Engineer's Guide to 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.

• Preface xiii Table of Engineering Applications xviiPart 1 Introduction1 Mathematica Environment and Basic Syntax 31.1 Introduction 31.2 Selecting Notebook Characteristics 41.3 Notebook Cells 81.4 Delimiters 121.5 Basic Syntax 121.5.1 Introduction 121.5.2 Templates: Greek Symbols and Mathematical Notation 151.5.3 Variable Names and Global Variables 181.6 Mathematical Constants 191.7 Complex Numbers 211.8 Elementary, Trigonometric, Hyperbolic, and a Few Special Functions 221.9 Strings 251.9.1 String Creation: StringJoin[] and ToString[] 251.9.2 Labeled Output: Print[], NumberForm[], EngineeringForm[], and TraditionalForm[] 261.10 Conversions, Relational Operators, and Transformation Rule 281.11 Engineering Units and Unit Conversions: Quantity[] and UnitConvert[] 301.12 Creation of CDF Documents and Documents in Other Formats 331.13 Functions Introduced in Chapter 1 34Exercises 352 List Creation and Manipulation: Vectors and Matrices 392.1 Introduction 392.2 Creating Lists and Vectors 392.2.1 Introduction 392.2.2 Creating a List with Table[] 452.2.3 Summing Elements of a List: Total[] 462.2.4 Selecting Elements of a List 472.2.5 Identifying List Elements Matching a Pattern: Position[] 492.3 Creating Matrices 512.3.1 Introduction 512.3.2 Matrix Generation Using Table[] 542.3.3 Accessing Elements of Arrays 552.4 Matrix Operations on Vectors and Arrays 562.4.1 Introduction 562.4.2 Matrix Inverse and Determinant: Inverse[] and Det[] 572.5 Solution of a Linear System of Equations: LinearSolve[] 582.6 Eigenvalues and Eigenvectors: EigenSystem[] 592.7 Functions Introduced in Chapter 2 61References 61Exercises 613 User-Created Functions, Repetitive Operations, and Conditionals 693.1 Introduction 693.2 Expressions and Procedures as Functions 693.2.1 Introduction 693.2.2 Pure Function: Function[] 743.2.3 Module[] 783.3 Find Elements of a List that Meet a Criterion: Select[] 803.4 Conditionals 823.4.1 If[] 823.4.2 Which[] 833.5 Repetitive Operations 833.5.1 Do[] 833.5.2 While[] 833.5.3 Nest[] 843.5.4 Map[] 843.6 Examples of Repetitive Operations and Conditionals 853.7 Functions Introduced in Chapter 3 92Exercises 924 Symbolic Operations 954.1 Introduction 954.2 Assumption Options 1014.3 Solutions of Equations: Solve[] 1014.4 Limits: Limit[] 1054.5 Power Series: Series[], Coefficient[], and CoefficientList[] 1084.6 Optimization: Maximize[]/Minimize[] 1124.7 Differentiation: D[] 1144.8 Integration: Integrate[] 1204.9 Solutions of Ordinary Differential Equations: DSolve[] 1264.10 Solutions of Partial Differential Equations: DSolve[] 1364.11 Laplace Transform: LaplaceTransform[] and InverseLaplaceTransform[] 1384.12 Functions Introduced in Chapter 4 145References 145Exercises 1465 Numerical Evaluations of Equations 1515.1 Introduction 1515.2 Numerical Integration: NIntegrate[] 1515.3 Numerical Solutions of Differential Equations: NDSolveValue[] and ParametricNDSolveValue[] 1545.4 Numerical Solutions of Equations: NSolve[] 1785.5 Roots of Transcendental Equations: FindRoot[] 1805.6 Minimum and Maximum: FindMinimum[] and FindMaximum[] 1825.7 Fitting of Data: Interpolation[] and FindFit[] 1865.8 Discrete Fourier Transforms and Correlation: Fourier[], InverseFourier[], and ListCorrelate[] 1895.9 Functions Introduced in Chapter 5 194References 195Exercises 1966 Graphics 2096.1 Introduction 2096.2 2D Graphics 2096.2.1 Basic Plotting 2096.2.2 Basic Graph Enhancements 2136.2.3 Common 2D Shapes: Graphics[] 2176.2.4 Additional Graph Enhancements 2226.2.5 Combining Figures: Show[] and GraphicsGrid[] 2386.2.6 Tooltip[] 2416.2.7 Exporting Graphics 2446.3 3D Graphics 2446.4 Summary of Functions Introduced in Chapter 6 253References 254Exercises 2547 Interactive Graphics 2637.1 Interactive Graphics: Manipulate[] 263References 287Exercises 287Part 2 Engineering Applications8 Vibrations of Spring–Mass Systems and Thin Beams 2938.1 Introduction 2938.2 Single Degree-of-Freedom Systems 2948.2.1 Periodic Force on a Single Degree-of-Freedom System 2948.2.2 Squeeze Film Damping and Viscous Fluid Damping 2988.2.3 Electrostatic Attraction 3028.2.4 Single Degree-of-Freedom System Energy Harvester 3048.3 Two Degrees-of-Freedom Systems 3078.3.1 Governing Equations 3078.3.2 Response to Harmonic Excitation: Amplitude Response Functions 3078.3.3 Enhanced Energy Harvester 3108.4 Thin Beams 3158.4.1 Natural Frequencies and Mode Shapes of a Cantilever Beam with In-Span Attachments 3158.4.2 Effects of Electrostatic Force on the Natural Frequency and Stability of a Beam 3188.4.3 Response of a Cantilever Beam with an In-Span Attachment to an Impulse Force 323References 3269 Statistics 3279.1 Descriptive Statistics 3279.1.1 Introduction 3279.1.2 Location Statistics: Mean[], StandardDeviation[], and  Quartile[] 3279.1.3 Continuous Distribution Functions: PDF[] and CDF[] 3299.1.4 Histograms and Probability Plots: Histogram[] and ProbabilityScalePlot [] 3319.1.5 Whisker Plot: BoxWhiskerChart[] 3329.1.6 Creating Data with Specified Distributions: RandomVariate[] 3349.2 Probability of Continuous Random Variables 3349.2.1 Probability for Different Distributions: NProbability[] 3349.2.2 Inverse Cumulative Distribution Function: InverseCDF[] 3379.2.3 Distribution Parameter Estimation: EstimatedDistribution[] and FindDistributionParameters[] 3379.2.4 Confidence Intervals: ⋯CI[] 3409.2.5 Hypothesis Testing: LocationTest[] and VarianceTest[] 3429.3 Regression Analysis: LinearModelFit[] 3439.3.1 Simple Linear Regression 3439.3.2 Multiple Linear Regression 3479.4 Nonlinear Regression Analysis: NonLinearModelFit[] 3519.5 Analysis of Variance (ANOVA) and Factorial Designs: ANOVA[] 3549.6 Functions Introduced in Chapter 9 35810 Control Systems and Signal Processing 35910.1 Introduction 35910.2 Model Generation: State-Space and Transfer Function Representation 35910.2.1 Introduction 35910.2.2 State-Space Models: StateSpaceModel[] 36010.2.3 Transfer Function Models: TransferFunctionModel[] 36210.3 Model Connections – Closed-Loop Systems and System Response: SystemsModelFeedbackConnect[] and SystemsModelSeriesConnect[] 36310.4 Design Methods 36910.4.1 Root Locus: RootLocusPlot[] 36910.4.2 Bode Plot: BodePlot[] 37110.4.3 Nichols Plot: NicholsPlot[] 37210.5 Signal Processing 37410.5.1 Filter Models: ButterworthFilterModel[], EllipticFilterModel[], ... 37410.5.2 Windows: HammingWindow[], HannWindow[], ... 38110.5.3 Spectrum Averaging 38510.6 Aliasing 38810.7 Functions Introduced in Chapter 10 390Reference 39111 Heat Transfer and Fluid Mechanics 39311.1 Introduction 39311.2 Conduction Heat Transfer 39411.2.1 One-Dimensional Transient Heat Diffusion in Solids 39411.2.2 Heat Transfer in Concentric Spheres: Ablation of a Tumor 39811.2.3 Heat Flow Through Fins 40111.3 Natural Convection Along Heated Plates 40511.4 View Factor Between Two Parallel Rectangular Surfaces 40811.5 Internal Viscous Flow 41111.5.1 Laminar Flow in Horizontal Cylindrical Pipes 41111.5.2 Flow in Three Reservoirs 41211.6 External Flow 41611.6.1 Pressure Coefficient of a Joukowski Airfoil 41611.6.2 Surface Profile in Nonuniform Flow in Open Channels 419References 423Index 425