# Essentials of Mathematica: With Applications to Mathematics and Physics

Springer Science & Business Media, Apr 13, 2007 - Science - 539 pages

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