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An Engineer’s Guide to Mathematica®
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An Engineer’s Guide to Mathematica®
by Edward B. Magrab
An Engineer's Guide to Mathematica
Preface
Table of Engineering Applications
Part 1 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
1.6 Mathematical Constants
1.7 Complex Numbers
1.8 Elementary, Trigonometric, Hyperbolic, and a Few Special Functions
1.9 Strings
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 1
Exercises
Notes
2 List Creation and Manipulation: Vectors and Matrices
2.1 Introduction
2.2 Creating Lists and Vectors
2.3 Creating Matrices
2.4 Matrix Operations on Vectors and Arrays
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
3.3 Find Elements of a List that Meet a Criterion: Select[]
3.4 Conditionals
3.5 Repetitive Operations
3.6 Examples of Repetitive Operations and Conditionals
3.7 Functions Introduced in Chapter 3
Exercises
Notes
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 4
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 5
References
Exercises
Notes
6 Graphics
6.1 Introduction
6.2 2D Graphics
6.3 3D Graphics
6.4 Summary of Functions Introduced in Chapter 6
References
Exercises
7 Interactive Graphics
7.1 Interactive Graphics: Manipulate[]
References
Exercises
Part 2 Engineering Applications
8 Vibrations of Spring–Mass Systems and Thin Beams
8.1 Introduction
8.2 Single Degree-of-Freedom Systems
8.3 Two Degrees-of-Freedom Systems
8.4 Thin Beams
References
9 Statistics
9.1 Descriptive Statistics
9.2 Probability of Continuous Random Variables
9.3 Regression Analysis: LinearModelFit[]
9.4 Nonlinear Regression Analysis: NonLinearModelFit[]
9.5 Analysis of Variance (ANOVA) and Factorial Designs: ANOVA[]
9.6 Functions Introduced in Chapter 9
Notes
10 Control Systems and Signal Processing
10.1 Introduction
10.2 Model Generation: State-Space and Transfer Function Representation
10.3 Model Connections – Closed-Loop Systems and System Response: SystemsModelFeedbackConnect[] and SystemsModelSeriesConnect[]
10.4 Design Methods
10.5 Signal Processing
10.6 Aliasing
10.7 Functions Introduced in Chapter 10
Reference
Notes
11 Heat Transfer and Fluid Mechanics
11.1 Introduction
11.2 Conduction Heat Transfer
11.3 Natural Convection Along Heated Plates
11.4 View Factor Between Two Parallel Rectangular Surfaces
11.5 Internal Viscous Flow
11.6 External Flow
References
Index
End User License Agreement
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An Engineer’s Guide to Mathematica®
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An Engineer’s Guide to Mathematica®
Part I
Introduction
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