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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 an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to…mehr
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 an overview of engineering analysis and an introduction to mathematical modeling, followed by vector calculus, matrices and linear algebra, and applications of first and second order differential equations. Fourier series and Laplace transform are also covered, along with partial differential equations, numerical solutions to nonlinear and differential equations and an introduction to finite element analysis. The book also covers statistics with applications to design and statistical process controls.
Drawing on the author's extensive industry and teaching experience, spanning 40 years, the book takes a pedagogical approach and includes examples, case studies and end of chapter problems. It is also accompanied by a website hosting a solutions manual and PowerPoint slides for instructors.
Key features:
Strong emphasis on deriving equations, not just solving given equations, for the solution of engineering problems.
Examples and problems of a practical nature with illustrations to enhance student's self-learning.
Numerical methods and techniques, including finite element analysis.
Includes coverage of statistical methods for probabilistic design analysis of structures and statistical process control (SPC).
Applied Engineering Analysis is a resource book for engineering students and professionals to learn how to apply the mathematics experience and skills that they have already acquired to their engineering profession for innovation, problem solving, and decision making.
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Autorenporträt
TAI-RAN HSU,San Jose State University, USA
TAI-RAN HSU is currently a Professor of Mechanical Engineering at San Jose State University (SJSU), San Jose, California, USA. He joined the SJSU as the Chair of the department in 1990 and served two terms until 1998, and also from 2012 to 2015. He served in a similar capacity at the University of Manitoba, Winnipeg, Canada before joining SJSU. Prior to his academic career, he worked as a design engineer with heat exchangers, steam power plant equipment, large steam turbines, and nuclear reactor fuel systems for major industries in Canada and U.S.A. He has published six books and edited another two on a wide ranging topics on finite element method in thermomechanics, microelectronics packaging, CAD, and MEMS and microsystems design and packaging. Additionally, he published over one hundred technical papers in archive journals and conference proceedings.
Inhaltsangabe
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 MathematicalModeling Terminology 26
2.2.1 The Numbers 26
2.2.1.1 Real Numbers 26
2.2.1.2 Imaginary Numbers 26
2.2.1.3 Absolute Values 26
2.2.1.4 Constants 26
2.2.1.5 Parameters 26
2.2.2 Variables 26
2.2.3 Functions 27
2.2.3.1 Form 1. Functions with Discrete Values 27
2.2.3.2 Form 2. Continuous Functions 27
2.2.3.3 Form 3. Piecewise Continuous Functions 28
2.2.4 Curve Fitting Technique in Engineering Analysis 30
2.2.4.1 Curve Fitting Using Polynomial Functions 30
2.2.5 Derivative 31
2.2.5.1 The Physical Meaning of Derivatives 32
2.2.5.2 Mathematical Expression of Derivatives 33
2.2.5.3 Orders of Derivatives 35
2.2.5.4 Higher-order Derivatives in Engineering Analyses 35
2.2.5.5 The Partial Derivatives 36
2.2.6 Integration 36
2.2.6.1 The Concept of Integration 36
2.2.6.2 Mathematical Expression of Integrals 37
2.3 Applications of Integrals 38
2.3.1 Plane Area by Integration 38
2.3.1.1 Plane Area Bounded by Two Curves 41
2.3.2 Volumes of Solids of Revolution 42
2.3.3 Centroids of Plane Areas 47
2.3.3.1 Centroid of a Solid of Plane Geometry with Straight Edges 49
2.3.3.2 Centroid of a Solid with Plane Geometry Defined by Multiple Functions 50
2.3.4 Average Value of Continuous Functions 52
2.4 Special Functions for MathematicalModeling 54
2.4.1 Special Functions in Solutions in MathematicalModeling 55
2.4.1.1 The Error Function and Complementary Error Function 55
2.4.1.2 The Gamma Function 56
2.4.1.3 Bessel Functions 56
2.4.2 Special Functions for Particular Physical Phenomena 58
2.4.2.1 Step Functions 58
2.4.2.2 Impulsive Functions 60
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
3.4.4.1 Scalar Multiplier 81
3.4.4.2 Dot Product 82
3.4.4.3 Cross Product 84
3.4.4.4 Cross Product of Vectors for Plane Areas 86
3.4.4.5 Triple product 86
3.4.4.6 Additional Laws of Vector Algebra 87
3.4.4.7 Use of Triple Product of Vectors for Solid Volume 87
