《工程师的Mathematica指南》- Edward B. Magrab

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"Engineers_Guide_to_Mathematica - 由Edward B. Magrab编写的Mathematica学习指南，适合工程师使用" 《Engineer's Guide to Mathematica》是由Edward B. Magrab教授编著的一本专门针对工程师的Mathematica使用手册。这本书首次出版于2014年，由John Wiley & Sons Ltd发行。该书旨在为工程领域的专业人士提供深入理解和应用Mathematica的强大工具。 Mathematica是一款强大的数学软件，广泛应用于科学计算、数据分析、可视化和算法开发等多个领域。本书详尽地介绍了Mathematica的基础知识，以及如何在实际工程问题中有效地利用它。Magrab教授通过实例展示了Mathematica在解决复杂工程问题时的高效性和灵活性，帮助读者提升计算能力并提高工作效率。内容涵盖了以下关键知识点： 1. **基础操作与语法**：包括变量定义、表达式操作、函数使用、控制结构（如循环和条件语句）等，这些都是使用Mathematica进行计算的基本元素。 2. **数值计算**：讲解了Mathematica处理数值问题的方法，如数值积分、微分方程求解、优化算法等。 3. **符号计算**：Mathematica的一大优势在于其符号运算能力，书中会介绍如何进行符号求解、化简和推导。 4. **图形绘制与数据可视化**：Mathematica提供了丰富的图形绘制功能，包括2D和3D图形，以及如何处理和展示工程数据。 5. **数学建模**：介绍如何使用Mathematica进行系统建模，如物理系统、控制系统、经济模型等。 6. **编程与算法**：讨论Mathematica的编程特性，包括编写自定义函数、模块化编程和算法设计。 7. **数据处理与分析**：涵盖数据导入/导出、统计分析、时间序列分析等，帮助工程师处理实验数据或模拟结果。 8. **应用实例**：书中包含大量来自工程实践的案例，如信号处理、控制系统设计、结构力学分析等，让读者能够将理论知识应用于实际问题。此外，书中还可能涉及了Mathematica与其他软件的集成，以及如何在电子格式中获取和使用Mathematica的内容。这本指南不仅适合初学者入门，也对有经验的Mathematica用户提供了深入的见解和技巧。《Engineer's Guide to Mathematica》是一本全面而实用的教程，它通过深入浅出的解释和实例，为工程师们提供了掌握和利用Mathematica解决工程问题的宝贵资源。无论是学习还是工作，这本书都能成为工程师们不可或缺的参考资料。

xiv Preface

The book has two interrelated parts. The rst part consists of seven chapters, which intro-

duce the fundamentals of Mathematica’s syntax and a subset of commands useful in solving

engineering problems. The second part makes extensive use of the material in these seven

chapters to show how, in a straightforward manner, one can obtain numerical solutions in

a wide range of engineering specialties: vibrations, uid mechanics and aerodynamics, heat

transfer, controls and signal processing, optimization, structures, and engineering statistics. In

this part of the book, the vast majority of the solutions are presented as interactive graphics

from which one can explore the results parametrically.

In Chapter 1, the basic syntax of Mathematica is introduced and it is shown how to inter-

mingle symbolic and numerical calculations, how to use elementary mathematical functions

and constants, and how to create and manipulate complex numbers. Several notational pro-

gramming constructs are both illustrated and tabulated and examples are given on how to

attach physical units to numerical and symbolic quantities. The basic structure of the notebook

interface and its customization are presented. In addition, the various templates that can be

used to simplify the integration of Greek letters, superscripts and subscripts, and other mathe-

matical symbols into the programming process, and the commands that represent many basic

mathematical functions and mathematical constants are illustrated.

In Chapter 2, the commands that can be used to create lists are discussed in detail and

their special construction to form vectors and matrices composed of numerical and/or sym-

bolic elements that are commonly employed to obtain solutions engineering applications are

introduced. The use of vectors and matrices is discussed in two distinctly different types of

applications: to perform operations on an element-by-element basis or to use them as entities

in linear algebra operations.

In Chapter 3, ways to create functions, exercise program control, and perform repetitive

operations are discussed. The concept of local and global variables is introduced and its

implications with respect to programming are illustrated.

In Chapter 4, two types of symbolic manipulations are illustrated. The rst is the simpli-

cation and manipulation of symbolic expressions to attain a compact form of the result. The

second is to perform a mathematical operation on a symbolic expression. The mathematical

operations considered are: differentiation, integration, limit, solutions to ordinary and partial

differential equations, power series expansion, and the Laplace transform.

In Chapter 5, several Mathematica functions that have a wide range of uses in obtaining

numerical solutions to engineering applications are presented: integration, solution to linear

and nonlinear ordinary and partial differential equations, solution of equations, determination

of the roots of transcendental equations, determining the minimum or maximum of a function,

tting curves and functions to data, and obtaining the discrete Fourier transform.

In Chapter 6, a broad range of 2D and 3D plotting functions are introduced and illus-

trated using numerous tables and examples from engineering topics. It is shown how to

display discrete data values and values obtained from analytical expressions in different

ways; that is, by displaying them using logarithmic compression, in polar coordinates, as

contours, or as surfaces. The emphasis is on the ways that the basic gure can be modied,

enhanced, and individualized to improve its visual impact by using color, inset gures and

text, gure titles, axes labels, curve labels, legends, combining gures, lled plot regions, and

tooltips.

In Chapter 7, the creation and implementation of interactive graphics and animations are

introduced and discussed in detail and illustrated with many examples. The control devices

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