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  • Gebundenes Buch

A resource book applying mathematics to solve engineering problemsApplied 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…mehr

Produktbeschreibung
A resource book applying mathematics to solve engineering problemsApplied 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.
  • Produktdetails
  • Verlag: Wiley / Wiley & Sons
  • Artikelnr. des Verlages: 1W119071200
  • 1. Auflage
  • Seitenzahl: 528
  • Erscheinungstermin: 30. April 2018
  • Englisch
  • Abmessung: 261mm x 184mm x 37mm
  • Gewicht: 1032g
  • ISBN-13: 9781119071204
  • ISBN-10: 1119071208
  • Artikelnr.: 48899619
Autorenporträt
TAI-RAN HSU, San Jose State University, USATAI-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 xviiSuggestions to instructors xxiAbout the companion website xxv1 Overview of Engineering Analysis 1Chapter Learning Objectives 11.1 Introduction 11.2 Engineering Analysis and Engineering Practices 21.2.1 Creation 21.2.2 Problem Solving 21.2.3 Decision Making 31.3 "Toolbox" for Engineering Analysis 51.4 The Four Stages in Engineering Analysis 81.5 Examples of the Application of Engineering Analysis in Design 101.6 The "Safety Factor" in Engineering Analysis of Structures 171.7 Problems 192 Mathematical Modeling 21Chapter Learning Objectives 212.1 Introduction 212.2 MathematicalModeling Terminology 262.2.1 The Numbers 262.2.1.1 Real Numbers 262.2.1.2 Imaginary Numbers 262.2.1.3 Absolute Values 262.2.1.4 Constants 262.2.1.5 Parameters 262.2.2 Variables 262.2.3 Functions 272.2.3.1 Form 1. Functions with Discrete Values 272.2.3.2 Form 2. Continuous Functions 272.2.3.3 Form 3. Piecewise Continuous Functions 282.2.4 Curve Fitting Technique in Engineering Analysis 302.2.4.1 Curve Fitting Using Polynomial Functions 302.2.5 Derivative 312.2.5.1 The Physical Meaning of Derivatives 322.2.5.2 Mathematical Expression of Derivatives 332.2.5.3 Orders of Derivatives 352.2.5.4 Higher-order Derivatives in Engineering Analyses 352.2.5.5 The Partial Derivatives 362.2.6 Integration 362.2.6.1 The Concept of Integration 362.2.6.2 Mathematical Expression of Integrals 372.3 Applications of Integrals 382.3.1 Plane Area by Integration 382.3.1.1 Plane Area Bounded by Two Curves 412.3.2 Volumes of Solids of Revolution 422.3.3 Centroids of Plane Areas 472.3.3.1 Centroid of a Solid of Plane Geometry with Straight Edges 492.3.3.2 Centroid of a Solid with Plane Geometry Defined by Multiple Functions 502.3.4 Average Value of Continuous Functions 522.4 Special Functions for MathematicalModeling 542.4.1 Special Functions in Solutions in MathematicalModeling 552.4.1.1 The Error Function and Complementary Error Function 552.4.1.2 The Gamma Function 562.4.1.3 Bessel Functions 562.4.2 Special Functions for Particular Physical Phenomena 582.4.2.1 Step Functions 582.4.2.2 Impulsive Functions 602.5 Differential Equations 622.5.1 The Laws of Physics for Derivation of Differential Equations 622.6 Problems 653 Vectors and Vector Calculus 73Chapter Learning Objectives 733.1 Vector and Scalar Quantities 733.2 Vectors in Rectangular and Cylindrical Coordinate Systems 753.2.1 Position Vectors 753.3 Vectors in 2D Planes and 3D Spaces 783.4 Vector Algebra 793.4.1 Addition of Vectors 793.4.2 Subtraction of Vectors 793.4.3 Addition and Subtraction of Vectors Using Unit Vectors in Rectangular Coordinate Systems 803.4.4 Multiplication of Vectors 813.4.4.1 Scalar Multiplier 813.4.4.2 Dot Product 823.4.4.3 Cross Product 843.4.4.4 Cross Product of Vectors for Plane Areas 863.4.4.5 Triple product 863.4.4.6 Additional Laws of Vector Algebra 873.4.4.7 Use of Triple Product of Vectors for Solid Volume 873.5 Vector Calculus 883.5.1 Vector Functions 883.5.2 Derivatives of Vector Functions 893.5.3 Gradient, Divergence, and Curl 913.5.3.1 Gradient 913.5.3.2 Divergence 913.5.3.3 Curl 913.6 Applications of Vector Calculus in Engineering Analysis 923.6.1 In Heat Transfer 933.6.2 In Fluid Mechanics 933.6.3 In Electromagnetism with Maxwell's Equations 943.7 Application of Vector Calculus in Rigid Body Dynamics 953.7.1 Rigid Body in RectilinearMotion 953.7.2 Plane CurvilinearMotion in Rectangular Coordinates 973.7.3 Application of Vector Calculus in the Kinematics of Projectiles 1003.7.4 Plane CurvilinearMotion in Cylindrical Coordinates 1033.7.5 Plane CurvilinearMotion with Normal and Tangential Components 1093.8 Problems 1144 Linear Algebra and Matrices 119Chapter Learning Objectives 1194.1 Introduction to Linear Algebra and Matrices 1194.2 Determinants and Matrices 1214.2.1 Evaluation of Determinants 1214.2.2 Matrices in Engineering Analysis 1234.3 Different Forms of Matrices 1234.3.1 Rectangular Matrices 1234.3.2 Square Matrices 1244.3.3 Row Matrices 1244.3.4 Column Matrices 1244.3.5 Upper Triangular Matrices 1244.3.6 Lower Triangular Matrices 1254.3.7 Diagonal Matrices 1254.3.8 Unit Matrices 1254.4 Transposition of Matrices 1254.5 Matrix Algebra 1264.5.1 Addition and Subtraction of Matrices 1264.5.2 Multiplication of a Matrix by a Scalar Quantity alpha 1274.5.3 Multiplication of Two Matrices 1274.5.4 Matrix Representation of Simultaneous Linear Equations 1284.5.5 Additional Rules for Multiplication of Matrices 1294.6 Matrix Inversion, [A].1 1294.7 Solution of Simultaneous Linear Equations 1314.7.1 The Need for Solving Large Numbers of Simultaneous Linear Equations 1314.7.2 Solution of Large Numbers of Simultaneous Linear Equations Using the Inverse Matrix Technique 1334.7.3 Solution of Simultaneous Equations Using the Gaussian Elimination Method 1354.8 Eigenvalues and Eigenfunctions 1414.8.1 Eigenvalues and Eigenvectors of Matrices 1424.8.2 Mathematical Expressions of Eigenvalues and Eigenvectors of Square Matrices 1424.8.3 Application of Eigenvalues and Eigenfunctions in Engineering Analysis 1464.9 Problems 1485 Overview of Fourier Series 151Chapter Learning Objectives 1515.1 Introduction 1515.2 Representing Periodic Functions by Fourier Series 1525.3 Mathematical Expression of Fourier Series 1545.4 Convergence of Fourier Series 1615.5 Convergence of Fourier Series at Discontinuities 1645.6 Problems 1696 Introduction to the Laplace Transform and Applications 171Chapter Learning Objectives 1716.1 Introduction 1716.2 Mathematical Operator of Laplace Transform 1726.3 Properties of the Laplace Transform 1746.3.1 Linear Operator Property 1746.3.2 Shifting Property 1756.3.3 Change of Scale Property 1756.4 Inverse Laplace Transform 1766.4.1 Using the Laplace Transform Tables in Reverse 1766.4.2 The Partial Fraction Method 1766.4.3 The Convolution Theorem 1786.5 Laplace Transform of Derivatives 1806.5.1 Laplace Transform of Ordinary Derivatives 1806.5.2 Laplace Transform of Partial Derivatives 1816.6 Solution of Ordinary Differential Equations Using Laplace Transforms 1846.6.1 Laplace Transform for Solving Nonhomogeneous Differential Equations 1846.6.2 Differential Equation for the Bending of Beams 1866.7 Solution of Partial Differential Equations Using Laplace Transforms 1926.8 Problems 1957 Application of First-order Differential Equations in Engineering Analysis 199Chapter Learning Objectives 1997.1 Introduction 1997.2 Solution Methods for First-order Ordinary Differential Equations 2007.2.1 Solution Methods for Separable Differential Equations 2007.2.2 Solution of Linear, Homogeneous Equations 2017.2.3 Solution of Linear, Nonhomogeneous Equations 2027.3 Application of First-order Differential Equations in Fluid Mechanics Analysis 2047.3.1 Fundamental Concepts 2047.3.2 The Bernoulli Equation 2057.3.3 The Continuity Equation 2067.4 Liquid Flow in Reservoirs, Tanks, and Funnels 2067.4.1 Derivation of Differential Equations 2077.4.2 Solution of Differential Equations 2087.4.3 Drainage of Tapered Funnels 2097.5 Application of First-order Differential Equations in Heat Transfer Analysis 2177.5.1 Fourier's Law of Heat Conduction in Solids 2177.5.2 Mathematical Expression of Fourier's Law 2187.5.3 Heat Flux in a Three-dimensional Space 2217.5.4 Newton's Cooling Law for Heat Convection 2277.5.5 Heat Transfer between Solids and Fluids 2277.6 Rigid Body Dynamics under the Influence of Gravitation 2337.7 Problems 2378 Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis 243Chapter Learning Objectives 2438.1 Introduction 2438.2 Solution Method for Typical Homogeneous, Second-order Linear Differential Equations with Constant Coefficients 2438.3 Applications in Mechanical Vibration Analyses 2468.3.1 What Is Mechanical Vibration? 2468.3.2 Common Sources for Vibration 2478.3.3 Common Types of Vibration 2478.3.4 Classification of Mechanical Vibration Analyses 2478.3.4.1 Free Vibration 2478.3.4.2 Damped Vibration 2488.3.4.3 Forced Vibration 2498.4 Mathematical Modeling of Free Mechanical Vibration: Simple Mass-Spring Systems 2498.4.1 Solution of the Differential Equation 2518.5 Modeling of Damped FreeMechanical Vibration: Simple Mass-Spring Systems 2548.5.1 The Physical Model 2548.5.2 The Differential Equation 2558.5.3 Solution of the Differential Equation 2568.6 Solution of Nonhomogeneous, Second-order Linear Differential Equations with Constant Coefficients 2588.6.1 Typical Equation and Solutions 2588.6.2 The Complementary and Particular Solutions 2588.6.3 The Particular Solutions 2598.6.4 Special Case for Solution of Nonhomogeneous Second-order Differential Equations 2638.7 Application in Forced Vibration Analysis 2648.7.1 Derivation of the Differential Equation 2648.7.2 Resonant Vibration 2668.8 Near Resonant Vibration 2738.9 Natural Frequencies of Structures and Modal Analysis 2778.10 Problems 2809 Applications of Partial Differential Equations in Mechanical Engineering Analysis 285Chapter Learning Objectives 2859.1 Introduction 2859.2 Partial Derivatives 2859.3 Solution Methods for Partial Differential Equations 2879.3.1 The Separation of VariablesMethod 2879.3.2 Laplace Transform Method for Solution of Partial Differential Equations 2889.3.3 Fourier Transform Method for Solution of Partial Differential Equations 2889.4 Partial Differential Equations for Heat Conduction in Solids 2919.4.1 Heat Conduction in Engineering Analysis 2919.4.2 Derivation of Partial Differential Equations for Heat Conduction Analysis 2919.4.3 Heat Conduction Equation in Rectangular Coordinate Systems 2929.4.4 Heat Conduction Equation in a Cylindrical Polar Coordinate System 2939.4.5 General Heat Conduction Equation 2939.4.6 Initial and Boundary Conditions 2939.5 Solution of Partial Differential Equations for Transient Heat Conduction Analysis 2989.5.1 Transient Heat Conduction Analysis in Rectangular Coordinate System 2989.5.2 Transient Heat Conduction Analysis in the Cylindrical Polar Coordinate System 3039.6 Solution of Partial Differential Equations for Steady-state Heat Conduction Analysis 3089.6.1 Steady-state Heat Conduction Analysis in the Rectangular Coordinate System 3089.6.2 Steady-state Heat Conduction Analysis in the Cylindrical Polar Coordinate System 3119.7 Partial Differential Equations for Transverse Vibration of Cable Structures 3149.7.1 Derivation of Partial Differential Equations for Free Vibration of Cable Structures 3149.7.2 Solution of Partial Differential Equation for Free Vibration of Cable Structures 3189.7.3 Convergence of Series Solutions 3229.7.4 Modes of Vibration of Cable Structures 3239.8 Partial Differential Equations for Transverse Vibration of Membranes 3289.8.1 Derivation of the Partial Differential Equation 3289.8.2 Solution of the Partial Differential Equation for Plate Vibration 3319.8.3 Numerical Solution of the Partial Differential Equation for Plate Vibration 3349.9 Problems 33610 Numerical Solution Methods for Engineering Analysis 339Chapter Learning Objectives 33910.1 Introduction 33910.2 Engineering Analysis with Numerical Solutions 34010.3 Solution of Nonlinear Equations 34110.3.1 Solution Using Microsoft Excel Software 34110.3.2 The Newton-RaphsonMethod 34210.4 Numerical Integration Methods 34710.4.1 The Trapezoidal Rule for Numerical Integration 34810.4.2 Numerical Integration by Simpson's One-third Rule 35210.4.3 Numerical Integration by Gaussian Quadrature 35610.5 Numerical Methods for Solving Differential Equations 36110.5.1 The Principle of Finite Difference 36210.5.2 TheThree Basic Finite-difference Schemes 36310.5.3 Finite-difference Formulation for Partial Derivatives 36610.5.4 Numerical Solution of Differential Equations 36710.5.4.1 The Second-order Runge-Kutta Method 36710.5.4.2 The Fourth-order Runge-Kutta Method 36910.5.4.3 Runge-Kutta Method for Higher-order Differential Equations 37010.6 Introduction to Numerical Analysis Software Packages 37510.6.1 Introduction to Mathematica 37510.6.2 Introduction to MATLAB 37610.7 Problems 37711 Introduction to Finite-element Analysis 381Chapter Learning Objectives 38111.1 Introduction 38111.2 The Principle of Finite-element Analysis 38311.3 Steps in Finite-element Analysis 38311.3.1 Derivation of Interpolation Function for Simplex Elements with Scalar Quantities at Nodes 38811.3.2 Derivation of Interpolation Function for Simplex Elements with Vector Quantities at Nodes 39011.4 Output of Finite-element Analysis 40111.5 Elastic Stress Analysis of Solid Structures by the Finite-elementMethod 40311.5.1 Stresses 40411.5.2 Displacements 40611.5.3 Strains 40611.5.4 Fundamental Relationships 40711.5.4.1 Strain-Displacement Relations 40711.5.4.2 Stress-Strain Relations 40811.5.4.3 Strain Energy in Deformed Elastic Solids 40911.5.5 Finite-element Formulation 40911.5.6 Finite-element Formulation for One-dimensional Solid Structures 41311.6 General-purpose Finite-element Analysis Codes 41711.6.1 Common Features in General-purpose Finite-element Codes 41911.6.2 Simulation using general-purpose finite-element codes 42011.7 Problems 42212 Statistics for Engineering Analysis 425Chapter Learning Objectives 42512.1 Introduction 42512.2 Statistics in Engineering Practice 42712.3 The Scope of Statistics 42812.4 Common Concepts and Terminology in Statistical Analysis 43012.4.1 The Mode of a Dataset 43012.4.2 The Histogram of a Statistical Dataset 43012.4.3 The Mean 43112.4.4 The Median 43312.4.5 Variation and Deviation 43312.5 Standard Deviation (sigma) and Variance (sigma2) 43412.5.1 The Standard Deviation 43412.5.2 The Variance 43412.6 The Normal Distribution Curve and Normal Distribution Function 43512.7 Weibull Distribution Function for Probabilistic Engineering Design 43712.7.1 Statistical Approach to the Design of Structures Made of Ceramic and Brittle Materials 43812.7.2 TheWeibull Distribution Function 43912.7.3 Estimation ofWeibull Parameters 44112.7.4 Probabilistic Design of Structures with Random Fracture Strength of Materials 44312.8 Statistical Quality Control 44712.9 Statistical Process Control 44812.9.1 Quality Issues in Industrial Automation and Mass Production 44812.9.2 The Statistical Process Control Method 44912.10 The "Control Charts" 45012.10.1 Three-Sigma Control Charts 45112.10.2 Control Charts for Sample Ranges (the R-Chart) 45312.11 Problems 456Bibliography 459A Table for the Laplace Transform 463B Recommended Units for Engineering Analysis 465C Conversion of Units 467D Application of MATLAB Software for Numerical Solutions in EngineeringAnalysis 469Index 483