We will look at partial differential equations commonly encountered in physics and nonlinear waves, and we will learn about some of their characteristic properties and special solutions. Some of the general techniques for solving PDEs will be presented.
Instructor: Sergey Dyachenko, Department of Mathematics, University at Buffalo.
- References: Open-source lecture notes are freely distributed with the permission of their author Professor B. Deconinck at https://www.acsu.buffalo.edu/~sergeydy/math_alliance/353.pdf
- Objectives: We will learn how to identify standard first and second-order PDEs, as well as some of the famous PDEs occuring in nonlinear science. We will learn how to find traveling wave solutions, we will understand what is wave dispersion. We will learn about solution of PDEs via the Fourier series.
- Prerequisites: Linear Algebra and Ordinary Differential Equations
- Meetings: Spring 2024
- Deadline: Spring 2024
- Type: Advanced undergraduate, Beginning graduate
- Size: Three students
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