# MATH 412: Partial Differential Equations

## Penn State University, Fall 2000

## MWF 2:30-3:20

Course # 664341
**Instructor**: Professor Andrew
Belmonte

**Contact info: **302 McAllister Building, telephone: 865-2491, email:
belmonte@math.psu.edu

**Office hours**: Wednesdays 3:30-4:30,
and by appointment.

**Class location**: 104 McAllister
Bldg.

**Prerequisites**: Math 230 or 231; Math 250 or 251.

**Web Page**: http://www.math.psu.edu/belmonte/math412.html

**Textbooks**:

*Applied Partial Differential Equations*, by J. D.
Logan (Springer 1998), ISBN 0-387-98439-9.

*Partial Differential Equations of Mathematical Physics and
Integral Equations*, by R. B. Guenther and J. W. Lee (Dover
1996), ISBN 0-486-68889-5.

**Updated Course Information**:

Material covered
in class so far |
Assigned
problems |

**The Course**:
Insofar as the book of nature is written in the language of
mathematics (as Galileo once said), most of the sentences are partial
differential equations. The purpose of this course is to introduce
you to these important equations - their origins, applications, and
how to solve them. In addition to being ubiquitous, many partial
differential equations (PDEs) are difficult to solve. We will develop
the mathematical theory of PDEs, and systematically explore several
of the most well-known cases. Throughout the course I will attempt to
strike a balance between the mathematical properties of the equations
or their solutions, and the physical implications; in many instances
your physical intuition corresponds to mathematical facts - and vice
versa!

The material we will cover can be divided into three topics:

I. The physical origins of PDEs

II. PDEs on unbounded domains

III. PDEs on bounded domains

In addition we will cover expansions in orthogonal
functions, in particular Fourier Series. These four main subjects
correspond to the four chapters of Logan, which we will essentially
be following.

**Exam Schedule**:
Midterm I: Monday, October 16th (in class).

Midterm II: Monday, November 20th (in class).

Final Exam: Wednesday, December 13th, 2:30-4:20 p.m.

Last modified 28 August 2000, by
belmonte@math.psu.edu