University of California at Berkeley
Mathematics 128A, Section 3: Spring 2002

Numerical Analysis

Announcements

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>

Overview

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.

Details

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.

Materials

Textbook

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

Optional readings

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.

Interesting links

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.

Handouts

Course Syllabus

Fixed-Point Iteration (+ Mathematica notebook)

Polynomial Interpolation (+ Mathematica notebook)

Chebyshev Polynomials (+ Mathematica notebook)

Bezier Curves (+ Mathematica notebook)

Midterm Sample Questions

Final Sample Questions

Assignments

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

Exams

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.

Policies

Grading

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

Late assignments

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.