Applied Engineering Analysis - Tai-Ran Hsu

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Applied Engineering Analysis Tai-Ran Hsu, San Jose State University, USA A resource book applying mathematics to solve engineering problems Applied Engineering Analysis is a concise textbookwhich demonstrates how toapply mathematics to solve engineering problems. It begins with a

Sommaire:

Preface xvii

Suggestions to instructors xxi

About the companion website xxv

1 Overview of Engineering Analysis 1

Chapter Learning Objectives 1

1.1 Introduction 1

1.2 Engineering Analysis and Engineering Practices 2

1.2.1 Creation 2

1.2.2 Problem Solving 2

1.2.3 Decision Making 3

1.3 Toolbox for Engineering Analysis 5

1.4 The Four Stages in Engineering Analysis 8

1.5 Examples of the Application of Engineering Analysis in Design 10

1.6 The Safety Factor in Engineering Analysis of Structures 17

1.7 Problems 19

2 Mathematical Modeling 21

Chapter Learning Objectives 21

2.1 Introduction 21

2.2 Mathematical Modeling Terminology 26

2.2.1 The Numbers 26

2.2.2 Variables 26

2.2.3 Functions 27

2.2.4 Curve Fitting Technique in Engineering Analysis 30

2.2.5 Derivative 31

2.2.6 Integration 36

2.3 Applications of Integrals 38

2.3.1 Plane Area by Integration 38

2.3.2 Volumes of Solids of Revolution 42

2.3.3 Centroids of Plane Areas 47

2.3.4 Average Value of Continuous Functions 52

2.4 Special Functions for Mathematical Modeling 54

2.4.1 Special Functions in Solutions in Mathematical Modeling 55

2.4.2 Special Functions for Particular Physical Phenomena 58

2.5 Differential Equations 62

2.5.1 The Laws of Physics for Derivation of Differential Equations 62

2.6 Problems 65

3 Vectors and Vector Calculus 73

Chapter Learning Objectives 73

3.1 Vector and Scalar Quantities 73

3.2 Vectors in Rectangular and Cylindrical Coordinate Systems 75

3.2.1 Position Vectors 75

3.3 Vectors in 2D Planes and 3D Spaces 78

3.4 Vector Algebra 79

3.4.1 Addition of Vectors 79

3.4.2 Subtraction of Vectors 79

3.4.3 Addition and Subtraction of Vectors Using Unit Vectors in Rectangular Coordinate Systems 80

3.4.4 Multiplication of Vectors 81

3.5 Vector Calculus 88

3.5.1 Vector Functions 88

3.5.2 Derivatives of Vector Functions 89

3.5.3 Gradient, Divergence, and Curl 91

3.6 Applications of Vector Calculus in Engineering Analysis 92

3.6.1 In Heat Transfer 93

3.6.2 In Fluid Mechanics 93

3.6.3 In Electromagnetism with Maxwell's Equations 94

3.7 Application of Vector Calculus in Rigid Body Dynamics 95

3.7.1 Rigid Body in Rectilinear Motion 95

3.7.2 Plane Curvilinear Motion in Rectangular Coordinates 97

3.7.3 Application of Vector Calculus in the Kinematics of Projectiles 100

3.7.4 Plane Curvilinear Motion in Cylindrical Coordinates 103

3.7.5 Plane Curvilinear Motion with Normal and Tangential Components 109

3.8 Problems 114

4 Linear Algebra and Matrices 119

Chapter Learning Objectives 119

4.1 Introduction to Linear Algebra and Matrices 119

4.2 Determinants and Matrices 121

4.2.1 Evaluation of Determinants 121

4.2.2 Matrices in Engineering Analysis 123

4.3 Different Forms of Matrices 123

4.3.1 Rectangular Matrices 123

4.3.2 Square Matrices 124

4.3.3 Row Matrices 124

4.3.4 Column Matrices 124

4.3.5 Upper Triangular Matrices 124

4.3.6 Lower Triangular Matrices 125

4.3.7 Diagonal Matrices 125

4.3.8 Unit Matrices 125

4.4 Transposition of Matrices 125

4.5 Matrix Algebra 126

4.5.1 Addition and Subtraction of Matrices 126

4.5.2 Multiplication of a Matrix by a Scalar Quantity ? 127

4.5.3 Multiplication of Two Matrices 127

4.5.4 Matrix Representation of Simultaneous Linear Equations 128

4.5.5 Ad...