Cover image for Applied Engineering Analysis

Applied Engineering Analysis

Author Tai-Ran Hsu
Release Date: 2018/04/01
ISBN: 9781119071204
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Book Description

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.

Table of Contents

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