Engineer''s Guide to Mathematica

"Provides the tools for the reader to generate Mathematica programs to obtain numerical solutions to a wide range of engineering topics."--

Sommario

Preface xiii
 
Table of Engineering Applications xvii
 
Part 1 Introduction
 
1 Mathematica Environment and Basic Syntax 3
 
1.1 Introduction 3
 
1.2 Selecting Notebook Characteristics 4
 
1.3 Notebook Cells 8
 
1.4 Delimiters 12
 
1.5 Basic Syntax 12
 
1.5.1 Introduction 12
 
1.5.2 Templates: Greek Symbols and Mathematical Notation 15
 
1.5.3 Variable Names and Global Variables 18
 
1.6 Mathematical Constants 19
 
1.7 Complex Numbers 21
 
1.8 Elementary, Trigonometric, Hyperbolic, and a Few Special Functions 22
 
1.9 Strings 25
 
1.9.1 String Creation: StringJoin[] and ToString[] 25
 
1.9.2 Labeled Output: Print[], NumberForm[], EngineeringForm[], and TraditionalForm[] 26
 
1.10 Conversions, Relational Operators, and Transformation Rule 28
 
1.11 Engineering Units and Unit Conversions: Quantity[] and UnitConvert[] 30
 
1.12 Creation of CDF Documents and Documents in Other Formats 33
 
1.13 Functions Introduced in Chapter 1 34
 
Exercises 35
 
2 List Creation and Manipulation: Vectors and Matrices 39
 
2.1 Introduction 39
 
2.2 Creating Lists and Vectors 39
 
2.2.1 Introduction 39
 
2.2.2 Creating a List with Table[] 45
 
2.2.3 Summing Elements of a List: Total[] 46
 
2.2.4 Selecting Elements of a List 47
 
2.2.5 Identifying List Elements Matching a Pattern: Position[] 49
 
2.3 Creating Matrices 51
 
2.3.1 Introduction 51
 
2.3.2 Matrix Generation Using Table[] 54
 
2.3.3 Accessing Elements of Arrays 55
 
2.4 Matrix Operations on Vectors and Arrays 56
 
2.4.1 Introduction 56
 
2.4.2 Matrix Inverse and Determinant: Inverse[] and Det[] 57
 
2.5 Solution of a Linear System of Equations: LinearSolve[] 58
 
2.6 Eigenvalues and Eigenvectors: EigenSystem[] 59
 
2.7 Functions Introduced in Chapter 2 61
 
References 61
 
Exercises 61
 
3 User-Created Functions, Repetitive Operations, and Conditionals 69
 
3.1 Introduction 69
 
3.2 Expressions and Procedures as Functions 69
 
3.2.1 Introduction 69
 
3.2.2 Pure Function: Function[] 74
 
3.2.3 Module[] 78
 
3.3 Find Elements of a List that Meet a Criterion: Select[] 80
 
3.4 Conditionals 82
 
3.4.1 If[] 82
 
3.4.2 Which[] 83
 
3.5 Repetitive Operations 83
 
3.5.1 Do[] 83
 
3.5.2 While[] 83
 
3.5.3 Nest[] 84
 
3.5.4 Map[] 84
 
3.6 Examples of Repetitive Operations and Conditionals 85
 
3.7 Functions Introduced in Chapter 3 92
 
Exercises 92
 
4 Symbolic Operations 95
 
4.1 Introduction 95
 
4.2 Assumption Options 101
 
4.3 Solutions of Equations: Solve[] 101
 
4.4 Limits: Limit[] 105
 
4.5 Power Series: Series[], Coefficient[], and CoefficientList[] 108
 
4.6 Optimization: Maximize[]/Minimize[] 112
 
4.7 Differentiation: D[] 114
 
4.8 Integration: Integrate[] 120
 
4.9 Solutions of Ordinary Differential Equations: DSolve[] 126
 
4.10 Solutions of Partial Differential Equations: DSolve[] 136
 
4.11 Laplace Transform: LaplaceTransform[] and InverseLaplaceTransform[] 138
 
4.12 Functions Introduced in Chapter 4 145
 
References 145
 
Exercises 146
 
5 Numerical Evaluations of Equations 151
 
5.1 Introduction 151
 
5.2 Numerical Integration: NIntegrate[] 151
 
5.3 Numerical Solutions of Differential Equations: NDSolveValue[] and ParametricND

Info autore

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.

Riassunto

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.

Dettagli sul prodotto

• Autori: Magrab, Eb Magrab, Edward B Magrab, Edward B. Magrab, Edward B. (Catholic University of America Magrab, Magrab Edward B.
• Editore: Wiley, John and Sons Ltd
• Lingue: Inglese
• Formato: Tascabile
• Pubblicazione: 13.05.2014
• EAN: 9781118821268
• ISBN: 978-1-118-82126-8
• Pagine: 456
• Categorie: Scienze naturali, medicina, informatica, tecnica > Tecnica > Meccanica, tecnica di produzione; Mathematik, Maschinenbau, Mathematica, Mathematische Modellierung, Mathematics, Mechanical Engineering, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Numerische Methoden u. Algorithmen, Numerical Methods & Algorithms, Computational / Numerical Methods, Rechnergestützte / Numerische Verfahren im Maschinenbau, Mathematical Modeling