You are previewing An Engineer's Guide to Mathematica.
O'Reilly logo
An Engineer's Guide to Mathematica

Book Description

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.

    Table of Contents

        1. 1.1 Introduction
        2. 1.2 Selecting Notebook Characteristics
        3. 1.3 Notebook Cells
        4. 1.4 Delimiters
        5. 1.5 Basic Syntax
        6. 1.6 Mathematical Constants
        7. 1.7 Complex Numbers
        8. 1.8 Elementary, Trigonometric, Hyperbolic, and a Few Special Functions
        9. 1.9 Strings
        10. 1.10 Conversions, Relational Operators, and Transformation Rule
        11. 1.11 Engineering Units and Unit Conversions: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Quantity[]</b></span> and and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>UnitConvert[]</b></span>
        12. 1.12 Creation of CDF Documents and Documents in Other Formats
        13. 1.13 Functions Introduced in Chapter 1
        14. Exercises
        15. Notes
        1. 2.1 Introduction
        2. 2.2 Creating Lists and Vectors
        3. 2.3 Creating Matrices
        4. 2.4 Matrix Operations on Vectors and Arrays
        5. 2.5 Solution of a Linear System of Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>LinearSolve[]</b></span>
        6. 2.6 Eigenvalues and Eigenvectors: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>EigenSystem[]</b></span>
        7. 2.7 Functions Introduced in Chapter 2
        8. References
        9. Exercises
        1. 3.1 Introduction
        2. 3.2 Expressions and Procedures as Functions
        3. 3.3 Find Elements of a List that Meet a Criterion: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Select[]</b></span>
        4. 3.4 Conditionals
        5. 3.5 Repetitive Operations
        6. 3.6 Examples of Repetitive Operations and Conditionals
        7. 3.7 Functions Introduced in Chapter 3
        8. Exercises
        9. Notes
        1. 4.1 Introduction
        2. 4.2 <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Assumption</b></span> Options Options
        3. 4.3 Solutions of Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Solve[]</b></span>
        4. 4.4 Limits: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Limit[]</b></span>
        5. 4.5 Power Series: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Series[]</b></span>, , <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Coefficient[]</b></span>, and , and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>CoefficientList[]</b></span>
        6. 4.6 Optimization: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Maximize[]/Minimize[]</b></span>
        7. 4.7 Differentiation: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>D[]</b></span>
        8. 4.8 Integration: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Integrate[]</b></span>
        9. 4.9 Solutions of Ordinary Differential Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>DSolve[]</b></span>
        10. 4.10 Solutions of Partial Differential Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>DSolve[]</b></span>
        11. 4.11 Laplace Transform: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>LaplaceTransform[]</b></span> and and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>InverseLaplaceTransform[]</b></span>
        12. 4.12 Functions Introduced in Chapter 4
        13. References
        14. Exercises
        1. 5.1 Introduction
        2. 5.2 Numerical Integration: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>NIntegrate[]</b></span>
        3. 5.3 Numerical Solutions of Differential Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>NDSolveValue[]</b></span> and and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>ParametricNDSolveValue[]</b></span>
        4. 5.4 Numerical Solutions of Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>NSolve[]</b></span>
        5. 5.5 Roots of Transcendental Equations: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>FindRoot[]</b></span>
        6. 5.6 Minimum and Maximum: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>FindMinimum[]</b></span> and and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>FindMaximum[]</b></span>
        7. 5.7 Fitting of Data: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Interpolation[]</b></span> and and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>FindFit[]</b></span>
        8. 5.8 Discrete Fourier Transforms and Correlation: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Fourier[]</b></span>, , <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>InverseFourier[]</b></span>, and , and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>ListCorrelate[]</b></span>
        9. 5.9 Functions Introduced in Chapter 5
        10. References
        11. Exercises
        12. Notes
        1. 6.1 Introduction
        2. 6.2 2D Graphics
        3. 6.3 3D Graphics
        4. 6.4 Summary of Functions Introduced in Chapter 6
        5. References
        6. Exercises
        1. 7.1 Interactive Graphics: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>Manipulate[]</b></span>
        2. References
        3. Exercises
        1. 8.1 Introduction
        2. 8.2 Single Degree-of-Freedom Systems
        3. 8.3 Two Degrees-of-Freedom Systems
        4. 8.4 Thin Beams
        5. References
        1. 9.1 Descriptive Statistics
        2. 9.2 Probability of Continuous Random Variables
        3. 9.3 Regression Analysis: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>LinearModelFit[]</b></span>
        4. 9.4 Nonlinear Regression Analysis: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>NonLinearModelFit[]</b></span>
        5. 9.5 Analysis of Variance (ANOVA) and Factorial Designs: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>ANOVA[]</b></span>
        6. 9.6 Functions Introduced in Chapter 9
        7. Notes
        1. 10.1 Introduction
        2. 10.2 Model Generation: State-Space and Transfer Function Representation
        3. 10.3 Model Connections – Closed-Loop Systems and System Response: <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>SystemsModelFeedbackConnect[]</b></span> and and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" class="codeLabel"><b>SystemsModelSeriesConnect[]</b></span>
        4. 10.4 Design Methods
        5. 10.5 Signal Processing
        6. 10.6 Aliasing
        7. 10.7 Functions Introduced in Chapter 10
        8. Reference
        9. Notes
        1. 11.1 Introduction
        2. 11.2 Conduction Heat Transfer
        3. 11.3 Natural Convection Along Heated Plates
        4. 11.4 View Factor Between Two Parallel Rectangular Surfaces
        5. 11.5 Internal Viscous Flow
        6. 11.6 External Flow
        7. References