“The book of the universe is written in the language of mathematics; without mathematics it is not possible to
understand a word of it.” Galileo Galilei
Course:
Math/CS 243A
Days and Times:
Advanced Numerical Analysis
TTh 5:30-6:45 in MH 320
Prerequisite: One semester of undergraduate numerical analysis such as our Math / CS 143M (M stands for
Matrices) or Math / CS 143C (C stands for Calculus). Also linear algebra, Calculus III and a programming course are
prerequisites. Courses that are nice to have but not essential (we will discuss any results needed from these courses):
partial differential equations, additional programming, related application courses in physics, chemistry, meteorology,
etc.
Instructor: Leslie Foster
Office: MH 312
Semester: Fall 2008
Telephones: 924-5123, Secretaries: 924-5100 email: foster@math.sjsu.edu web page: www.math.sjsu.edu/~foster/
Office hours (tentative): T Th 12:00-1:30, 6:45-7:15, by appointment or (for questions related to the course) any time I’m not
busy
Text: Numerical Solution of Partial Differential Equations: Finite Difference Methods by G. D. Smith, Third
Edition, Oxford Press, 1985, 1986, 1987, 1989,1992, 1996, 1998, . . .
Other
Text
Books
(in
a
rough
order
of
increasing
difficulty):
Finite Difference Methods for Ordinary and Partial Differential Equations by Randall J. LeVeque; Numerical solution
of partial differential equations: an introduction by K. W. Morton and D. F. Mayers; Numerical Methods for Partial
Differential Equations by G. Evans, J. Blackledge and P. Yardley; The finite difference method in partial differential
equations by A. R. Mitchell and D. F. Griffiths; Digital Computer Treatment of Partial Differential Equations by V.
Vermuri and Walter J. Karplus; Numerical Methods for Partial Differential Equations by William F. Ames;
Numerical Solution of Partial Differential Equations in Science and Engineering by Leon Lapidus and George F.
Pinder; Finite Difference Schemes and Partial Differential Equations by John C. Strikwerda. A internet site with
good reference material http://www.amath.washington.edu/~rjl/booksnotes.html . We may also cover some material
from Computer Solution of Sparse Positive Definite Systems by Alan George and Joseph Liu and Direct Methods for
Sparse Linear Systems by Timothy Davis.
Learning Objectives:
To learn tools and techniques to analyze PDEs related to science and engineering including: types of PDEs. finitedifference methods applied to parabolic, elliptic and hyperbolic equations; explicit and implicit schemes; multi-level
schemes; convergence and stability; error control; theory of characteristics; semi-discrete approximations; iterative
methods of solution (including conjugate gradients) and acceleration techniques; matrix and eigensystem analysis;
direct methods for sparse systems; perturbation of matrices; applications to heat flow and computational
aerodynamics; shock waves in traffic and fluid flow, electrical potential, and structural mechanics.
Computing in the course: We will augment the material in the text with numerical examples. You will find it
convenient to use Matlab for some of the computer work. Initially I will provide Matlab programs implementing
some of the numerical methods that we discuss and ask that you do runs that illustrate some of the theory. Later you
will need to write some of your own code. I have a license to distribute Matlab 5.3 for you to take home and use for
the semester. The most recent version of Matlab is version 7 which is available on the Math Department labs in
MH221. Note that Matlab 7 (but not Matlab 5.3) and Maple 8 come with PDE packages that implement many of the
method that we will discuss. Since we will want to see how the methods are implemented Matlab 5.3 will suffice for
most of our purposes. However it may be useful at times to try out the “professional” versions of the method. An
excellent Matlab introduction and reference is Matlab Guide by Higham and Higham, SIAM Press.
Math 110L: I encourage you to enroll in Math 110L in order to have access to Matlab 7 (and Maple 8) in the
department lab. This costs you nothing if you are a regularly enrolled student.
Project: I am considering a project for the later part of the semester. This will involve looking at and writing about
literature in journal articles and may include, if you choose to do this, experimenting with numerical PDE packages
available on internet.
Requirements and Points
Midterm
Final
~5 Assignments
Potential Project
Total
Points Each
100
150
20
50-100
Basis of Grade
Curve within reason. The
curve for each individual
test/assignment/project will be
announced in class when the
assignment is returned. If
not announced the curve is
90/80/70/60 for A/B/C/D.
350-500
Approximate Course Schedule:
Parabolic PDE’s
Computer Arithmetic
Hyperbolic PDE’s
Elliptical PDE’s
4 weeks
1 week
5 weeks
5 weeks
Make-up exams and quizzes: None except under very unusual circumstances and then only if you contact me (via
phone, message, in person, note, ...) before the exam. Make-up exams will be more difficult.
Cheating: Don’t. On homework assignments you may discuss the assignments with other students but don’t copy
their work.
Additional information / requirements please see http://www.math.sjsu.edu/math/courses/mathgs.htm