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Applied Engineering Analysis

ISBN: 978-1-119-07120-4
400 pages
April 2018, ©2016
Applied Engineering Analysis (1119071208) cover image


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 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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Table of Contents



BCC-an introduction of the book




About the companion website

Chapter 1 Overview of Engineering Analysis

Chapter Learning Objectives

1.1 Introduction

1.2 Engineering Analysis and Engineering Practice

1.3 “Tool Box” for Engineering Analysis

1.4 The Four Stages in Engineering Analysis

1.5 Examples on Application of Engineering Analysis in Design

1.6 Safety Factors in Engineering Analysis of Structures


Chapter 2 Mathematical Modeling

Chapter Learning Objectives

2.1  Introduction

2.2  Terminologies used in Mathematical Modeling

2.3 Applications of Integrals

2.5  Differential Equations


Chapter 3 Vectors and Vector Calculus

Chapter Learning Objectives

3.1 Vector and Scalar Quantities

3.2 Vectors in Rectangular and Cylindrical Coordinate Systems

3.3 Vectors in 2-D Planes and 3-D Spaces

3.4 Vector Algebra

3.5 Vector Calculus

3.6 Application of Vector Calculus in Engineering Analysis

3.7 Application of Vector Calculus in Rigid Body Dynamics


Chapter 4 Linear Algebra and Matrices

Chapter Learning Objectives

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

4.7 Solution of Simultaneous Linear Equations

4.8 Eigenvalues and Eigenfunctions


Chapter 5  Overview of Fourier Series  

Chapter Learning Objectives

5.1 Introduction 

5.2 Periodic Functions by Fourier Series

5.3 Mathematical Expressions of Fourier Series 

5.4 Convergence of Fourier Series   

5.5  Convergence of Fourier Series at Discontinuities


Chapter 6 Introduction to Laplace Transform and Applications 

Chapter Learning Objectives

6.1 Introduction

6.2 Mathematical Operator of Laplace Transform

6.3 Properties of Laplace Transform

6.4 Inverse Laplace Transform

6.5 Laplace Transform of Derivatives

6.6 Solution of ODE Using Laplace Transform

6.7 Solution of Partial differential Equations Using Laplace Transform 


Chapter 7 Application of First Order Differential Equations in Engineering Analysis 

Chapter Learning Objectives

7.1 Introduction

7.2 Solution Methods for First Order Ordinary Differential Equations

7.3 Applications 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


Chapter 8 Application of Second Order Differential Equations in Mechanical Vibration Analysis

Chapter Learning Objectives

8.1 Introduction

8.2 Solution Method for Typical Homogeneous, Second Order Linear Differential Equations with Constant Coefficients

8.3 Application 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 Non-homogeneous, 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


Chapter 9  Application of Partial Differential Equations in Mechanical Engineering Analysis

Chapter Learning Objectives

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


Chapter 10 Numerical Solution Methods for Engineering Analysis

Chapter Learning Objectives

10.1 Introduction

10.2 Engineering Analysis with Numerical Solutions

10.3 Solution of Nonlinear Equations

10.4 Numerical Integration Methods

10.5  Numerical Solution Methods for Solving Differential Equations

10.6 Introduction to Numerical Analysis Software Packages


Chapter 11  Introduction to Finite Element Analysis (61 pages)

Chapter Learning Objectives

11.1 Introduction

11.2 The Principle of Finite Element Analysis

11.3 Steps in the Finite Element Analysis

11.4 Output of Finite Element Analysis

11.5 Elastic Stress Analysis of Solid Structures by Finite Element Method

11.6  General Purpose Finite Element Analysis Codes


Chapter 12  Statistics for Engineering Analysis

Chapter Learning Objectives

12.1 Introduction

12.2 Statistics in Engineering Practices

12.3 The Scope of Statistics

12.4 Common Terminologies in Statistical Analysis

12.5 Standard Deviation and Variance

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”




Appendix 1 Table for Laplace Transform

Appendix 2 Recommended Units for Engineering Analysis

Appendix 3 Conversion of Units

Appendix 4 Application of MATLAB IN Problem solving (contributed by Vaibhav Tank)

INDEX (to be developed by the appointee of the Publisher)

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Author Information

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. 

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