工程人员的Mathematica®指南：2014年最新版

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《工程师手册：Mathematica®指南》是一本由Edward B. Magrab撰写的专业书籍，针对工程师群体量身打造，于2014年首次出版。该书由John Wiley & Sons, Ltd发行，版权所有。作者根据1988年的英国版权法，声明了其作为本书作者的身份，所有权利受到保护。这本书的核心内容是为工程专业人士提供深入理解并应用Mathematica这款强大的数学软件的实用指南。Mathematica是一款广泛用于数值计算、符号计算、图形建模和数据分析的高级计算机代数系统（CAS）。它被设计用于解决复杂问题，尤其是在科学、工程和技术领域，包括但不限于： 1. **符号计算**：书中详述如何在Mathematica中进行高级数学运算，如微积分、线性代数、复变函数等，这对于解决理论问题和证明非常有帮助。 2. **数值分析**：读者可以学习如何处理数值数据，执行求解算法，以及使用Mathematica的内置数值工具箱进行精确计算和优化。 3. **图形与可视化**：书中展示了如何利用Mathematica的强大图形功能，创建高质量的图表、图像和动态演示，以清晰地展示复杂的数据关系和模型结果。 4. **编程与脚本编写**：对于工程师而言，了解如何编写简洁高效的Mathematica脚本和程序至关重要，以自动化重复任务和实现大规模数据分析。 5. **实际应用示例**：书中包含大量实际工程案例，涵盖了诸如控制系统设计、信号处理、电路分析、流体力学模拟等各种领域的具体应用，帮助读者将理论知识转化为实践能力。 6. **资源与社区**：作者还介绍了Mathematica丰富的在线资源，如文档、教程、论坛和用户社区，以支持持续的学习和问题解决。《工程师手册：Mathematica®指南》旨在提供一个系统且实用的学习路径，使工程师能够充分利用Mathematica的功能，提升工作效率，应对现代工程挑战。无论是在课堂教育还是专业实践中，这本书都是提升工程师数学软件技能的重要参考资料。

equations, solution of equations, determination of the roots of transcendental equations, determining the minimum or

maximum of a function, fitting 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 illustrated 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 figure can be modified, enhanced, and individualized to improve its

visual impact by using color, inset figures and text, figure titles, axes labels, curve labels, legends, combining figures, filled

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 that are considered are the slider/animator, slider, 2D

sliders, radio buttons, setter buttons, popup menus, locators, angular gauges, and horizontal gauges.

In Chapter 8, the response of single and two degree-of-freedom systems and thin elastic beams are determined when

they are subject to various loadings, damping, initial conditions, boundary conditions, and nonlinearities.

In Chapter 9, the commands used to determine the mean, median, root mean square, variance, and quartile of discrete

data are presented and the display of these data using histograms and whisker plots are illustrated. It is shown how to

display the results from a regression analysis using a probability plot, a plot of the residuals, and confidence bands. The

ways to perform an analysis of variance (ANOVA) and to setup and analyze factorial designs are introduced with

examples.

In Chapter 10, the modeling and analysis of control systems using transfer function models and state-space models are

presented. It is shown how to connect system components to form closed-loop systems and to determine their time-domain

response. Examples are given to show how to optimize a system’s response with a PID controller and any of its special cases

using different criteria. The creation and use of different models of high-pass, low-pass, band-pass, and band-stop filters

are presented and the effects of different types of windows on the short-time Fourier transform are illustrated. The

spectral analyses of sinusoidal signals in the presence of noise are presented using root mean square averaging and using

vector averaging.

In Chapter 11, several topics in heat transfer and fluid mechanics are examined numerically and interactive environments

are developed to explore the characteristics of the different systems. The general topic areas include: conduction,

convection, and radiation heat transfer, and internal and external flows.

Edward B. Magrab

Bethesda, MD

USA

October, 2013

Table of Engineering Applications

Topic Example or Section

Controls

State-Space Models Section 10.2.2

Transfer Function Models Section 10.2.3

Model Connections – Closed-Loop Systems and System Response Section 10.3

PID Control System Example 10.1

Root Locus Section 10.4.1

Bode Plot Section 10.4.2

Nichols Plot Section 10.4.3

Engineering Mathematics

Evaluating a Fourier Series Example 2.1

Convergence of a Series Example 2.2

Summing a Double Series Example 2.3

Solution of a System of Equations Example 2.4

Secant Method Example 3.14

Solution of a System of Equations Example 4.2

Radius of Curvature Example 4.10

Euler–Lagrange Equation Example 4.11

Fourier Coefficients Example 4.13

Cauchy Integral Formula Example 4.18

System of First-Order Equations and the Matrix Exponential Example 4.23

Laplace Transform Solution of an Inhomogeneous Differential Equation #1 Example 4.29

Laplace Transform Solution of an Inhomogeneous Differential Equation #2 Example 4.31

Limit Using Assumptions Example 4.4

Perturbation Solution #1 Example 4.7

Perturbation Solution #2 Example 4.8

Poincare Plot Example 5.11

Nonlinear Ordinary Differential Equation Example 5.12

Second-Order Differential Equation: Periodic Inhomogeneous Term Example 5.15

Interpolation Function from Some Data Example 5.24

Function’s Parameters for a Fit to Some Data Example 5.25

Parametric Solution to a Nonlinear Differential Equation Example 5.26

Fluid Mechanics

Flow Around a Cylinder Example 6.6

Air Entrainment by Liquid Jets Example 5.14

Flow Around an Ellipse Example 7.6

Laminar Flow in Horizontal Cylindrical Pipes Section 11.5.1

Flow in Three Reservoirs Section 11.5.2

Pressure Coefficient of a Joukowski Airfoil Section 11.6.1

Surface Profile in Nonuniform Flow in Open Channels Section 11.6.2

Heat Transfer

Heat Conduction in a Slab Example 5.13

One-Dimensional Transient Heat Diffusion in Solids Section 11.2.1

Heat Transfer in Concentric Spheres: Ablation of a Tumor Section 11.2.2

Heat Flow Through Fins Section 11.2.3

Natural Convection Along Heated Plates Section 11.3

View Factor Between Two Parallel Rectangular Surfaces Section 11.4

Kinematics

Four-Bar Linkage Example 7.7

Signal Processing

Spectral Analysis of a Sine Wave Example 5.27

Spectral Analysis of a Sine Wave of Finite Duration Example 5.28

Cross-Correlation of a Signal with Noise Example 5.29

Sum of Two Sinusoidal Signals Example 7.2

Steerable Sonar/Radar Array Example 7.3

Effects of Filters on Sinusoidal Signals Example 10.2

Effects of Windows on Spectral Analysis Example 10.3

Spectrum Averaging Example 10.4

Aliasing Example 10.5

Statistics

Histograms Example 9.1

Whisker Plot Section 9.1.5

Confidence Intervals Section 9.2.4

Hypothesis Testing Section 9.2.5

Simple Linear Regression Section 9.3.1

Multiple Linear Regression Section 9.3.2

Nonlinear Regression Analysis Section 9.4

Two-Factor ANOVA Example 9.2

Four-Factor Factorial Analysis Example 9.3

Structures

Analysis of Beams Example 4.20

Deformation of a Timoshenko Beam Example 4.21

Beam with a Concentrated Load Example 5.4

Beam with an Overhang Example 5.5

Beam with Abrupt Change in Properties Example 5.6

Deflection of a Uniformly Loaded Solid Circular Plate Example 5.16

von Mises Stress in a Stretched Plate with a Hole Example 7.4

Analysis of Beams Example 7.5

Vibrations

Natural Frequencies of a Three Degrees-of-Freedom System Example 2.5

Natural Frequency Coefficient of a Two Degrees-of-Freedom System Example 3.5

Natural Frequencies of Beams Example 4.5

Peak Amplitude Response of a Single Degree-of-Freedom System Example 4.9

Response of a Two Degrees-of-Freedom System Example 4.30

Two Degrees-of-Freedom System Revisited Example 5.7

Particle Impact Damper Example 5.8

Change in Period of a Nonlinear System Example 5.9

Single Degree-of-Freedom System Example 5.10

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工程人员的Mathematica®指南：2014年最新版

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hands-on start to wolfram mathematica

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Mathematica 如何画函数H1[s_] := 1/s; H2[s_] := 1/(s - 2); H3[s_] := 1/(s^2 + 16); H4[s_] := 1/(s^2 + 2s + 2); H5[s_] := 1/((s - 0.5)^2 + 16),H6[s_] := 1/((s + 0.5)^2 + 16); H7[s_] := 1/(s^3 + 2s^2 + 2s + 1); H8[s_] := (s^2 - 2*s + 0.8)/(s^3 + 2s^2 +1) 零点和极点分布图

用Mathematica求分式f[s]=5 s (s^2 + 4 s + 5)/(s^3 + 5 s^2 + 16 s + 30)零点和极点，并用 不同的符号画图将零点和极点表示出来

用mathematica求函数F(s)=(s^2–4)/(s^4+2s^3–3s^2+2s+1)的零点和极点，并用不同的符号画图将零点和极点表示出来 给出mathematica代码

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mathematica 求（-M^2+2*M*(k-1)-3*k+3*s)*(3+d*M)-3*(M*b+6*s+2*s*d*M)<0的条件，其中参数M,k,b,d,s都为正

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Mathematica 如何求出函数F1[s_] := (s^2 - 4)/(s^4 + 2s^3 - 3s^2 + 2s + 1) 和F2[s_] := 5s(s^2 + 4s + 5)/(s^3 + 5s^2 + 16s + 30)的零点和极点，并将零点和极点画出来

用Mathematica求分式f[s]=5 s (s^2 + 4 s + 5)/(s^3 + 5 s^2 + 16 s + 30)零点和极点，并用不同的符号画图将零点和极点表示出来

用mathematica求函数F(s)=(s^2–4)/(s^4+2s^3–3s^2+2s+1)的零点和极点，并用不同的符号画图将零点和极点表示出来给出mathematica代码

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