Midterm
March 10th, 7:00 PM - 9:00 PM, Thompson 102
Instructor: Hans Johnston
Office: 1526 LGRT
Phone: (413) 545-2817
Office Hours: M 3:30-4:30, W 3:15-4:30,Th 2:30-4
Email: johnston at math umass edu
Course description: The course will introduce foundational numerical methods used for problems that arise in many scientific fields. Properties such as accuracy of methods, their stability and efficiency will be considered. Students will gain practical programming experience in implementing the methods using MATLAB, which will be taught through incrasingly complex codes over the term, with examples in class and students homework assignments. From time to time we will also discuss practical considerations of implementing these methods on modern computer architectures using C, C++ or Fortran. Today's average smartphone can computationally crush a 1990's era Cray C90, which cost $10 million at the time ($18 million in today's $) for sixteen 244Mhz vector processors and 8GB of RAM.
Topics: Application of computational methods to models arising in science and engineering, concentrating mainly on the solution of partial differential equations. Topics include finite differences, finite elements, boundary value problems, fast Fourier transforms.
Grading:
The grading of the course will be as follows. There will be a midterm
exam and a final
exam, each
worth 35%,
and homework (lowest 2 dropped) worth 30%.
Free MATLAB software: Here is a link to the
OIT MATLAB website.
Access to MATLAB in OIT Labs: Here is a link to the OIT Computer Classrooms website.
MATLAB Help: Here are a few PDF files and links for help with MATLAB:
OCTAVE Homepage: Octave is an open source program that is mostly compatible with MATLAB.
"Careful with That Axe, Eugene":
1/22
First day of class.
1/27
Interpolation and Numerical Integration review.
Read sections 4.1-4.2 and 5.1 and 5.2.1-5.2.2.
1/31
Assigned HW1 , due 2/7.
Here are the m-files fp_example.m
and graphsetup.m .
2/10
More on numerical integration (quadrature) and the Poisson equation.
Read sections 9.1-9.2 .
2/14
Finite difference methods for the Poisson equation.
Assigned HW2 , due 2/21.
2/18
Here are the m-files fdbvp_2d.m
and driver_fdbvp_2nd.m .
2/21
Matrix similarity and diagonalization.
Assigned HW3 , due 2/28.
2/28
DFT and FFT.
Assigned HW4 , due 3/6.
3/4
Cooley and Tukey and the FFT.
Here is the m-file recfft.m .
Read section 13.3 Ascher & Grief .
4/3
2nd and 4th order 1D Poisson solvers. (Class notes PDF )
Here are the m-files createP.m ,
poiss1d_2P.m ,
poiss1d_4P.m ,
ACCURACY_poiss1d_2P.m ,
ACCURACY_poiss1d_4P.m
4/6
Compact discretizations and Neumann BCs I.
Assigned HW5 , due 4/17.
HW5 Latex file hw5_students.tex
Here are the m-files createcosP.m ,
poiss1d_2PNeumann.m
4/8
Compact discretizations and Neumann BCs II:
PDF (3.5MB)
Video (44.7MB)
Here are the m-files mydst.m ,
mydct.m
Zoom Class (starts 10:00AM):
ID 894 433 822
4/10
Neumann BCs:
PDF (3.9MB)
Video (38.6MB)
4/15
Neumann BCs II:
Video (59.7MB)
Homework Solutions: