# MATH 412: Partial Differential Equations

## TR 9:45-11:00 AM

Course # 127177

Instructor: Professor Andrew Belmonte

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

Office hours: Mon 9:30-11, Wed 3-4, and by appointment.

Class location: 115 McAllister Bldg.

Grader:   Seunghoon Bang (bang@math.psu.edu).

Prerequisites: Math 250 or 251.

Web Page: http://www.math.psu.edu/belmonte/03math412.html

Textbooks:

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

• Elementary Applied Partial Differential Equations, by R. Haberman (Prentice-Hall 1998), ISBN 0-13-263807-X.

• Updated Course Information:

 Assigned problems Projects PDE Links of Interest

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

A main focus of the course will be The Big Four: the transport, heat, wave, and Laplace equations. In addition we will cover expansions in orthogonal functions, and the use of Fourier and Laplace transforms in solving PDEs. In the beginning we will essentially follow Logan, and we will use Haberman more as the semester progresses. The structure of the course will follow Logan's text.

Exam Schedule:

Midterm I:   Thursday, March 6th (in class).

Midterm II:   Tuesday, April 15th (in class).

Final Exam:   Monday, May 5th, 10:10-Noon.

Last modified 18 March 2003, by belmonte@math.psu.edu