This course provides an introduction to the field of partial differential equations through a study of the classical equations of mathematical physics. The methods discussed proceed from classical to modern. The course begins with the method of characteristics for first-order equations and then proceeds to look at general second-order equations in terms of the classification problem and weak solutions via the theory of distributions. Then the standard second-order partial differential equations of mathematical physics, namely, the heat, wave, and Laplace equations, are studied. The focus is initially on weak solutions, then moves to the qualitative nature of solutions, what conditions imply uniqueness and why, and what consitutes well-posedness. In particular, how do these features change from one class of problems to another.

Math 444 Syllabus
Lecture by lecture description of materials to be covered

Grading
Grading procedures, contact information, progress reports, etc.

Reading Sources
A listing of six texts, with descriptions, that provide alternate perspectives on course topics

Overview Notes A set of notes for each topic to be covered that summarize the topic from a broader perspective

Topic 1: The Study of First Order PDEs and the Method of Characteristics

Assignments and Exams
A list of the homework assignments and the dates of tests and exams

Additional Materials
Mathematica modules, some published solutions, miscellaneous items, etc.