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End User License Agreement
by Tai-Ran Hsu
Applied Engineering Analysis
Cover
Title Page
Copyright
Dedication
Preface
Suggestions to instructors
About the companion website
Chapter 1: Overview of Engineering Analysis
1.1 Introduction
1.2 Engineering Analysis and Engineering Practices
1.3 “Toolbox” for Engineering Analysis
1.4 The Four Stages in Engineering Analysis
1.5 Examples of the Application of Engineering Analysis in Design
1.6 The “Safety Factor” in Engineering Analysis of Structures
Problems
Chapter 2: Mathematical Modeling
2.1 Introduction
2.2 Mathematical Modeling Terminology
2.3 Applications of Integrals
2.4 Special Functions for Mathematical Modeling
2.5 Differential Equations
Problems
Chapter 3: Vectors and Vector Calculus
3.1 Vector and Scalar Quantities
3.2 Vectors in Rectangular and Cylindrical Coordinate Systems
3.3 Vectors in 2D Planes and 3D Spaces
3.4 Vector Algebra
3.5 Vector Calculus
3.6 Applications of Vector Calculus in Engineering Analysis
3.7 Application of Vector Calculus in Rigid Body Dynamics
Problems
Chapter 4: Linear Algebra and Matrices
4.1 Introduction to Linear Algebra and Matrices
4.2 Determinants and Matrices
4.3 Different Forms of Matrices
4.4 Transposition of Matrices
4.5 Matrix Algebra
4.6 Matrix Inversion, [A]−1
4.7 Solution of Simultaneous Linear Equations
4.8 Eigenvalues and Eigenfunctions
Problems
Chapter 5: Overview of Fourier Series
5.1 Introduction
5.2 Representing Periodic Functions by Fourier Series
5.3 Mathematical Expression of Fourier Series
5.4 Convergence of Fourier Series
5.5 Convergence of Fourier Series at Discontinuities
Problems
Chapter 6: Introduction to the Laplace Transform and Applications
6.1 Introduction
6.2 Mathematical Operator of Laplace Transform
6.3 Properties of the Laplace Transform
6.4 Inverse Laplace Transform
6.5 Laplace Transform of Derivatives
6.6 Solution of Ordinary Differential Equations Using Laplace Transforms
6.7 Solution of Partial Differential Equations Using Laplace Transforms
Problems
Chapter 7: Application of First-order Differential Equations in Engineering Analysis
7.1 Introduction
7.2 Solution Methods for First-order Ordinary Differential Equations
7.3 Application of First-order Differential Equations in Fluid Mechanics Analysis
7.4 Liquid Flow in Reservoirs, Tanks, and Funnels
7.5 Application of First-order Differential Equations in Heat Transfer Analysis
7.6 Rigid Body Dynamics under the Influence of Gravitation
Problems
Chapter 8: Application of Second-order Ordinary Differential Equations in Mechanical Vibration Analysis
8.1 Introduction
8.2 Solution Method for Typical Homogeneous, Second-order Linear Differential Equations with Constant Coefficients
8.3 Applications in Mechanical Vibration Analyses
8.4 Mathematical Modeling of Free Mechanical Vibration: Simple Mass–Spring Systems
8.5 Modeling of Damped Free Mechanical Vibration: Simple Mass–Spring Systems
8.6 Solution of Nonhomogeneous, Second-order Linear Differential Equations with Constant Coefficients
8.7 Application in Forced Vibration Analysis
8.8 Near Resonant Vibration
8.9 Natural Frequencies of Structures and Modal Analysis
Problems
Chapter 9: Applications of Partial Differential Equations in Mechanical Engineering Analysis
9.1 Introduction
9.2 Partial Derivatives
9.3 Solution Methods for Partial Differential Equations
9.4 Partial Differential Equations for Heat Conduction in Solids
9.5 Solution of Partial Differential Equations for Transient Heat Conduction Analysis
9.6 Solution of Partial Differential Equations for Steady-state Heat Conduction Analysis
9.7 Partial Differential Equations for Transverse Vibration of Cable Structures
9.8 Partial Differential Equations for Transverse Vibration of Membranes
Problems
Chapter 10: Numerical Solution Methods for Engineering Analysis
10.1 Introduction
10.2 Engineering Analysis with Numerical Solutions
10.3 Solution of Nonlinear Equations
10.4 Numerical Integration Methods
10.5 Numerical Methods for Solving Differential Equations
10.6 Introduction to Numerical Analysis Software Packages
Problems
Chapter 11: Introduction to Finite-element Analysis
11.1 Introduction
11.2 The Principle of Finite-element Analysis
11.3 Steps in Finite-element Analysis
11.4 Output of Finite-element Analysis
11.5 Elastic Stress Analysis of Solid Structures by the Finite-element Method
11.6 General-purpose Finite-element Analysis Codes
Problems
Chapter 12: Statistics for Engineering Analysis
12.1 Introduction
12.2 Statistics in Engineering Practice
12.3 The Scope of Statistics
12.4 Common Concepts and Terminology in Statistical Analysis
12.5 Standard Deviation (σ) and Variance (σ2)
12.6 The Normal Distribution Curve and Normal Distribution Function
12.7 Weibull Distribution Function for Probabilistic Engineering Design
12.8 Statistical Quality Control
12.9 Statistical Process Control
12.10 The “Control Charts”
Problems
Bibliography
Appendix 1: Table for the Laplace Transform
Appendix 2: Recommended Units for Engineering Analysis
Appendix 3: Conversion of Units
Appendix 4: Application of MATLAB Software for Numerical Solutions in Engineering Analysis: Contributed by Vaibhav Tank
Index
End User License Agreement
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