M545 Introduction to Partial Differential Equations
Fall Semester 2003 Hours to be arranged in the fall
Instructor DuChateau
M545 is an introduction to linear partial differential equations. We will begin with an overview the qualitative aspects of the classical theory to provide a foundation for the remainder of the course which focuses on the meaning of and methods for constructing weak solutions. This includes an introduction to Hilbert space methods as well as an introductory treatment of distribution theory and its applications to solving problems in partial differential equations. We do not require a specific course prerequisite as the results will be developed as we go along. However, a reasonable amount of mathematical maturity is necessary.
Grades are based on problems which are to be done outside of class and handed in from time to time. There are no exams.
There is no required text, instead the lectures are based on notes which are available below, together with the course syllabus.
Laplace's Equation (updated Sep 4)
Extra Problems I (added 2 problems on Sep 9)
The Heat Equation (updated Sep 15)
The Wave Equation (updated Sep 22)
Introduction to Function Spaces (last updated on Oct 13)
Supplement: Additional techniques
Solving PDE's with the Fourier Transform (problems)
Solving PDE's by Eigenfunction Expansion (problems)
The course will roughly follow parts of the text “Partial Differential Equations” by L. C. Evans but this text is too advanced for this course. Some less advanced texts, all of which are available in inexpensive Dover editions, are the following:
Partial Differential Equations of Mathematical Physics by Guenther and Lee
Applied Partial Differential Equations by DuChateau and Zachmann
A First Course in Partial Differential Equations by Weinberger
Introduction to Partial Differential Equations by Zachmonoglou and Thoe
Equations of Mathematical Physics by Tikhonov and Samarskii