Math 640: Numerical Analysis

Math 640 - Numerical Analysis
Spring - 2008

Course Goals:

To familiarize students with additional types of problems (beyond those studied in MATH 541) where numerical methods are used to approximate solutions; to analyze, compare, and contrast the basic numerical method algorithms in these areas; to investigate real life applications of these numerical methods; to further develop students ability to implement and utilize numerical methods in MATLAB or other mathematical software; and for students to hone their presentation skills by becoming proficient with LATEX, a professional typesetting s ystem for scientific documents.

Course Description and Topics:

This course will focus on numerical techniques in:

solving linear systems of equations (direct and iterative methods)
solving differential equations

solving boundary-value problems for ordinary differential equations (shooting methods, finite difference methods)
solving partial differential equations (explicit and implicit methods)

solving systems of nonlinear equations (quasi-Newton, steepest descent)
approximation theory (least squares approximation, Fast Fourier Transforms)

Convergence and stability issues associated with each technique will also be discussed. There will be a significant component of the class that comes from implementing or using these methods to complete homework projects.

Homework listings can be found at the following link: Homework Assignments

Materials for the course have been sorted by class meetings and topics:

Miscellaneous Materials for Class

Course Syllabus
Test #1 Material: Solving Systems of Linear Equations
- Part 1: Direct Methods
  - Handout on Gaussian Elimination Algorithm (PDF)
  - Maple Worksheet on Gaussian Elimination with Fixed Digit Arithmetic: GaussianElimFixedDigits.mws
  - Maple Worksheet on Gaussian Elimination and Pivoting Strategies: PartialPivoting.mws
  - Handout on Special Types of Matrices (PDF)
  - Homework #1:
    - Assignment in PDF and LaTeX along with needed images (GreatLakes.jpg, Loop.png,OhmsLaw.png, and ResistorCircuit.png)
    - MATLAB code: NaiveGauss.m, BigSystem.m, BigSysProblem.m, and bdry.m
- Part 2: Iterative Methods
  - Handout on Norms and Eigenvalues (PDF)
  - Handout on Jacobi, Gauss-Seidel and SOR Iterative Methods (PDF)

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