Math104B Introduction to Numerical Analysis

 http://www.math.ucsb.edu/~hdc/teaching/Math104B

Class:  T R 9:30-10:45 GIRV 1115 

Instructor: Prof. Hector D. Ceniceros. SH 6710, Email: hdc@math.ucsb.edu, phone: 893-3462 .  Email etiquette: When sending email include your name, course,  and a proper salutation otherwise the email will not be replied. Office Hours:   TR 1-2pm.

TA:  Daniel Salazar  Office hours Monday 9-10am and Mathlab hours Thursday 5-7pm.

Course description:
The main focus of the course will be on numerical methods for the solution of systems of linear equations (Chapters 6 and 7 from your textbook) with both direct and iterative methods.  We will then study some approximation theory (Chaper 8) and, time permitting, approximation of eigenvalues (Chapter 9).

Textbook:
Numerical Analysis by R. L. Burden and J. D. Faires. Brooks/Cole Publishing Company, 8th Edition. We will cover (partially or completely ) Chapters 5, 6, 7,  9 and time permitting Chapter 8. A copy of the book has been put on library reserve.

Prerequisites:
Math 104 A.  Knowledge of Matlab, C, C++ or FORTRAN.  You will be required to write several somewhat simple programs.  Matlab is recommended as it reduces substantially the programing load especially when dealing with vectors  and matrices. Octave is also a freeware alternative to Matlab.

Homework assignments:
Homework will be assigned every week  and is due a week after, in class,  at the beginning of the lecture.  No late homework please!
Programming assignments:  When given a programming assignment write your own codes and attach them to your homework. Include and comment your code runs and results clearly.

Grade:
Homework 30%,  Midterm 30 % ( Thursday February 11,  9:30-10:45am), and  Final 40 % (Wednesday March 17, 8-11am)
No makeup exams will be given. You may bring a 3x5 note card and a calculator to the exams.

Homework 1 (January 12).
Here is a sample code as a reference but note that this code might be purposely wrong! so write your own.
1. Implement the Gaussian Elimination Algorithm (6.1) and
    (a) Test your implementation.
    (b) Use it to solve prob. 6.1: 5abcd.
2. Do prob. 6.1: 10 and 20.

Homework 2 (January 21).  Download problems here. 

Homework 3 (January 28).
1. Do Section 7.1, exercises 1, 4.
2. Do Section 7.2 exercises  2, 4.
3. Implement the Jacobi and the Gauss-Seidel  methods to find an approximation for the solution of  a linear system Ax=b .
Use your computer programs to do problems 7.3.6 and 7.3.8   and compare the convergence of both methods.
You can check the answer with matlab's A\b command. Turn in printouts of both the codes and the results.
4. Do Probs. 7.3: 10 and 16.
5. Do  Probs. 7.4:  2 and 4.     

February 18, Special Guest Lecture by Dr. Mark Meloon, from Toyon about work in the industry. Attendance will be taken.

Practice Midterm

Homework 4 (February 25).
Implement the Conjugate Gradient Method (algorithm 7.5) and do problems 7.5: 7 and 8.
Turn in both the code and the results.

Homework 5 (Due March 9)
8.1 Probs. 4 and 7.
8.2 Probs 2, 4, 11, and 12 .
8.5 Probs. 2 and 6.

Practice Final