Applied Linear Algebra and Numerical Analysis

Course Description

Textbook

• Gerald W. Recktenwald's Numerical Methods with MATLAB Prentice Hall, 2000. Available at the University Bookstore.
• Matlab scripts from Recktenwald's book can be downloaded from http://www.prenhall.com/recktenwald

• John H. Mathews and Kurtis D. Fink, Numerical Methods using MATLAB Prentice Hall.
• Richard L. Burden and J. Douglas Faires, Numerical analysis.

Syllabus

• Matlab and Floating Point Arithmetic
• Series approximations: Tayler, Asymptotic, and maybe others
• Scalar root finding and function minimization
• Matrix Algebra, Gaussian Elimination
• Least Squares, Interpolation
• Integration
• Ordinary Differential Equations

Learning Objectives and Instructor Expectations

Although the subject matter of Applied Linear Algebra and Numerical Analysis can be made rather difficult, I will attempt to present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will only be of importance in developing the student's intuition for the subject matter. Applications will be emphasized.

I will let you know clearly what you need to learn and what can be skipped. Homeworks are used to reinforce ideas and methods introduced in class lectures. Exams emphasize basic techniques as applied to simple, fundamental problems.

Schedule and Homework

Grading

Scripts

• Montecarlo integration over the circle

• Backward substitution to solve Ux=b where U is an upper triangular matrix.
• Forward substitution to solve Lx=b, where L is a lower triangular matrix.
• The script that does elimination on an augmented matrix to put it in upper triangular form.

• Gaussian elimination with trivial or partial pivoting strategies.
• LU factorization without pivoting.

• vandermonde.m solves the Vandermonde system to compute the interpolating polynomial.
• lagrange.m uses Lagrange's formula to find the interpolating polynomial.
• newtonpoly.m uses the iterative Newton approach to calculate the interpolating polynomial.

• For computing the Legendre polynomial of of degree n, you can use the recursive script legendre.m.
• Low order Gauss-Legendre nodes and weights on the interval [-1,1] can be constructed with the following naive implementation: gaussLegendre.m.

• A simple implementation of the power method for calculating the eigenvector associated with the dominant(largest) eigenvalue.

• MSCC: Mathematical Sciences Computing Center home page.
• Matlab is available on goodall for undergraduates and mead for staff and faculty. These are unix machines, with 24 hour remote access. Information about these systems can be found here. If you don't already have an account on one of these machines, the instructions for setting one up are here.
• Directions for modem access

• List of Matlab Resources at Mathworks site
• Matlab Hypertext Reference, Portland State University
• Matlab Quick Reference Guide, University of Waterloo
• Many other Matlab tutorials can be found on the web with any search engine, e.g. Google.