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.

**
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.

**
Additional Supplementary Materials
**
will be available on-line

**
Tentative Syllabus for Spring Semester:
**

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

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

- Homework Assignment #1
- Homework Assignment #2
- Homework Assignment #3
- Homework Assignment #4
- Homework Assignment #5
- Homework Assignment #6

**
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.

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

**
Grading:
**

- Homework and Computer Projects: 50%
- Hour Exams: 25% each
- There will be no Final Exam

**
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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