Fourier Analysis and Partial Differential Equations

Course Description

Textbook

Other: Tung, K.K.: Partial Differential Equations and Fourier Analysis--A Short Introduction. Available here.

Additional Notes: From time to time, additional notes and supplements will be put on course web or distributed in class.

Syllabus

1. Introduction, bases
2. Physical Origins of Partial Differential Equations
3. Types of Partial Differential Equations
4. Diffusion Examples; Solutions by Separation of Variables
5. Fourier Series, Eigenfunction Expansions
6. Wave Examples; Solutions by d'Alembert's Method
7. Nonhomogeneous Partial Differential Equations
8. Solutions of Laplace's Equation
9. Utility of Fourier and Laplace Transforms
10. First Order Partial Differential Equations; Method of Characteristics

Learning Objectives and Instructor Expectations

Although the subject matter of Partial Differential Equations can be made rather difficult, I will attempt to present the course material in as simple a manner as possible. More theoretical aspects, such as proofs, will not be given or required. Instead, applications and the physical bases will be emphasized.

I will let you know clearly what you need to learn and what can be omitted. Homework is used to reinforce class lectures and not as a way to introduce material that is not covered in class. Exams will emphasize basic techniques as applied to simple and fundamental problems. There will be no deliberately obscure questions in exams to test your mental dexterity.

Schedule and Homework

Follow links in the table below to obtain a copy of the homework in PostScript (.ps) or Adobe Acrobat (.pdf) format. You may also obtain here solutions to some of the homework and exam problems. An item shown below in plain text is not yet available. For additional information regarding viewing and printing the homework and solution sets, click here.

Grading

You may view your homework and exam grades on-line.