# Essentials of Mathematica

## With Applications to Mathematics and Physics

• Nino Boccara
Book

1. Front Matter
Pages i-xxx
2. ### Essential Commands

1. Front Matter
Pages 1-4
2. Pages 5-54
3. Pages 55-75
4. Pages 77-102
5. Pages 103-149
6. Pages 151-172
7. Pages 173-218
8. Pages 219-233
9. Pages 235-268
3. ### Applications

1. Front Matter
Pages 269-272
2. Pages 273-277
3. Pages 279-283
4. Pages 285-287
5. Pages 289-299
6. Pages 301-302
7. Pages 303-309
8. Pages 311-320
9. Pages 321-326
10. Pages 327-339

### Introduction

Essentials of Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergraduate and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. The text assumes no previous exposure to Mathematica. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy-to-read Mathematica programs. It includes many detailed graphics, with instructions to students on how to achieve similar results.

The aim of Essentials of Mathematica is to provide the reader with Mathematica proficiency quickly and efficiently. The first part, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. The second part covers a broad range of applications in physics and applied mathematics, including negative and complex bases, the double pendulum, fractals, the logistic map, the quantum harmonic oscillator, the quantum square potential, the Van der Pol oscillator, the Duffing oscillator, multilane bidirectional pedestrian traffic, public-key encryption, tautochrone curves, Iterated function systems, motion of a bead on a rotating circle, Mersenne and perfect numbers, Lindenmayer systems, skydiving, Lorenz equations, the Foucault's pendulum, and Julia and Mandelbrot sets.

### Keywords

Analysis Mathematica Potential computational science engineering mathematical software numerical programming statistics

#### Authors and affiliations

• Nino Boccara
• 1
1. 1.Department of Physics (M/C 273)University of Illinois at ChicagoChicagoUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-0-387-49514-9
• Copyright Information Springer Science+Business Media, LLC 2007
• Publisher Name Springer, New York, NY
• eBook Packages Physics and Astronomy
• Print ISBN 978-0-387-49513-2
• Online ISBN 978-0-387-49514-9