使用Mathematica解决工程问题的工程师指南
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"AN ENGINEER’S GUIDE TO MATHEMATICA" 是一本由 Edward B. Magrab 编写的书籍，旨在帮助读者掌握使用 Mathematica 进行符号和数值解算工程问题的技能，并通过标注图形展示数值结果。
在工程领域，Mathematica 是一个强大的计算软件，它集成了符号计算、数值计算、数据可视化和编程等功能，使得工程师能够高效地解决复杂的问题。本书主要面向工程背景的读者，无论他们是初学者还是有一定经验的 Mathematica 用户，都能从中获益。
书中可能涵盖以下几个方面的知识点：
1. **Mathematica 基础**：介绍 Mathematica 的基本操作，包括语法、表达式结构、变量定义、函数调用等，这些都是编写程序的基础。
2. **符号计算**：讲解如何使用 Mathematica 进行高级数学运算，如微积分、线性代数、微分方程的求解，这对于处理理论模型和分析问题至关重要。
3. **数值计算**：介绍如何进行数值求解，包括数值积分、优化问题、数值微分以及大型方程组的求解，这些都是工程实际问题中常见的计算任务。
4. **图形和可视化**：探讨如何利用 Mathematica 创建高质量的图形，以直观地表示数据和解出的结果，这在报告和交流中非常有用，特别是对于理解复杂的工程问题和设计。
5. **编程和算法**：深入到 Mathematica 的编程层面，学习如何编写高效的程序，创建自定义函数，以及使用控制流语句（如循环和条件语句）来实现复杂的算法。
6. **应用实例**：书中可能会包含多种工程领域的实例，如结构力学、电路分析、信号处理、热力学等，通过这些实例帮助读者将学到的知识应用于实际问题。
7. **数据处理与分析**：可能涉及如何使用 Mathematica 处理和分析实验数据，进行统计建模或预测，这是工程研究中的重要步骤。
8. **互动与动态演示**：Mathematica 支持创建交互式的应用程序，读者可以学习如何构建这些工具，以更好地理解和探索工程问题。
9. **文档与报告**：介绍如何使用 Mathematica 制作专业级别的技术报告，包括插入图形、公式和自动参考文献管理。
10. **代码调试和优化**：指导读者如何调试代码，找出潜在错误，并优化程序性能，以提高计算效率。
通过阅读和实践《AN ENGINEER’S GUIDE TO MATHEMATICA》，读者不仅可以掌握 Mathematica 的使用技巧，还能培养解决工程问题的系统思维和创新方法。同时，这本书也提醒读者尊重版权，合法使用和分享其中的知识产权内容。
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 modied,
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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