Essentials of Mathematica: With Applications to Mathematics and Physics

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Springer Science & Business Media, Apr 13, 2007 - Science - 539 pages
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Essential 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 undergrad and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs.

The first section, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. Its aim is to provide the reader with Mathematica proficiency quickly and efficiently.

The second section covers a broad range of applications in physics, engineering and applied mathematics, including Egyptian Fractions, Happy Numbers, Mersenne Numbers, Multibases, Quantum Harmonic Oscillator, Quantum Square Potential, Van der Pol Oscillator, Electrostatics, Motion of a Charged Particle in an Electromagnetic Field, Duffing Oscillator, Negative and Complex Bases, Tautochrone Curves, Kepler’s Laws, Foucault’s Pendulum, Iterated Function Systems, Public-Key Encryption, and Julia and Mandelbrot Sets.

The first part - examples, not long explanations. The second part-attractive applications.

 

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Contents

A Panorama of Mathematica
5
Numbers
55
Algebra 77
76
Analysis
103
Lists
151
Finding Grouping and Counting Elements
162
Graphics
173
Statistics
219
The Brachistochrone
285
Convolution and Laplace Transform
301
Duffing Oscillator 311
310
Egyptian Fractions
321
Electrostatics
327
van der Waals Equation
509
Bidirectional Pedestrian Traffic 519
518
References
529

Basic Programming _ 235
234
Axially Symmetric Electrostatic Potential
273

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