Math 151B, Section 1

Applied Numerical Methods

Spring2002@UCLA

Course description:

Most of the numerical methods used to solve problems in engineering and the physical sciences are synthesized from a "core" set of numerical procedures. These procedures concern the solution of linear and non-linear equations, numerical integration, numerical differentiation, etc. The goal of 151A/B is to familiarize students with the algorithms that are used to implement these "core" numerical procedures. We'll be covering the mathematical foundation and properties of these algorithms as well as implementation details. By the end of the quarter the students should be competent at choosing and implementing any of the "core" procedures we've covered, as well as be competent at generalizing their knowledge to address issues involving the procedures that we didn't cover. For the computer implementations, we'll be using Matlab. Previous familiarity with this package is not required for enrollment. Math 151B: Numerical solution of differential equations, two-point boundary value problems, iterative solution of linear equations, topics in approximation theory.

Textbook: R.L. Burden and J.D. Faires, Numerical Analysis, 7^th ed. , Brooks/ Cole (required text).

Prerequisites: Math 115A, 151A, and Program in Computing 3 or 10A or equivalent.

Lectures: MWF 9:00AM -9:50AM, MS 6229

Discussion Section: Tuesday, 9.00AM - 9.50AM, MS 6229

Useful Links:

Class Web Page: http://www.math.ucla.edu/~hliu/151b.1.02s/index.html

Instructor: Hailiang Liu

Office : MS 7620-D
Office hours: Mon. 2:00--3:00P, Wed. 12:00--1:30P
Tel: 310 825 4201
E-mail : hliu@math.ucla.edu

Teaching Assistant: Chiu-Yen KAO
- Office: IPAM 1129C
- E-mail: ckao@math.ucla.edu
- Office hours: T & F, 10:00A-11:00A
- Discussion time: T 9:00A-9:50A, MS6229

Homework Assignments:

There will be 8 homework assignments for this course.

Homework assignments consist of both theoretical and computational work.

For the computational assignments, we will be using Matlab.

The homework assignments will be assigned and graded every week.

The homework will be collected every week, no late homework will be accepted.

Computing:

Examinations: There will be a midterm exam and a final exam.

Midterm: Monday, May 6, 9:00AM--9:50AM, MS6229

Final: Wed. June 12, 8:00AM--11:00AM, MS6229

The examinations are closed-book and closed-note.

No calculators, graphing calculators or computers are allowed during the exams.

No exams at a time other than the designated ones will be allowed. (exceptions for illness with document proof, or emergency).

Grading Policy: Homework assignments: 35%. Midterm: 25%. Final: 40%.

Chapters and Topics:

Chapter 5. Initial Value Problems for ODEs (4 weeks)
5.1   Basic Theory of Initial value problems
5.2   Euler's method
5.3   Higher order Taylor methods
5.4   Runge-Kutta Methods
5.5   Error Control
5.6    Multi-step Methods
5.7    Adaptive methods
5.8    Extrapolation methods
5.9    Higher order equations and systems
5.10 Stability
5.11 Stiff equations

Chapter 7. Iterative Techaniques in Matrix Algebra (1.5 weeks)
7.1 Norms of Vecors and Matrices
7.3 Iterative techaniques for solving linear systems;
7.4 Error estimates for iterative methods.
Chapter 8 Approximate Theory (2 weeks)
8.1   Discrete least squares approximation
8.2 Orthogonal polynomial
8.5 Trigonometric polynomial approximation
8.6 Fast Fourier Transforms
Chapter 11. Boundary Value Problems for ODEs (1.5 weeks)
11.1 Shooting method for linear problems
11.2 Shooting method for nonlinear problems
11.3 Finite difference methods for linear problems
11.4 Finite difference methods for nonlinear problems

Homework Assignments: Due each Wednesday, on Lecture Section

HW SECTIONS/PROBLEMS DUE DATE&

1 Section 5.2    #3,   #4,   #7 Wed. April   10

2 Section 5.2 #9; Section 5.3 #3a; Section 5.4 #1ab, #2ab, #10ab. Wed. April 17

3 Section 5.11 #1bc,    #2,   #6.   #9,    pp340 example 3. (for stable ranges run Stab_range.m ) Wed. April 24

4 Section 5.6    #3ab,    #5ab,    #10,   #11   Wed. May 1

5 Section 5.9 #1ab;   Section 10    #4, #5, #7 Wed. May 15

6 Section 11.3 #1ab, #5; Section 7.3 #1a, #3 (1a) Wed. May 15

7 Section 7.3 #5(a), #9, #11(a); Section 7.4 #1 (a), (c),   #2(a);   Wed. May 22

8 Section 8.1 #6abc, #8; Section 8.2 #1abc, #2abc, #7a, #12a;
** Section 8.5 #2, #7ab, #13; Section 8.6, #2, #6, #8 **
Wed. May 29
** not graded"

HW	SECTIONS/PROBLEMS	DUE DATE&
1	Section 5.2 #3, #4, #7	Wed. April 10
2	Section 5.2 #9; Section 5.3 #3a; Section 5.4 #1ab, #2ab, #10ab.	Wed. April 17
3	Section 5.11 #1bc, #2, #6. #9, pp340 example 3. (for stable ranges run Stab_range.m )	Wed. April 24
4	Section 5.6 #3ab, #5ab, #10, #11	Wed. May 1
5	Section 5.9 #1ab; Section 10 #4, #5, #7	Wed. May 15
6	Section 11.3 #1ab, #5; Section 7.3 #1a, #3 (1a)	Wed. May 15
7	Section 7.3 #5(a), #9, #11(a); Section 7.4 #1 (a), (c), #2(a);	Wed. May 22
8	Section 8.1 #6abc, #8; Section 8.2 #1abc, #2abc, #7a, #12a; Section 8.5 #2, #7ab, #13; Section 8.6, #2, #6, #8	Wed. May 29 ** not graded"