Applied Linear Algebra and Numerical Analysis

Course Description

Textbook

Syllabus

(1) Introduction and Review: Computer arithmetic, review of calculus & Taylor series.

(2) Root Finding & Fixed Point Iteration: Bisection, Secant, False Position & Newton's Method, Fixed point iteration.

(3) Applied Linear Algebra: Gaussian Elimination, Pivoting, LU Decomposition, Eigenvalues & Eigenvectors, Iterative Techniques for Linear Systems, Matrix Norms, Newton's Method for Systems of Nonlinear Equations.

(4) Interpolation & Curve Fitting: Vandermonde, Lagrange & Newton Interpolation, Divided Differences, Curve Fitting, Spline Interpolation.

(5) Numerical Differentiation & Integration: Numerical Differentiation, Numerical Integration, Romberg Integration, Gaussian Quadrature.

(6) Ordinary Differential Equations: Introduction & Euler's Method, Multistep methods, Runge-Kutta, Boundary Value Problems.

Learning Objectives and Instructor Expectations

To gain an understanding of the algorithms of applied linear algebra and numerical analysis, how they work, how they (sometimes) fail, why they work, and why they fail.

You will be expected to be able to apply the algorithms that we study in this course, both by hand and on the computer. Applying them on the computer can take much more time than working them out by hand. Instead of applying the algorithm to a single problem, you will have to write a program that will solve any problem that could be presented and that will tell you when the algorithm has failed. This requires a different set of skills than solving problems by hand and may be very challenging for those of you who have not programmed (or programmed in MATLAB) before. In addition, you will also be expected to understand how the algorithms work and how and why they fail.

Schedule and Homework

Grading

You may view your homework and exam grades on-line. Before doing so for the first time, you must request a password. If your student number begins with one or more zeros (e.g. 0012345), remove the leading zeros when you enter your student number to check your grade. (Enter 12345 instead of 0012345.)

Matlab Resources

Here is a list of some Matlab resources available on the net:

• MATLAB Help Desk at the Mathworks web site. This page allows you to search for help on a given function by typing its name (e.g. plot) into the box on the right hand side of the page.
• If you are not familiar with MATLAB, please explore the tutorials and information available on the above web page under "Learning MATLAB": Getting Started, Using MATLAB, and an index of examples throughout their online documentation.
• Matlab Hypertext Reference, Portland State University
• Matlab Quick Reference Guide, University of Waterloo

Here are some short tutorials that have been prepared by me and others in past quarters:

• MATLAB tutorial, a general introduction.
• brief tutorial on working with matrices in MATLAB
• tutorial on plotting in MATLAB (ps file). This tutorial is five years old, but should still be helpful in beginning to work with plotting in MATLAB.

Tutorials