Essentials of Mathematica: With Applications to Mathematics and Physics (Hardcover

Description

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.

《Mathematica基礎：數學和物理應用》是根據在伊利諾伊大學芝加哥分校教授給高年級本科生和研究生的課程講義而編寫的。該書教授如何使用Mathematica來解決各種數學和物理問題。本書假設讀者對Mathematica沒有任何先備知識。書中有許多詳細的例子，要求學生逐步構建易於閱讀的Mathematica程序。書中還包含許多詳細的圖形，並提供學生實現類似結果的指導。

《Mathematica基礎》的目標是快速且有效地提高讀者的Mathematica技能。第一部分介紹了各種Mathematica命令的使用，避免了冗長的討論和過於複雜的技巧。第二部分涵蓋了物理和應用數學的廣泛應用，包括負數和複數基數、雙擺、分形、羅吉斯蘭德映射、量子諧振子、量子方势、范德波爾振子、杜芬振子、多車道雙向行人交通、公鑰加密、等時曲線、迭代函數系統、圓周運動中的珠子運動、梅森數和完美數、林登邁爾系統、跳傘運動、洛倫茲方程、傅科摆、朱利亚集和曼德博集。