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## Advanced Mathematical Methods for Engineers

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- 1st Edition - May 20, 2024
- Author: Zhihe Jin
- Language: English
- Paperback ISBN:9 7 8 - 0 - 3 2 3 - 9 5 3 9 7 - 9
- eBook ISBN:9 7 8 - 0 - 3 2 3 - 9 5 3 9 6 - 2

Engineering Analysis: Advanced Mathematical Methods for Engineers introduces graduate engineering students to the fundamental but advanced mathematics tools used in engineeri… Read more

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*Engineering Analysis: Advanced Mathematical Methods for Engineers* introduces graduate engineering students to the fundamental but advanced mathematics tools used in engineering application, especially in mechanical, aerospace, and civil engineering. Most engineering problems are described by differential equations, particularly partial differential equations (PDEs). Deformation and failure in solid structures, fluid flow, heat transfer, and mass diffusion are all governed by PDEs in general. Many physical quantities in engineering are tensors, including deformation gradient, strain rates, stresses, elastic stiffness, and thermal conductivity of composite materials. This book helps engineering graduate students develop the skills to establish the mathematical models of engineering problems and to solve the problems described by the mathematical models.

- Incorporates numerous engineering examples to help students better understand mathematical concepts and methods for developing mathematical models and finding the solutions of engineering problems
- Integrates the MATLAB computation tool with many MATLAB programs to enhance students’ ability to solve engineering problems
- Includes tensor analysis to better prepare students for advanced engineering courses such as theory of elasticity, fluid dynamics, and heat transfer. Inclusion of tensor analysis also allows a unified treatment of vector and tensor calculus

Graduate engineering students studying advanced engineering math primarily in mechanical and aerospace engineering programs / Navstem estimates the overall US academic market size at 32,000 students. The number of students taking engineering analysis/advanced math at the graduate level is estimated to be about half, or approximately 16,000 students

- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- About the Author
- Acknowledgments
- Preface
- Part I: Ordinary Differential Equations – Advanced Topics
- Chapter 1. Ordinary Differential Equations and Power Series Solutions
- Abstract
- 1.1 Review of First-Order Linear Ordinary Differential Equations
- 1.2 Review of Second-Order Linear Ordinary Differential Equations
- 1.3 Power Series Solutions
- 1.4 Legendre’s Equation and Legendre Polynomials
- 1.5 Summary
- Problems
- Chapter 2. The Frobenius Method
- Abstract
- 2.1 Ordinary Differential Equations with a Regular Singular Point
- 2.2 Frobenius Series Solutions
- 2.3 Bessel’s Equation and Bessel Functions
- 2.4 Summary
- Problems
- Chapter 3. The Laplace Transform Method
- Abstract
- 3.1 The Laplace Transform
- 3.2 Solutions of Initial Value Problems for Ordinary Differential Equations
- 3.3 The Shifting Theorems
- 3.4 Convolution and Dirac Delta Function
- 3.5 Forced Vibration of a Mass–Spring–Damper System
- 3.6 Forced Vibration of a Two-Degree-of-Freedom Mass–Spring System
- 3.7 Laplace Transform by MATLAB®
- 3.8 Summary
- Problems
- Chapter 4. Numerical Solutions of Ordinary Differential Equations
- Abstract
- 4.1 Introduction
- 4.2 Euler’s Method
- 4.3 The Runge–Kutta Method
- 4.4 Convergence and Stability of Numerical Methods
- 4.5 System of First-Order ODEs and Higher-Order ODEs
- 4.6 Boundary Value Problems: The Finite Difference Method
- 4.7 Boundary Value Problems: The Shooting Method
- 4.8 Summary
- Problems
- Part II: Fourier Analysis
- Chapter 5. Fourier Series
- Abstract
- 5.1 Fourier Series of a Function
- 5.2 Fourier Series of a Periodic Function
- 5.3 The Gibbs Phenomenon
- 5.4 Fourier Cosine and Sine Series
- 5.5 Integration and Differentiation of Fourier Series
- 5.6 Vibration of a Mass–Spring–Damper System Excited by a Periodic Force
- 5.7 Summary
- Problems
- Chapter 6. Fourier Transforms
- Abstract
- 6.1 The Fourier Integral
- 6.2 The Fourier Transform
- 6.3 Fourier Sine and Cosine Transforms
- 6.4 Fourier Transform by MATLAB®
- 6.5 Summary
- Problems
- Part III: Partial Differential Equations
- Chapter 7. Partial Differential Equations in Engineering
- Abstract
- 7.1 Partial Differential Equations
- 7.2 The Wave Equation
- 7.3 The Heat Equation
- 7.4 Laplace’s Equation
- 7.5 Partial Differential Equations in Cylindrical and Spherical Coordinates
- 7.6 Classification of Second-Order Partial Differential Equations
- 7.7 The Superposition Principle for Linear Problems
- 7.8 Wave Propagation in an Infinite String—d’Alembert’s Solution
- 7.9 Summary
- Problems
- Chapter 8. Separation of Variables Method
- Abstract
- 8.1 Free Vibration of a Finite String with Fixed Ends
- 8.2 Forced Vibration of a Finite String with Fixed Ends
- 8.3 Heat Conduction in a Finite Bar with a Convection End
- 8.4 Nonhomogeneous Heat Conduction Problems
- 8.5 Free Vibration of a Rectangular Membrane
- 8.6 Heat Conduction in a Rectangular Plate
- 8.7 Laplace’s Equation—Dirichlet Problem for a Rectangular Plate
- 8.8 Laplace’s Equation—The Neumann Problem for a Rectangular Plate
- 8.9 Sturm–Liouville Theory and Eigenfunction Expansions
- 8.10 Summary
- Problems
- Chapter 9. Separation of Variables Method—Circular and Spherical Regions
- Abstract
- 9.1 Laplace’s Equation—Dirichlet Problem for a Circular Plate
- 9.2 Laplace’s Equation—Neumann Problem for an Infinite Plate with a Circular Hole
- 9.3 Steady State Heat Conduction in a Sphere
- 9.4 Heat Conduction in an Infinite Circular Cylinder
- 9.5 Vibration of a Circular Membrane
- 9.6 Fourier–Legendre and Fourier–Bessel Series Expansions
- 9.7 Summary
- Problems
- Chapter 10. Integral Transform Methods
- Abstract
- 10.1 Heat Conduction in a Semi-infinite Bar—Laplace Transform Solution
- 10.2 Heat Conduction in an Infinite Bar—Fourier Transform Solution
- 10.3 Wave Propagation in a Semi-infinite String
- 10.4 Steady State Heat Conduction in a Semi-infinite Plate
- 10.5 Steady State Heat Conduction in a Quarter-Plane
- 10.6 Summary
- Problems
- Chapter 11. The Finite Difference Method
- Abstract
- 11.1 Laplace’s Equation
- 11.2 The Heat Equation
- 11.3 The Wave Equation
- 11.4 Summary
- Problems
- Part IV: Tensor Analysis
- Chapter 12. Cartesian Tensors
- Abstract
- 12.1 The Summation Convention
- 12.2 The Kronecker Delta and the Permutation Symbol
- 12.3 Index Notations for Vectors and Their Products
- 12.4 Transformation of Coordinates
- 12.5 Cartesian Tensors
- 12.6 Tensor Algebra
- 12.7 The Quotient Rule
- 12.8 Second-Order Tensors
- 12.9 Isotropic Tensors
- 12.10 Summary
- Problems
- Chapter 13. Tensor Analysis
- Abstract
- 13.1 Tensor Functions
- 13.2 Derivatives of Tensor Functions
- 13.3 Tensor Fields
- 13.4 The Integral Theorems
- 13.5 The Heat and Wave Equations, Revisited
- 13.6 Summary
- Problems
- Bibliography
- Index

- No. of pages: 500
- Language: English
- Edition: 1
- Published: May 20, 2024
- Imprint: Academic Press
- Paperback ISBN: 9780323953979
- eBook ISBN: 9780323953962

ZJ

Zhihe Jin is a Professor in the Department of Mechanical Engineering at the University of Maine. He obtained his Ph.D. in Engineering Mechanics from Tsinghua University in 1988. His research areas include fracture mechanics, thermal stresses, poromechanics, biomechanics and thermoelectricity. His research is mainly concerned with the mathematical theories and solutions of fracture, deformation, heat conduction, porous fluid flow and thermoelectric energy conversion efficiency. He has published more than 100 refereed journal papers and 6 book chapters. He also co-authored a textbook on fracture mechanics published in 2011 (Sun & Jin, Fracture Mechanics 1e, Elsevier). He has taught 11 undergraduate and graduate courses including Mechanical Engineering Analysis at the University of Maine.

Affiliations and expertise

Department of Mechanical Engineering, University of Maine, Maine, USARead *Engineering Analysis* on ScienceDirect