Programming: Students are expected to have access to and acquaintance with
MATLAB version 4.2 or later. Student versions are adequate.
Text: Any old Numerical Analysis text that includes the topics to be covered in
this course will serve well enough at least for a start. A text tuned to MATLAB
is "Numerical Computing with MATLAB" by Dr. Cleve Moler. It is available
printed from S.I.A.M, Philadelphia; or the book's 12 chapters and MATLAB
.m files may be downloaded from The Mathworks : click on
"Textbook by Cleve Moler".
Among the topics to be covered in class are these:
--Computer Arithmetic, Floating-Point, Roundoff
--Equation-solving, linear and nonlinear
--Eigenvalues/vectors of matrices
--Failure modes of MATLAB's functions for the above
--Palliatives for failure modes; Iterative Refinement
--Other iterative methods
--Integration - Quadrature and ODEs; impediments to error-control
--Simple Elliptic and Parabolic PDEs
These topics have been determined partly by the instructor's inclinations and
partly by the needs expressed by students taking the course. To this end, each
student has submitted an account of his/her background, plans and topic choices.
Background: Upper div'n Math. classes taken; numerical and programming experience.
Plans: What do you intend to do after you graduate?
Topic choices: List some you think you will need or are curious to learn.
The instructor's inclinations are revealed by the postings on his web pages.
As an error-analyst, the instructor tends to question computed results:
-- What evidence corroborates a result's claimed or presumed accuracy?
-- If inadequately accurate, how can a result be recomputed more accurately?
A Final Exam was scheduled, but the class has chosen credit by project instead.
Each student should choose a project as soon as possible. If you cannot think
of a suitable project after six weeks, come to the instructor for suggestions.
What kinds of projects can earn credit instead of a final exam?
Original research or novel results are not necessary for this undergraduate
course. A suitable project consists of a scientific paper written well enough
to be publishable in principle. It may explore in greater depth a topic
covered in class, or cover a topic that could have been covered in class
but wasn't. The project can report on an application of numerical methods to
an interesting problem relevant to your intended career. Credit will be
earned not so much for a program as for the mathematical analysis that
justifies it. Why did you choose your program's method(s) instead of others?
How do its results compare with what you intended? If discrepancies occurred,
what have you done about them? When and why should your program's results be
trusted? How do you know?
In effect, a project is practice for a thesis or for a report to your
client or employer explaining how and why your work has been worthwhile.