MATH 412 Partial Differential Equations Penn State University
Tu / Th 9:45  11 AM

Instructor:
Andrew Belmonte
Contact info:
322 McAllister Building, telephone: 8652491, email: belmonte.AT.math.psu.edu
Office hours:
Mon 2:304, Tues 34, Wed 1112,
or by appointment.
Class location: 014 Henderson Bldg Registrar Schedule Number: 920407
Prerequisites: Math 230 or 231 and Math 250 or 251. For more information, please contact the instructor.
Course Text (required):
We live in a threedimensional world defined by the passage of time, so it should not surprise us that many of the equations describing that world are partial differential equations (PDEs). The purpose of this course is to introduce you to these important equations  their origins, their applications, in some cases how to solve them, or at least what can be said about them mathematically. We will develop the mathematical theory of PDEs, and systematically explore several of the most wellknown cases. One theme of the course will be the relationship between the mathematical properties of the equations and their physical basis; in many instances physical intuition corresponds surprisingly well to the mathematical aspects of the solution to the PDE.
There is not one technique for solving PDEs, but many  depending for instance if it is more like a wave equation (hyperbolic) or a heat equation (parabolic).
Many of the topics we will cover can be classified under what the text calls ``flows, vibrations, and diffusions". In addition we will cover expansions in orthogonal functions, eigenvalue theory, some aspects of functional analysis, the use of Fourier and Laplace transforms to solve PDEs, and the notion of weak derivatives.
The structure of the course will follow the main text (Strauss), including most of Chapters 17 and 912, with some selections from Chapters 1314 depending on student interests.
Midterm I: Thursday, February 28th (in class).
Midterm II: Thursday, April 17th (in class).
Final Exam: Tuesday, May 6th: 6:508:40 PM  124 Agricultural Engineering  MAP of campus