Essentials of Mathematica

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.

Klappentext

This book teaches how to use Mathematica to solve a wide variety of problems in mathematics and physics. It is based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students. The book is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first part, in which the reader learns how to use a variety of Mathematica commands, contains examples, not long explanations; the second part contains attractive applications.

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.