Math 464A, Numerical Analysis

Lecture:  MWF 9:30, Benson 115
Instructor:  Jim Morrow
Phone:  543-1161

E-mail:  morrow@math.washington.edu
Web address: http://www.math.washington.edu/~morrow/464 97/464.html

Office Hours: MW 8:30-9:20, C439 Padelford
Quiz Section: Th 9:30, WFS 201
TA:  Rafal Goebel
Office Hours: T 9:30-10:20, W 4:00-4:50

E-mail:  goebel@math.washington.edu
Web address: http://www.math.washington.edu/~goebel

Texts:  Numerical Analysis (required)
Authors  L. W. Johnson & R. D. Riess

Introduction to Scientific Computing (recommended)

Author  Charles Van Loan

Numerical Analysis is available at Professional Copy (4200 University Avenue NE). Introduction to Scientific Computing is available at the University Bookstore.

Math 464-5-6 is an introduction to numerical analysis. In Math 464 we will introduce several topics, some of which will be covered in more detail in Math 465. The topics for Math 464 are

1. Machine arithmetic

2. Numerical solutions of systems of linear equations

3. Numerical Solution of non-linear equations

4. Polynomial interpolation and splines 5. Introduction to numerical integration

The homework will count 20% of the course grade. There will be one 50 minute midterm test which will count 20% of the course grade. There will be four computer projects which all together will count for 20% of the grade. The midterm test will be closed book but you will be allowed to bring notes on one side of a notebook size sheet of paper. There will be a two hour closed book final exam which will count 40% of the course grade. For the final you will be allowed to bring notes on both sides of a notebook size sheet of paper. You may use scientific calculators in which no formulas or text has been stored on the midterm and final.

I suggest that you use Matlab for the computational parts of the course. The Engineering Copy Center sells a “Matlab Primer” that will probably be all you need for this course. Matlab is installed on the MSCC computers.

The following books have been placed on reserve in the Mathematics Research Library:

1. Numerical Analysis by Johnson and Riess (QA297 .J63)

2. Elementary Numerical Analysis : An Algorithmic Approach by Conte and de Boor (QA297 .C65 1980)

3. Numerical Analysis by Kincaid and Cheney (QA297 .K563)

4. Handbook for Matrix Computations by Coleman and Van Loan (QA188 .C64)

Classroom participation is encouraged. If you feel the urge to interrupt me with a question, I will not be offended, I will be delighted. I may not give you an instant answer but I do encourage your questions. I would like for you to understand that mathematics does not consist of one minute answers to one minute questions. You should not feel that every problem has a brief solution (or even any solution). Math is not simply arithmetic. After many days (months, years) of thought you may find an elegant simple explanation to some problem. It might also happen that by luck you leap to the right explanation. In any case do not be discouraged if you have difficulties. The best tactic is to keep thinking. Faulty ideas are much better than no ideas.

Here are the homework assignments:

DATE ASSIGNMENT (from Johnson & Riess)
Oct. 2 §1.3: 1b(iii, iv), 4(replace hex with binary), 8,
Oct. 9 additional problems I and II; §2.1: 4, 6, 10, 11; §2.2.4: 4, 5, 9, 10, 16, 19
Oct. 16 §2.3: 3, 7, 8, 9, 12a, 12b; §2.4: 5, 7, 8, 9, 13
Oct. 23 §2.5: 1, 3, 4, 5a, 6a, 7
Oct 30 §4.3.1: 1, 4, 6, 9; §4.3.2: 5; §4.3.3: 2, 7, 9, 12
Oct. 31 MIDTERM
Nov. 6 §4.4.1: 2, 3, 4
Nov. 13 §5.1: 4; §5.2.1: 1a, 3a, 4a, 11
Nov. 20 §5.2.2: 1, 2, 5, 8, 10; §5.2.4: 3abd, 5, 6, 10, 13
Nov. 26 §5.2.6: 1, 3; §6.2.2: 2, 3, 4, 8, 9, 14
Dec. 4 §6.2.4: 7, 9, 10, 11
Dec. 16 8:30-10:20 a.m., FINAL EXAM

These assignments are due at the beginning of class on the due date. Raf Goebel will discuss the homework in the quiz section, so you must turn it in on time.

There will also be four computer assignments which will be due as follows:

Oct 24 Tridiagonal linear systems
Nov. 7 Gauss-Seidel method
Nov. 21 Newton’s method, fixed point iteration and the secant method
Dec. 8 Polynomial interpolation

November 11, 27, and 28 are holidays. The Midterm will be on Friday, October 31, and the final is at 8:30 a.m. on Tuesday, December 16.

Additional Problems:

I Describe a method to compute f(x) = \frac{1−cos x}{x} when |x| is very small.

II Describe a method to compute f(x) = log x − 1, when x is close to e.