Magrab的《工程师指南》：自学Mathematica的权威教程

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"《工程师的Mathematica®指南》是一本由Edward B. Magrab撰写的专业教材，旨在为学习和应用Mathematica®提供一个清晰且详尽的资源。这本书专为工程师设计，适合那些希望深入理解和掌握这一强大的数学软件工具的人。作者是来自美国马里兰大学的专家，其2014年的首次出版体现了他对Mathematica®的深厚理解和实践经验。本书不仅包含了基本的编程入门知识，还涵盖了高级功能和实际工程应用中的案例，使得读者能够在实践中提升技能。它系统地讲解了Mathematica®的功能，包括符号计算、图形绘制、数据分析、算法实现等方面，帮助读者从基础操作到复杂问题求解都能得心应手。版权方面，该书遵循1988年英国版权、设计和专利法，强调了原创作者权益，并规定未经许可，不得以任何形式复制、存储或传输内容，除非符合法律规定的条件。Wiley出版社也提供了电子版的选项，但某些纸质版中包含的内容可能在电子版中不可用。对于想要自学Mathematica®或者提升现有技能的工程师来说，《工程师的Mathematica®指南》是一本不可或缺的参考资料，它以实用性和理论相结合的方式，让读者能够有效地利用Mathematica®进行工程计算和问题解决，提高工作效率。无论你是初学者还是进阶用户，都能从中找到有价值的知识和实例来支撑自己的工作实践。"

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

awiderangeofengineeringspecialties: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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