Office: 1526 LGRT
Phone: (413) 545-2817
Office Hours: M 3-4:30, W 11:45-1:15
Email: johnston at math umass edu
Textbook: A First Course in Numerical Methods, by
Ascher & Greif (SIAM)
(UMass Library FREE ebook)
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: We will cover the following topics (not necessarily in this order):
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":
First day of class. Taylor polynomials and Taylor series.
Here are the m-files fp_example.m and graphsetup.m .
Read sections 1.1-1.3 and 2.1-2.2
Assigned HW1 , due 2/7/19.
M-files: taylor_exp_ex.m taylor_exp_ex.m , fp_example_h_h2.m
Conditioning, stability, and finite precision
Roots of nonlinear equations and the bisection method.
Read sections 3.1-3.3.
Assigned HW2 , due 2/19/19 to my office or mailbox by 4:30pm.
Fixed point methods.
More on fixed point methods.
Read section 3.4: Newton's method and variants.
Assigned HW3 , due 2/28.
More on Newton's method.
Order of convergence and the secant method.
Assigned HW4 , due 3/5.
The order convergence of the secant method is the Golden Ratio.
Intro to Numerical Linear Algebra.
Read sections 4.1-4.2 and 5.1-5.3.
Assigned HW5 , due 2/28/19.
M-files: mylu_nop.m , mylu_solve_nop.m
Norms, conditioning, and 2-point boundary value problems.
Assigned HW6 , due 4/4.
Iterative methods for linear systems.
M-files: my_lu.m , my_trilu.m , my_trilu_solve.m
Read sections 10.1-10.3.
Assigned HW7 , due 4/23/19.