Math 280 (Spring 2003)
Numerical Methods for Integration and Interpolation

 
 
What is new? Problem Set II (PS) is due June 2. The prol.txt, gaus.txt files are here.


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    General Information

    This is a graduate level course in numerical analysis and computation, with an emphasis on techniques in numerical integration and interpolation in bases such as polynomials, trigonometric polynomials, and Prolate Spheroidal Wave Functions. The course will consist of two parts, the first a classical treatment of numerical integration and interpolation, and the second a summary of some recent developments. Algorithms will be illustrated with applications in varies fields. The course might be of interest to mathematicians, engineers and scientists.

    Lectures: (tentative schedule)

    • MW 2:40-4:00pm, Kerr 593

    Instructor:

    • Hong Xiao, 571 Kerr, 752-3827, xiaoh@mathdotucdavis.edu (change "dot" to "." before sending emails)
    • Office Hours: Tu F 3:10-4:00pm, or by appointment

    Textbook  and References

    The following books are used as references.
    • Numerical Methods by G. Dahlquist, A. Bjorck, Prentice-Hall, Inc.
    • Signal Analysis, by A. Papoulis, McGraw-Hill.
    • Foundations of Time-Frequency Analysis by K. Grochenig, Birkhauser.

    Contents

      Part One
    • Introduction, basics of numerical methods
    • Classical polynomial integration and interpolation (Newton-Cotes, Lagrange interpolation, Runge phenomenon)
    • Trigonometric integration and interpolation (review)
    • Chebyshev interpolation, fast Fourier transform
    • Chebyshev systems
    • Gaussian quadrature, Root Finding

      Part Two
    • Band-limited functions, bases for band-limited functions
    • Uncertainty Principle, Time-Frequency analysis (brief)
    • Prolate Spheroidal Wave Functions, numerical evaluation, asymptotic formulae
    • Quadratures and interpolation of band-limited functions
    • Generalized Gaussian quadrature, Chebyshev systems, interpolation
    • Applications

    Prerequisite

    Math 21, 128, 167, or their equivalents, or with permission of the instructor.
     

    Computing Environment Issues

    To do your programming assignments, you may log on a machine in the Undergraduate Lab (Room 451) of the Mathematics Department or use your PC if it has the necessary software. If you have been working on your project on other machine clusters or on your own PC, you need to transfer the relevant files onto your Mathematics account first. To apply for a math account, you may visit the website at
    Information about the Math computing environment is available at the Math Computing Homepage , or available by mailing your specific questions to Administor . You are also encouraged to come and talk with the TA when encountering difficulties.

    Grading Policies (tentative)

    Your grade for the course will be dertermined based on the following:
    • Programming Projects: 40%
    • Final Report: 60%

    xiaoh@mathdotucdavis.edu (change "dot" to "." before sending emails)