Office: 1526 LGRT
Phone: (413) 545-2817
Office Hours: M & Th 3-4
Email: johnston at math umass edu

Topics: We will cover the following topics (not necessarily in this order):

• Fourier series and the Fourier Transform
• Laplace operator, Heat and Helmholtz equations
• Fast Poisson solvers and the Fast Fourier Transform
• Time integration and stability issues
• Two and three dimensional Navier-Stokes equations

Access to MATLAB at UMass: Here is a link to the OIT Computer Classrooms website.

MATLAB Help: Here are a few PDF files and links for help with MATLAB:

• MATLAB Quick Reference (PDF)
• MATLAB Plotting Guide (PDF) (from MSCC, University of Washington, 1996)
• MATLAB Help Desk at the MathWorks site.

OCTAVE Homepage: Octave is an open source program that is mostly compatible with MATLAB.

Misc:

• Trefethen's essay on Numerical Analysis.
• Cooley & Tukey FFT paper.

Class Activity

1/20	First day of class. Read sections 13.1-13.2.
1/29	Heat equation and separation of variables. Assigned HW #1, due 2/5/16.
2/12	Tridiagonal solver. Assigned HW #2, due 2/22/16.
2/17	1D finite difference Poisson solver. Here is the m-file driver_fdbvp_2nd.m , a driver rotuine for the 1D second order Poisson solver.
2/26	Discrete Fourier Transform. Assigned HW #3, due 3/4/16. Here are the m-files createP.m and poiss1d_2P.m .
3/9	Fast Fourier Transform. Here is the m-file recfft.m .
3/21	FFTW and DFTs of real sequences. Here are the m-files fftw_speed_500_520.m , fftw_speed_1009_1035.m , realseq_ex.m .
3/25	Aliasing. Here is the m-file aliasing.m .
3/28	DST implemented using a DFT. Assigned HW #4 , due 4/4/16. Here is the m-file dst.m .
4/20	DCT implemented using a DFT. Assigned HW #5 , due 4/29. Here is the m-file mydct.m .

Homework Solutions:

• HW #1 solutions
• HW #2 solutions
• HW #3 solutions
• HW #4 solutions