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Syllabus

Topics. This course is directed at students with some mathematical maturity and prior exposure to multivariable calculus and linear algebra. Familiarity with a computer programming language is also necessary. Topics to be discussed include:

• Basics: using a computer for numerical analysis, computer arithmetic and algebra, truncation error, error propagation, condition number and stability, principles of mathematical modeling, complexity of symbolic and numerical computations;
• Problems of approximation: discretization and sampling, approximation of functions, convergence of approximation;
• Algorithms of mathematical analysis: initial value problems, boundary value problems, linear systems, implicit versus explicit methods; integration, roots of functions;
• Algorithms of linear algebra: matrix multiplication, solution versus inversion, eigenvalues and eigenvectors, orthonormal bases, orthogonal projections;
• Fast Fourier transform applications: the Danielson-Lanczos FFT, filtering, convolution, differentiation, multiplication of polynomials, interpolation.

Prerequisites. Math 309, either Math 318 or Math 308, and some knowledge of computer programming.

Time. Classes meet Wednesday, 6:00 pm to 9:00 pm, in Cupples I, Room 199, except on 9/25, 10/23, and 11/20, when they will meet in the instructor's office.

Text. The lectures will follow G. H. Golub and J. M. Ortega, Scientific Computing and Differential Equations: An Introduction to Numerical Methods, Academic Press, 1992. ISBN:0-12-289255-0.

Homework. Collaboration in pairs will be allowed, but each individual must turned in a set of homework solutions. Problem sets will be assigned as follows: You are encouraged to work additional exercises from the indicated problem sections, although the homework grade will be based only on the exercises listed below. Please return your solutions to the instructor by the end of class. Problem sets will be assigned as follows:

FALL, 2002: HW #1, due Wed, Sep 11 HW #2, due Wed, Sep 18 HW #3, due Wed, Sep 25 HW #4, due Wed, Oct 2 HW #5, due Wed, Oct 9	HW #6, due Wed, Oct 16 HW #7, due Wed, Oct 23 HW #8, due Wed, Oct 30 HW #9, due Wed, Nov 6 HW #10, due Wed, Nov 13 HW #11, due Wed, Nov 20

Standard C sources for exercise solution programs will become available after the HW is collected.
Solutions are due at the end of class on the due date. Late homework will not be accepted. The problems will occasionally require a complete proof. The homework will be judged for correctness and clarity. When the problem requires a computed solution, it must be accompanied by a correct, well-documented computer program which will be judged for its understandability.

Tests. There will be midterm examinations in class on Wednesday, October 9, 2002, and Wednesday, November 13, 2002. There will be one cumulative final examination emphasizing the remaining material, held 10:30am--12:30pm on Wednesday, December 18, 2002, in Cupples I, Room 113.

Grading. One letter grade will be assigned for homework, one for the two midterm examinations, and one for the final examination. These three will contribute equally to the course grade. Students taking the Cr/NCr or P/F options will need a grade of D or better to pass.

Computing. Students are encouraged to use C and MATLAB on the computers available in the Arts and Sciences Computing Center for both symbolic and numerical computations.

Office Hours. Tuesdays 4-5pm, or by appointment.