Essentials of Mathematica: With Applications to Mathematics and Physics

ISBN-13: 9780387495132 / Angielski / Twarda / 2007 / 539 str.

Nino Boccara

Opis

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."

Recenzje

From the reviews:

"Mathematica is a software package that makes mathematics easier for scientists and engineers. ... The range of examples is amazing ... . The book is well written ... . Summing Up: Highly recommended. Upper-division undergraduates through professionals." (P. Cull, CHOICE, Vol. v4 (3), November, 2007)

"The book ensures a thorough training in Mathematica, which is one of the most popular software packages ... . The structure of the volume was designed to cover the objectives of different groups of readers, with various levels of knowledge, from beginners needing assistance for the basic exploitation of the package, to experienced users focusing on specific types of problems. ... reflects a considerable teaching experience which also recommends it as a valuable companion for educators interested in preparing or upgrading lecture notes and seminars." (Octavian Pastravanu, Zentralblatt MATH, Vol. 1134 (12), 2008)

Spis treści

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.

O autorze

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.

Blurb

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.