University of California
Department of Applied Science
Numerical Methods : 210-A (Fall Quarter 2004)

CRN: 63367

Room 211 Wellman

Tu, Th 12.10 to 1.30

Course Description:
A study of numerical methods to model and solve engineering problems using a computer. Students learn to analyze and interpret the numerical solutions obtained.

Topics include roots of algebraic and transcendental equations, linear systems, interploation, approximation, curve fitting, numerical differentiation and integration, and ordinary differential equations.
The MATLAB programming language is encouraged. Some prior programming experience in any language is preferred but not required. MATLAB will not be taught in the class, but extensive tutorial information is available on the class web site. MATLAB coding assistance will NOT be available.

Textbook:
Myron B. Allen III and Eli L. Issaacson, Numerical Analysis for Applied Science, Wiley-Interscience, 1998, ISBN: 0-47-55266-6

A Useful Reference:

J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, Springer-Verlag, New York 1980.

Topics Covered

210A: Chapters 0, 1, 2, 3, 5, 6, 7 plus MATLAB (some material is posted on the Web. This will not be taught in the class)

210B: Chapters 0, 4, 8, 9 plus supplemental material

Prerequisites:
See catalog

Instructor:
Dr. Rao Vemuri, 18 Hertz hall, Livermore, rvemuri@ucdavis.edu
The instructor comes to Davis only on Tu and Th. Ask for appointment or contact him by e-mail

Homeworks:
Each week, a set of about 10 homework problems will be assigned. The homework will be due the following week in class. Homework solutions will be posted. Late homework will not be accepted. No exceptions.
For full credit, your hand-ins MUST be legible and well-organized. Treat each homework assignment as a mini take-home examination. Do them without the assistance of others. You can look at other text books, but not help each other.


Exams:
One in-class mid-term examination and one final will be given.

Course Topics:

  • Module 0: Students are strongly advised to find out the computational infrastructure available on campus. Learn MATLAB programming using notes on-line. Learn about structured programming using MATLAB. Program logic and flow control concepts, subroutines and functions, recursion, I/O control, basic data plotting routines.
    1. Linear Algebra Tutorial 1
    2. Linear Algebra Tutorial 2
    3. Linear Algebra Tutorial 3

4.      ATutorial introduction to MATLAB

5.      MATLAB Example1

6.      MATLAB Example 2

7.      Programming with MATLAB

Interpolation, Extrapolation and Approximation

Curve fitting, interpolation and extrapolation, linear regression, polynomial regression

         Module 3 (Read Chapter 2)
Direct methods for Linear Systems and Error Analysis

Solution of linear systems using Gauss elimination and LU decomposition, matrix inversion

  • Module 4 (Read Chapter 3)

Solution of Non-linear equations

Roots of equations using bisection, fixed point iteration, Newton-Raphson, Secant methods

Eigenvalue problems

Grading:
Homeworks   60 % (about 35% for paper-pencil exercises, 25% computer exercises)
Exam #1       20 % (will be held late in the quarter, probably closed book to simulate the Comprehensive Examination)
Final 20%
MATLAB is a trademark of The MathWorks, Inc.

 

rvemuri@ucdavis.edu

Last updated: 11 September 2004