Instructor: Professor Di Qi
OFFICE: Math 644
OFFICE HOURS: Wednesday and Friday 12:00-1:00 PM
E-MAIL: qidi@purdue.edu
URL:
http://www.math.purdue.edu/~qi117
Grader: Stanley Gao
Grader's OFFICE: MATH 1031
E-MAIL: gao757@purdue.edu
I will post here lecture notes for each class. While these notes contain all of the information you need to know, reading going beyond this is essential to the class and will be indicated here. I will refer mostly to the textbooks of Lai and Zhang, Trefethen, and LeVeque, but there will also be links to papers or notes by other people. I will also refer to the Lecture Notes by Prof. Xiangxiong Zhang.
For more materials on numerical ODEs and time integration schemes consult my precious class on Numerical Solutions of ODEs.
A nice gallery of PDEs and numerical solutions can be found in The (Unfinished) PDE Coffee Table Book by N. Trefethen.
The use of Fourier techniques in PDEs, both their analysis and numerical solution, will come up many times in this class. There are three separate but related topics to consider here. The first is the FFT as a discrete unitary transform (linear algebra), and using the Fourier series as an approximation to periodic functions (approximation theory), and FFTs as as a tool to solve PDEs.
You can also review my previous slides on Fourier transforms and solving initial value problems using Fourier series.
By far the most popular/efficient library for FFTs is FFTW, see documentation for what normalization it uses. FFTW is used under the hood in Matlab/numpy, but they may use differet normalization, see for example the Matlab's fft/ifft convention.
These are topics that we will not cover in class but I have some materials/references already. Some of these are suited for a final project.
Students will be assigned a project and are expected to present their results in the last week of the class. There will be no midterm and final exams. The grade will be based on projects and attendance (60%) and final presentation (40%).