Partial Differential Equations

MATH 442

Section 1: MWF 1:50-2:40 pm -- Wells Hall C212

Instructor:

Andrew Christlieb
D304 Wells Hall
tel: 517-353-3831
fax: 517-432-1562
christli@umich.edu
office hours:
MW 10:30--12:00
Or by Appoiment


Course description Prerequisites Textbook Syllabus Computer language Homework Grading

Course Description

This course is devoted to the use of Fourier series and other orthogonal expansions in the solution ofinitial-value and boundary-value problems for second-order linear partial differential equations. Emphasis is on concepts and calculation.

Classical representation and convergence theorems for Fourier series; method of separation of variables for the solution of the one-dimensional heat and wave equation; the heat and wave equations in higher dimensions; eigenfunction expansions; spherical and cylindrical Bessel functions; Legendre polynomials; methods for evaluating asymptotic integrals (Laplace's method, steepest descent); Laplace's equation and harmonic functions, including the maximum principle. As time permits, additional topics will be selected from: Fourier and Laplace transforms; applications to linear input-output systems, analysis of data smoothing and filtering, signal processing, time-series analysis, and spectral analysis; dispersive wave equations; the method of stationary phase; the method of characteristics.

Prerequisites

Ordinary Differential Equations (MTH 235 or MTH 255H or MTH 340)

Textbook

Applied Partial Differential Equations with Fourier Series and Boundary Value Problems. Pearson Prentice Hall, 2004.
By: R. Haberman.

Syllabus

Download syllabus: (.pdf)

Computer language

In this course, we will make use of Matlab for visualization, a technical computing environment for numerical computation and visualization produced by The MathWorks, Inc. A Matlab manual is available in the MSCC Lab. Also available is a MATLAB tutorial written by Peter Blossey:

Download MATLAB plotting tutorial [MSCC, University of Washington, 1996]: ( .pdf)

Here is a list of some Matlab resources available on the net:

Alternatively, a free package called Sage, built on python, can be used to accomplish the exact same things as Matlab. The two packages that need to be loaded into sage are Numpy and Mathplotlib. These to packages come with Sage and enable the Sage environment to do much, if not all, of what Matlab can do. You can download Sage, as well as read online tutorials about Sage at

Online tutorials describing Numpy (a matlab rip off) and Mathplotlib (a nice free plotting package), can be found at

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in Adobe Acrobat (.pdf) format.

Homework Sets Date
Homework #1:(.pdf) Out: Jan 11
In: Jan 18
Homework #2: (.pdf) Out: Jan 18
In: Jan 29
Homework #3: (.pdf) Out: Jan 29
In: Feb 5
Homework #4: (.pdf) Out: Feb. 15
In: Feb 22
Homework #5: (.pdf) Out: Feb 22
In: Feb 26
Homework #6: (.pdf) Out: Mar 3
In: Mar 19
Homework #7: (.pdf) Out: Mar 19
In: Apr. 2
Homework #8: (.pdf) Out: Apr 12
In: Apr 21
Homework #9: Out:
In:
Homework #10: Out:
In:

Grading

50% - 8 to 10 Homework assignments
20% - 1 Mid-Term Exams
30% - Final exam