Topics in Differential Equations
 Math 934: Topics in Differential Equations

University of NebraskaLincoln, spring 2017

Syllabus
Course Documents
 Matlab Intro [pdf]. My introduction to Matlab worksheet.
 talk.pdf. My slides about Fourier transforms and PDEs.
 Logistic Worksheet [pdf]. My code for the logistic problem: logisticChaos.m
 RungeKutta Project [pdf] My ndimensional rk4 code rk4_ndim.m and rk4_error.m code.
 A backward Euler solver: backward_euler.m which requires a Newton's method solver: Newton.m
 The Discrete Fourier Transform [pdf] A writeup by Prof. Steven Johnson about how the DFT is used to compute derivatives.
 FFTderivatives.m My code to compute derivatives using the FFT.
 FFT Theory [pdf] A writeup on the (correct!) algorithm to compute the FFT.
 heatProject.pdf My code for the logistic problem: heat_rk4.m
 Link to John Bowman's slides on dealiasing. [pdf]
 burgersProject.pdf (Code will be posted after all projects are in.)
 IMEX.pdf A discussion of mixed implicit/explicit methods.
 Read page 15 and Section 2.3. If you need more mathematical background, read chapter A, starting on page 225.
 transport_naive.m My code to "simulate" the transport equation with the (unstable) Euler method.
 transport_lf.m My code to simulate the transport equation with the leapfrog method.
 wave_lf.m My code to simulate the wave equation with the leapfrog method.
 Project_FEM_Poisson.pdf A project to code a 1D Poisson solver in Matlab.
"Think twice, code once." Anonymous