*Mathematica* is an environment for technical computing that
integrates numerical, symbolic, graphical, and typesetting tools. These tools
help one to focus more upon the conceptual development and visualization of the
solution to a problem than on details of algebra or procedural programming. The
concepts and tools are presented in a systematic fashion using an interactive,
tutorial format in which students use the program in class. While many
books offer examples of how to do things with *Mathematica*, here you will learn
how *Mathematica* actually works so that its methods will begin to seem natural and
almost self-evident as you begin to think in *Mathematica* style. Detailed
applications to interesting problems in physics, biology, and other fields will
be presented.

**Goal:** conceptual and operational mastery of the tools and techniques
most relevant to scientists and engineers

**Prerequisites:** calculus and basic physics. No prior experience with
*Mathematica* is needed. The course is intended for a broad audience, not
just for physics students.

**Instructor: **James
J. Kelly Phone: 405-6110
e-mail:jjkelly@physics.umd.edu

**Class schedule:** TuTh 2:00 - 3:15 in ENGR 3140 (AT&T Teaching
Theater)

**Class format:** tutorial style where each student has a computer and
interacts with the material during class

**Courseware:** available electronically from https://ttclass.umd.edu/users/class/phys426
(password protected). Note that Internet Explorer will present the site in
web folder format, which facilitates drag-and-drop copying.

**Program:** *Mathematica Version 5*

**Office hours:** TuTh 10-12 in Room 2215 C

Although I prefer that you use the scheduled office hours, I am often available at other times also. Please come frequently.

**Required text:** none. The tutorial courseware and online versions of
the *The Mathematica Book* will be sufficient.

**Useful supplements:**

*Mathematica for Physics*, R.L. Zimmerman and F.I. Olness, Addison-Wesley, 2002 (2nd ed.)*A Physicist's Guide to Mathematica*by P.T. Tam, Academic Press, 1997*Mathematica for Scientists and Engineers*by R. Gass, Prentice Hall, 1998*Mathematica by Example*by M.L. Abell and J.P. Braselton, Academic Press, 1997*Mastering Mathematica*by J.W. Gray, Academic Press, 1998 (2nd ed.)

**Homework:** will be assigned at weekly or bi-weekly intervals.
Completed work should be submitted electronically in the form of *Mathematica*
notebooks containing both the problems and their solutions. Keep your own
copies -- comments and corrections will be made within the files submitted.

**Project:** the term project should be a well-written *Mathematica*
notebook that develops the solution to a problem of interest to the student.
The project schedule and guidelines may be found at project guide.

**Exams:** none

**Grading:** homework 50%, project 50%

**Getting started**- brief survey of capabilities
- interacting with the front end
- basic concepts and first look at some important functions

**Programming techniques**- types of functions
- arguments and options
- variable scoping and modular programming
- functional programming
- recursive techniques
- examples
- cicada - synchronized emergence of insect populations
- iterated function systems -- logistic map, fractals, etc.
- cobweb diagram for logistic equation

**Plotting**- basic syntax
- embellishments
- manipulating graphics objects
- plot types
- graphics primitives
- animation

**Symbolic manipulation**- internal representation of expressions
- pattern matching
- simplification

**Algebra**- symbolic transformations
- solving equations
- example: binary collisions
- eigensystems
- example: normal modes of linear triatomic molecule
- complex variables

**Calculus**- differentiation
- limits and expansions
- integration

**Differential equations**- symbolic methods
- numerical methods
- stiff equations
- examples
- home run
- van der Pol oscillator
- Duffing equation
- chemical oscillators

**Time series analysis**- General properties of Fourier series
- Frequency analysis for periodic behavior
- Chaotic systems

**Useful links:**

- notebooks for Phys603: statistical physics
- notebooks for Phys604: mathematical methods of physics
- Wolfram Research: home of
*Mathematica*and links to associated products - Mathematica Information Center: collection of articles, applications, and enhancements

*Last revised: 13 January 2004*