# MATH 412: Partial Differential Equations

## 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.