Math 5588      Elementary Partial Differential Equations       Spring, 2005

Professor Peter J. Olver
School of Mathematics
Institute of Technology
University of Minnesota
Minneapolis, MN 55455 		540 Vincent Hall
Phone: 612-624-5534
Fax: 612-626-2017
e-mail: olver@math.umn.edu
http://www.math.umn.edu/~olver
Lectures:    T, Th 4:45-6:00pm    ME 102
Office Hours:   T 11:00-12:00, 3:30-4:30, or by appointment

Course Description:   Math 5587-8 is a year course that introduces the basics of partial differential equations, guided by applications in physics and engineering. Both analytical and numerical solution techniques will be discussed. Specific topics to be covered during the year include, in rough order:

Classification of PDEs; the heat, wave, Laplace, Poisson and Helmholtz equations; characteristics; the maximum principle; separation of variables; Fourier series; harmonic functions; distributions; Green's functions and fundamental solutions; special functions, including Bessel functions and spherical harmonics; finite element method; Fourier and Laplace transforms; nonlinear PDEs; shocks and solitons. Choice of supplementary topics and applications will depend on the interests of the class.

Prerequisites: Strong background in linear algebra, multi-variable calculus and ordinary differential equations (3000 level). Some mathematical sophistication. Other topics will be introduced as needed.

Text:   Walter A. Strauss, Partial Differential Equations: an Introduction, John Wiley & Sons, New York, 1992.

Supplementary Texts:   Nakhle H. Asmar, Partial Differential Equations, Second Edition, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 2005.

Richard Haberman, Elementary Applied Partial Differential Equations, Third Edition, Prentice-Hall, Inc., Upper Saddle River, New Jersey, 1998.

Additional Supplementary Materials  will be available on-line

Tentative Syllabus for Spring Semester:

  1. Heat and wave equations in two space dimensions (Strauss 10.1,2,4)
  2. Special functions, including Bessel functions, Legendre functions and spherical harmonics (Strauss 10.5,6)
  3. Laplace, heat and wave equations in three dimensions (Strauss 7.1--4,9.4, 10.3)
  4. The Schrödinger equation and the hydrogen atom (Strauss 9.4--5, 10.7)
  5. Numerical methods - finite difference and finite elements (Strauss 8.1--5)
  6. Nonlinear first order equations and shocks (Strauss 14.1)
  7. Nonlinear diffusion and Burgers' equation
  8. Dissipation, nonlinear waves, solitons, and the Korteweg--deVries equation (Strauss 14.2)
  9. (time permitting) The calculus of variations (Strauss 14.3)

Homework:   Problems and computer projects will be assigned in class.

Hour Exams:   There will be two midterm exams. Make-up exams will only be given in exceptional circumstances, and then only when notice is given to me before hand and a suitable written excuse forthcoming.

First Midterm:    Tuesday, March 8. Will cover two-dimensional heat and wave equations, series solutions of ordinary differential equations, and Bessel functions.

Second Midterm:    Thursday, April 28. Will cover three-dimensional heat, wave and Laplace equations, and basic numerics for heat and wave equations.

Grading:

Incompletes:   Only given in extreme circumstances, and only when the student has satisfactorily completed all but a small portion of the work in the course. Students must make prior arrangements with the professor well before the end of the quarter.

Grading Standards and Student Conduct:   Students are expected to be familiar with University of Minnesota policies on grading standards and student conduct, including the consequences for students who violate standards of academic honesty.

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