Course Information
| Instructor | Dr. Changhui Tan |
| Lectures | Tu Th 1:15pm - 2:30pm, at LeConte 310 |
| Office | LeConte 422 |
| Office Hours | Tu Th 11:00am - 12:00pm, or by appointment |
| Textbooks | Walter A. Strauss, Partial Differential Equations: An Introduction. (ISBN: 978-0470054567) |
| References | Lawrence C. Evans, Partial Differential Equations. (ISBN: 978-0821849743) |
| J. David Logan, Applied Partial Differential Equations. (ISBN: 978-3319124933) |
Course Description
- A partial differential equation (PDE) is an equation that contains unknown multivariable functions and their partial derivatives. PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. In this course, we will address many of the mathematical issues on various types of PDEs. We will also discuss boundary value problems on PDE, and related applications in physics and other natural sciences. A brief outline of topics to be covered is as follows.
- List of Topics:
- An introduction to PDEs and associated applications.
- First-order linear and nonlinear PDE:
- Linear transport equations, the Burgers equation, and other first-order nonlinear PDE.
- Local existence theory on initial/boundary value problems of first-order PDE.
- Method of characteristics. - Second-order linear PDE, 3 basic equations:
- The wave equation and the heat equation (diffusion).
- Boundary conditions, the Fourier method.
- The Laplace equation: fundamental solution, Green's function in unbounded and bounded domains. - Other selected topics will be covered if time permits.
Homework Assignments
- Homework assignments will be assigned and collected each week. The tentative due date is on Tuesday in class.
- The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
- Last update: 4/22, Solution for Homework 5 is available. Typo: for all Fourier coefficients, 2/L factor should be 1/L.
Download Homework Assignments and Solutions.
Exams
- There will be a 75 minutes in-class midterm exam. The date will be on March 5th.
- There will be a 150 minutes take-home final exam.
- In both exams, you can use the textbook, your own lecture notes, and your own homework assignments. Other communications and help are not allowed.
- Last update: 4/27, the final exam is avilable to be downloaded.
- Download Exams and Solutions.
Grades
- Your grade is distributed as below:
-
Class Participation » 10% Homework » 40% Midterm exam » 20% Final exam » 30%
Contact Information
- Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.