Chapter 7: Iterative solutions to linear systems of equations.

Week 9,10:

• Chapter 8: Approximation Theory

During class, we will discuss the theory to many of the numerical methods. Some examples of algorithms will be given as well. It will then be a significant part of the homework assignments to use and implement the algorithms discussed. It is strongly encouraged that the numerics problems are done using Matlab. We will also give some support if you want to use C++ or FORTRAN. There won't be any support if you plan to use another programming language. An introduction to Matlab will be given in the first discussion period.

Prerequisites: Lower division mathematics course sequence