An Engineer’s Guide To Mathematica

Description

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