Essentials of Mathematica

This book teaches how to use Mathematica to solve a wide variety of 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.

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.

Aims to provide the reader with Mathematica proficiency quickly and efficiently, using many detailed examples of constructing programs step-by-step

Although there are several books on this topic in publication, this book does not assume a previous exposure of the reader to the mathematica software

Shows that teaching mathematics and physics will greatly benefit from the use of Mathematica

Autorentext
Dr. Nino Boccara is Professor Emeritus of Physics at the University of Illinois at Chicago, Professor Emeritus of Mathematics at the Ecole Supérieure de Physique et Chimie de la Ville de Paris, and Former Director of Research in Theoretical Physics at the CNRS.

Inhalt
Essential Commands.- A Panorama of Mathematica.- Numbers.- Algebra.- Analysis.- Lists.- Graphics.- Statistics.- Basic Programming.- Applications.- Axially Symmetric Electrostatic Potential.- Motion of a Bead on a Rotating Circle.- The Brachistochrone.- Negative and Complex Bases.- Convolution and Laplace Transform.- Double Pendulum.- Duffing Oscillator.- Egyptian Fractions.- Electrostatics.- Foucault Pendulum.- Fractals.- Iterated Function Systems.- Julia and Mandelbrot Sets.- Kepler's Laws.- Lindenmayer Systems.- Logistic Map.- Lorenz Equations.- The Morse Potential.- Prime Numbers.- Public-Key Encryption.- Quadratrix of Hippias.- Quantum Harmonic Oscillator.- Quantum Square Potential.- Skydiving.- Tautochrone.- van der Pol Oscillator.- van der Waals Equation.- Bidirectional Pedestrian Traffic.