An Engineer's Guide to Mathematica (eBook)

Edward B. Magrab (Autor)

eBook Download: PDF

2014
John Wiley & Sons (Verlag)
978-1-118-82124-4 (ISBN)

Infos

Free Mathematica 10 Update Included! Now available from www.wiley.com/go/magrab

Updated material includes:
- Creating regions and volumes of arbitrary shape and determining their properties: arc length, area, centroid, and area moment of inertia
- Performing integrations, solving equations, and determining the maximum and minimum values over regions of arbitrary shape
- Solving numerically a class of linear second order partial differential equations in regions of arbitrary shape using finite elements

An Engineer's Guide to Mathematica enables the reader to attain the skills to create Mathematica 9 programs that solve a wide range of engineering problems and that display the results with annotated graphics. This book can be used to learn Mathematica, as a companion to engineering texts, and also as a reference for obtaining numerical and symbolic solutions to a wide range of engineering topics. The material is presented in an engineering context and the creation of interactive graphics is emphasized.

The first part of the book introduces Mathematica's syntax and commands useful in solving engineering problems. Tables are used extensively to illustrate families of commands and the effects that different options have on their output. From these tables, one can easily determine which options will satisfy one's current needs. The order of the material is introduced so that the engineering applicability of the examples increases as one progresses through the chapters. The second part of the book obtains solutions to representative classes of problems in a wide range of engineering specialties. Here, the majority of the solutions are presented as interactive graphics so that the results can be explored parametrically.

Key features:

• Material is based on Mathematica 9
• Presents over 85 examples on a wide range of engineering topics, including vibrations, controls, fluids, heat transfer, structures, statistics, engineering mathematics, and optimization
• Each chapter contains a summary table of the Mathematica commands used for ease of reference
• Includes a table of applications summarizing all of the engineering examples presented.
• Accompanied by a website containing Mathematica notebooks of all the numbered examples

An Engineer's Guide to Mathematica is a must-have reference for practitioners, and graduate and undergraduate students who want to learn how to solve engineering problems with Mathematica.

Dr. Magrab is Emeritus Professor of Mechanical Engineering at the University of Maryland, College Park, Maryland. Before joining the University of Maryland, he was Chief of the Sound Section, head of the Robot Metrology Group, and led the development of the vertical machining workstation in the Automated Manufacturing Research Facility at the National Institute of Standards and Technology (NIST). He went to NIST after being a professor in the Department of Mechanics at the Catholic University of America in Washington DC. Dr. Magrab is a Life Fellow of the American Society of Mechanical Engineers and a registered professional engineer in Maryland. He has authored eight other textbooks, published numerous journal articles, and has over 35 years of university-level teaching experience on many engineering subjects. His research interests include analytical and experimental investigations in vibrations, acoustics, and the integration of design and manufacturing. He holds one patent.

Inhalt

AN ENGINEER’S GUIDE TO MATHEMATICA® 3
Contents 9
Preface 15
Table of Engineering Applications 19
Part I Introduction 23
1 Mathematica® Environment and Basic Syntax 25
1.1 Introduction 25
1.2 Selecting Notebook Characteristics 26
1.3 Notebook Cells 30
1.4 Delimiters 34
1.5 Basic Syntax 34
1.5.1 Introduction 34
1.5.2 Templates: Greek Symbols and Mathematical Notation 37
1.5.3 Variable Names and Global Variables 40
1.6 Mathematical Constants 41
1.7 Complex Numbers 43
1.8 Elementary, Trigonometric, Hyperbolic, and a Few Special Functions 44
1.9 Strings 47
1.9.1 String Creation: StringJoin[] and ToString[] 47
1.9.2 Labeled Output: Print[], NumberForm[], EngineeringForm[], and TraditionalForm[] 48
1.10 Conversions, Relational Operators, and Transformation Rule 50
1.11 Engineering Units and Unit Conversions: Quantity[] and UnitConvert[] 52
1.12 Creation of CDF Documents and Documents in Other Formats 55
1.13 Functions Introduced in Chapter 56
Exercises 57
2 List Creation and Manipulation: Vectors and Matrices 61
2.1 Introduction 61
2.2 Creating Lists and Vectors 61
2.2.1 Introduction 61
2.2.2 Creating a List with Table[] 67
2.2.3 Summing Elements of a List: Total[] 68
2.2.4 Selecting Elements of a List 69
2.2.5 Identifying List Elements Matching a Pattern: Position[] 71
2.3 Creating Matrices 73
2.3.1 Introduction 73
2.3.2 Matrix Generation Using Table[] 76
2.3.3 Accessing Elements of Arrays 77
2.4 Matrix Operations on Vectors and Arrays 78
2.4.1 Introduction 78
2.4.2 Matrix Inverse and Determinant: Inverse[] and Det[] 79
2.5 Solution of a Linear System of Equations: LinearSolve[] 80
2.6 Eigenvalues and Eigenvectors: EigenSystem[] 81
2.7 Functions Introduced in Chapter 2 83
References 83
Exercises 83
3 User-Created Functions, Repetitive Operations, and Conditionals 91
3.1 Introduction 91
3.2 Expressions and Procedures as Functions 91
3.2.1 Introduction 91
3.2.2 Pure Function: Function[] 96
3.2.3 Module[] 100
3.3 Find Elements of a List that Meet a Criterion: Select[] 102
3.4 Conditionals 104
3.4.1 If[] 104
3.4.2 Which[] 105
3.5 Repetitive Operations 105
3.5.1 Do[] 105
3.5.2 While[] 105
3.5.3 Nest[] 106
3.5.4 Map[] 106
3.6 Examples of Repetitive Operations and Conditionals 107
3.7 Functions Introduced in Chapter 114
Exercises 114
4 Symbolic Operations 117
4.1 Introduction 117
4.2 Assumption Options 123
4.3 Solutions of Equations: Solve[] 123
4.4 Limits: Limit[] 127
4.5 Power Series: Series[], Coefficient[], and CoefficientList[] 130
4.6 Optimization: Maximize[]/Minimize[] 134
4.7 Differentiation: D[] 136
4.8 Integration: Integrate[] 142
4.9 Solutions of Ordinary Differential Equations: DSolve[] 148
4.10 Solutions of Partial Differential Equations: DSolve[] 158
4.11 Laplace Transform: LaplaceTransform[] and InverseLaplaceTransform[] 160
4.12 Functions Introduced in Chapter 167
References 167
Exercises 168
5 Numerical Evaluations of Equations 173
5.1 Introduction 173
5.2 Numerical Integration: NIntegrate[] 173
5.3 Numerical Solutions of Differential Equations: NDSolveValue[] and ParametricNDSolveValue[] 176
5.4 Numerical Solutions of Equations: NSolve[] 200
5.5 Roots of Transcendental Equations: FindRoot[] 202
5.6 Minimum and Maximum: FindMinimum[] and FindMaximum[] 204
5.7 Fitting of Data: Interpolation[] and FindFit[] 208
5.8 Discrete Fourier Transforms and Correlation: Fourier[], InverseFourier[], and ListCorrelate[] 211
5.9 Functions Introduced in Chapter 216
References 217
Exercises 218
6 Graphics 231
6.1 Introduction 231
6.2 2D Graphics 231
6.2.1 Basic Plotting 231
6.2.2 Basic Graph Enhancements 235
6.2.3 Common 2D Shapes: Graphics[] 239
6.2.4 Additional Graph Enhancements 244
6.2.5 Combining Figures: Show[] and GraphicsGrid[] 260
6.2.6 Tooltip[] 263
6.2.7 Exporting Graphics 266
6.3 3D Graphics 266
6.4 Summary of Functions Introduced in Chapter 275
References 276
Exercises 276
7 Interactive Graphics 285
7.1 Interactive Graphics: Manipulate[] 285
References 309
Exercises 309
Part II Engineering Applications 313
8 Vibrations of Spring–Mass Systems and Thin Beams 315
8.1 Introduction 315
8.2 Single Degree-of-Freedom Systems 316
8.2.1 Periodic Force on a Single Degree-of-Freedom System 316
8.2.2 Squeeze Film Damping and Viscous Fluid Damping 320
8.2.3 Electrostatic Attraction 324
8.2.4 Single Degree-of-Freedom System Energy Harvester 326
8.3 Two Degrees-of-Freedom Systems 329
8.3.1 Governing Equations 329
8.3.2 Response to Harmonic Excitation: Amplitude Response Functions 329
8.3.3 Enhanced Energy Harvester 332
8.4 Thin Beams 337
8.4.1 Natural Frequencies and Mode Shapes of a Cantilever Beam with In-Span Attachments 337
8.4.2 Effects of Electrostatic Force on the Natural Frequency and Stability of a Beam 340
8.4.3 Response of a Cantilever Beam with an In-Span Attachment to an Impulse Force 345
References 348
9 Statistics 349
9.1 Descriptive Statistics 349
9.1.1 Introduction 349
9.1.2 Location Statistics: Mean[], StandardDeviation[], and Quartile[] 349
9.1.3 Continuous Distribution Functions: PDF[] and CDF[] 351
9.1.4 Histograms and Probability Plots: Histogram[] and ProbabilityScalePlot[] 353
9.1.5 Whisker Plot: BoxWhiskerChart[] 354
9.1.6 Creating Data with Specified Distributions: RandomVariate[] 356
9.2 Probability of Continuous Random Variables 356
9.2.1 Probability for Different Distributions: NProbability[] 356
9.2.2 Inverse Cumulative Distribution Function: InverseCDF[] 359
9.2.3 Distribution Parameter Estimation: EstimatedDistribution[] and FindDistributionParameters[] 359
9.2.4 Confidence Intervals: CI[] 362
9.2.5 Hypothesis Testing: LocationTest[] and VarianceTest[] 364
9.3 Regression Analysis: LinearModelFit[] 365
9.3.1 Simple Linear Regression 365
9.3.2 Multiple Linear Regression 369
9.4 Nonlinear Regression Analysis: NonLinearModelFit[] 373
9.5 Analysis of Variance (ANOVA) and Factorial Designs: ANOVA[] 376
9.6 Functions Introduced in Chapter 380
10 Control Systems and Signal Processing 381
10.1 Introduction 381
10.2 Model Generation: State-Space and Transfer Function Representation 381
10.2.1 Introduction 381
10.2.2 State-Space Models: StateSpaceModel[] 382
10.2.3 Transfer Function Models: TransferFunctionModel[] 384
10.3 Model Connections – Closed-Loop Systems and System Response: SystemsModelFeedbackConnect[] and SystemsModelSeriesConnect[] 385
10.4 Design Methods 391
10.4.1 Root Locus: RootLocusPlot[] 391
10.4.2 Bode Plot: BodePlot[] 393
10.4.3 Nichols Plot: NicholsPlot[] 394
10.5 Signal Processing 396
10.5.1 Filter Models: ButterworthFilterModel[], EllipticFilterModel[],… 396
10.5.2 Windows: HammingWindow[], HannWindow[],… 403
10.5.3 Spectrum Averaging 407
10.6 Aliasing 410
10.7 Functions Introduced in Chapter 412
Reference 413
11 Heat Transfer and Fluid Mechanics 415
11.1 Introduction 415
11.2 Conduction Heat Transfer 416
11.2.1 One-Dimensional Transient Heat Diffusion in Solids 416
11.2.2 Heat Transfer in Concentric Spheres: Ablation of a Tumor 420
11.2.3 Heat Flow Through Fins 423
11.3 Natural Convection Along Heated Plates 427
11.4 View Factor Between Two Parallel Rectangular Surfaces 430
11.5 Internal Viscous Flow 433
11.5.1 Laminar Flow in Horizontal Cylindrical Pipes 433
11.5.2 Flow in Three Reservoirs 434
11.6 External Flow 438
11.6.1 Pressure Coefficient of a Joukowski Airfoil 438
11.6.2 Surface Profile in Nonuniform Flow in Open Channels 441
References 445
Index 447

Produkt-Details

• Erscheint lt. Verlag: 20.3.2014
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Computerprogramme / Computeralgebra
• Themenwelt: Technik ► Maschinenbau
• Schlagworte: Book • Companion • Computational / Numerical Methods • ConText • Creation • Electrical & Electronics Engineering • Elektrotechnik u. Elektronik • emphasized • enables • Engineering • engineering topics • engineers • Guide • Maschinenbau • Material • Mathematica • Mathematical Modeling • Mathematics • Mathematik • Mathematische Modellierung • mechanical engineering • Numerical • Numerical Methods & Algorithms • Numerische Methoden u. Algorithmen • Programs • Range • Reader • Rechnergestützte / Numerische Verfahren im Maschinenbau • Rechnergestützte / Numerische Verfahren im Maschinenbau • Reference • Skills • Solutions • Symbolic • texts • wide
• ISBN-10: 1-118-82124-6 / 1118821246
• ISBN-13: 978-1-118-82124-4 / 9781118821244