Phys/Chem 229
& Phys 100 Computational Methods
with Mathematica
Prof.
Office:
FRH 2115 x42254
Lab: RH
113 x46621
Class:
Tuesday and Thursday
Recitation:
Tuesday 2:00-3:00 and Thursday
11:30-12:30
Office hours:
24 hours email, and by appointment
You need a punch code to give you access to the
instructional computer facility MSTB 110 which is across the parking lot from Reines and Rowland Halls.
The code will be sent in an email. When using these machines, you should
log in with the user name "student" and the
password "mst".
In this course we will develop the use of
Mathematica as a tool to learn the methods of mathematical physics and to do
problems selected from classical mechanics, electromagnetism, quantum mechanics
and statistical mechanics. You are strongly encouraged to purchase a personal
copy of Mathematica software. Student versions are available in the bookstore
for about $140; the current version is 5.2.
Lectures will follow Taborek, MathematicaHandbook , which is an ebook that can be read only in Mathematica. The ebook will be installed on the machines in MSTB 110.
You can purchase your own personal copy for $30 from mathematicahandbook.com; for this
class, you should buy the Standard version. Some other conventional references
are suggested below.
Homework problems will be assigned every
Tuesday, and will be due 9 days later on Thursday. This
will be a paperless class: homework assignments will be in the form of
Mathematica notebooks that you obtain by downloading from the Homework assignments
page. Completed assignments should be returned by ftp as described here. The grade will be based
70% on homework and 30% on a final exam.
In addition to learning Mathematica syntax and
programming techniques, we will discuss mathematical topics including:
Ordinary differential equations: power series
solutions; special functions; asymptotic
analysis;
systems, greens functions, transfer function
Eigenvalues
and normal modes
Complex integration and residues
Fourier series and the relation to Fourier
transforms
Vector analysis
Separation of variables in partial differential
equations; boundary value problems
Calculus of Variations
Dimensional Analysis
Perturbation theory
Variational
methods
Curve fitting
References
Other Mathematica references include ( in increasing order of difficulty and sophistication):
“Engineering Mathematics with Mathematica”, J.S.
Robertson, McGraw Hill 1995
“A Physicist’s Guide to Mathematica”, P. T. Tam,
Academic 1997
“Mathematica for Physics”, R. L. Zimmerman and
F. I. Olnes, Addison-Wesley 2002
“Mathematica for Scientists and Engineers” , T. B. Bahder, Addison Wesley 1995
“Mathematica in Theoretical Physics”, G. Bauman,
Springer, 1993
“Quantum Methods with Mathematica”, J.M. Feagin, Telos, 1994
Standard books on mathematical physics (in order
of difficulty}:
“Mathematical Methods in the Physical Sciences”,
M. Boas, Wiley, 1983 (undergraduate book used at UCI)
“Mathematical Methods for Physicists”, G. Arfken, Academic 1985 ( slightly
fancier than Boas)
“Mathematical Methods of Physics”, J. Mathews
and R. Walker, Benjamin 1970 (standard graduate text)
“Advanced Mathematical Methods for Scientists
and Engineers”, C. Bender and S. Orszag, McGraw Hill
1978 (one of my personal favorites)
“Methods of Mathematical Physics, Vols I and II”, P. M. Morse and H. Feshbach,
McGraw Hill, 1953 ( the textbook they used to teach
Feynman)
“Mathematical Handbook of Formulas and Tables”,
M.R. Spiegel, McGraw Hill, 1968
“Tables of Integrals, Series and Products”,
“Handbook of Mathematical Functions”, M. Abromowitz and
The last three are definitive tables with lots
of information about special functions. They are dusty old books. The modern
version can be found at http://functions.wolfram.com/