University of California at Berkeley

Mathematics 128A, Section 3: Spring 2002

Overview
| Details
| Materials
| Assignments
| Exams
| Policies

After the Spring break, the homework assignments are handed out and collected on Tuesday.

Note the change in the final exam schedule.

For accounting purposes, attach a listing of your programs to the homework or send it to <fomel@math.berkeley.edu>

This course introduces students to numerical methods for solving mathematical problems. Numerical analysis deals with computational problems involving continuous functions of real and complex variables.

The intended syllabus includes:

- Computer arithmetics
- Interpolation and approximation
- Numerical differentiation and integration
- Numerical solution of nonlinear equations, systems of linear equations and ordinary differential equations

Using programming assignments, students will acquire experience with solving numerical analysis problems on a computer. There will be an in-class midterm and a final exam.

- Lectures:
- Tuesday and Thursday, 12:30-2:00, Room 105 Stanley Hall.
- Discussion Section:
- Monday, 3:00-4:00, Room 3 Evans Hall.
- Instructor:
- Sergey Fomel
<fomel@math.berkeley.edu>

(510) 486-5695

*Office hours*: Tuesday and Thursday, 3:00-4:30, or by appointment, Room 857 Evans. - Teaching Assistant:
- Michael Burns
<burns@math.berkeley.edu>

*Office hours*: Monday 2:00-3:00 and Wednesday 4:00-6:00, Room 1087 Evans. - Prerequisites:
- Familiarity with Calculus, Linear Algebra, and Differential Equations. Programming in the language of your choice.

Burden and Faires, Numerical Analysis, 7th edition, Brooks/Cole, 2001, ISBN: 0-534-38216-9.

- Heath, Scientific Computing: An Introductory Survey, 2nd edition, McGraw-Hill, 2002, ISBN: 0-07-239910-4.
- Cheney and Kincaid, Numerical Mathematics and Computing, 4th edition, Brooks/Cole, 1999, ISBN: 0-534-35184-0.
- Gerald and Wheatley, Applied Numerical Analysis, 6th edition, Addison-Wesley, 1999, ISBN: 0-201-87072-X.
- Shampine, Allen, and Pruess, Fundamentals of Numerical Computing, John Wiley and Sons, 1997, ISBN: 0-471-16363-5.

- Numerical Analysis FAQ: Frequently asked questions about scientific computing and numerical analysis.
- Matlab primer for version 4: PDF file.
- GSL: The GNU Scientific Library A free open-source numerical library for C programmers.
- Numerical Recipes in C A popular collection of numerical algorithms.
- Netlib A huge collection of mathematical software.
- Gnuplot A free program for scientific plotting.

Fixed-Point Iteration (+ Mathematica notebook)

Polynomial Interpolation (+ Mathematica notebook)

Chebyshev Polynomials (+ Mathematica notebook)

Bezier Curves (+ Mathematica notebook)

Assignment 1: Computer Arithmetics

Due: Thursday, January 31

Answers

Assignment 2: Nonlinear Equations: Bisection and Regula Falsi

Due: Thursday, February 7

Answers

Assignment 3: Nonlinear Equations: Newton, Steffensen, and Others

Due: Thursday, February 14

Answers

Assignment 4: Interpolation: Polynomial Interpolation

Due: Thursday, February 21

Answers

Assignment 5: Interpolation: Polynomial Interpolation 2

Due: Thursday, February 28

Answers

Assignment 6: Interpolation: Spline Interpolation

Due: Thursday, March 7

Answers

Assignment 7: Approximation: Polynomial Approximation

Due: Thursday, March 21

Answers

Assignment 8: Numerical Differentiation

Due: Tuesday, April 9

Answers

Assignment 9: Numerical Integration

Due: Thursday, April 18

Answers

Assignment 10: Ordinary Differential Equations: One-Step Methods

Due: Tuesday, April 23

Answers

Assignment 11: Ordinary Differential Equations: Multistep Methods

Due: Tuesday, April 30

Answers

Assignment 12: Systems of Linear Equations

Due: Tuesday, May 14

Answers

- Midterm:
- Tuesday, March 12, in class.
- Final:
- Wednesday, May 22, 5:00-8:00 pm, 3 Evans Hall.

Alternate exam time will be offered for students taking courses with conflicting exam periods.

40% homework assignments; 20% midterm; 40% final exam

Weekly assignments are due in class. Late homework is not permitted. Your two lowest homework grades will be dropped to allow for missed assignments.

Last updated: Wed May 15 14:33:46 PDT 2002.