# Math 495/595: Partial Differential Equations

## Course Information

Professor: Kiril Datchev

Email: kdatchev@purdue.edu

Lectures: Tuesdays and Thursdays, 12:00 to 1:15, in SCHM 309.

Office hours: Wednesdays 1-3 in MATH 602 or by appointment.

Textbook: * Introduction to Partial Differential Equations*, by David Borthwick.

Partial differential equations describe laws of nature governing all moving
bodies, notably waves, electricity, heat, gases, fluids, and astronomical objects. In this course, we will analyze these using techniques including conservation equations, characteristics, integral solution formulas, energy methods, scaling, function spaces, Fourier series, maximum principles, variational
methods, mostly following the textbook, as time and student interest allows.

Grading is based on almost weekly homework assignments and a final project.

### Homework

Homework is due on paper in class on Thursdays. Here are the assignments:

Homework 1, due January 18th.

Homework 2, due January 25th.

Homework 3, due February 1st.

Homework 4, due February 8th.

Homework 5, due February 15th.
See also these notes on the Laplacian in polar coordinates and spherical harmonics.

Homework 6, due February 22nd.

Homework 7, due February 29th.

Homework 8, due March 7th.

Topics for the final project.

Homework 9, due March 21st.

Homework 10, due March 28th, is Borthwick Exercises 10.1 and 10.2.

Homework 11, due April 4th.

Homework 12 is to work on your final project.

### Additional Reading

Three classic excellent and very polished introductions to partial differential equations, all titled *Partial Differential Equations*, are the books of
Walter A. Strauss, Lawrence C. Evans, and
Michael E. Taylor.

Strauss is easier than Borthwick, Evans is more difficult, and Taylor is more difficult still.

Finally, a list of general policies and procedures can be found here.