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.
1. Engineering Analysis - p. Page i 2. Cover - p. Page i 3. Title page - p. Page ii 4. Table of Contents - p. Page iii 5. Copyright - p. Page iii 6. Contents - p. Page v 7. Dedication - p. Page v 8. About the Author - p. Page vi 9. Acknowledgments - p. Page vii 10. Preface - p. Page viii 11. List of Illustrations - p. Page xii 12. List of Tables - p. Page xiii 13. Chapter 1 : Ordinary Differential Equations and Power Series Solutions - p. Page xiii 14. Chapter 2 : The Frobenius Method - p. Page 34 15. Chapter 3 : The Laplace Transform Method - p. Page 63 16. Chapter 4 : Numerical Solutions of Ordinary Differential Equations - p. Page 109 17. Chapter 5 : Fourier Series - p. Page 153 18. Chapter 6 : Fourier Transforms - p. Page 192 19. Chapter 7 : Partial Differential Equations in Engineering - p. Page 212 20. Chapter 8 : Separation of Variables Method - p. Page 246 21. Chapter 9 : Separation of Variables Method—Circular and Spherical Regions - p. Page 307 22. Chapter 10 : Integral Transform Methods - p. Page 344 23. Chapter 11 : The Finite Difference Method - p. Page 364 24. Chapter 12 : Cartesian Tensors - p. Page 393 25. Chapter 13 : Tensor Analysis - p. Page 432 26. Bibliography - p. Page 460 27. Index - p. Page 460
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.
1. Engineering Analysis - p. Page i 2. Cover - p. Page i 3. Title page - p. Page ii 4. Table of Contents - p. Page iii 5. Copyright - p. Page iii 6. Contents - p. Page v 7. Dedication - p. Page v 8. About the Author - p. Page vi 9. Acknowledgments - p. Page vii 10. Preface - p. Page viii 11. List of Illustrations - p. Page xii 12. List of Tables - p. Page xiii 13. Chapter 1 : Ordinary Differential Equations and Power Series Solutions - p. Page xiii 14. Chapter 2 : The Frobenius Method - p. Page 34 15. Chapter 3 : The Laplace Transform Method - p. Page 63 16. Chapter 4 : Numerical Solutions of Ordinary Differential Equations - p. Page 109 17. Chapter 5 : Fourier Series - p. Page 153 18. Chapter 6 : Fourier Transforms - p. Page 192 19. Chapter 7 : Partial Differential Equations in Engineering - p. Page 212 20. Chapter 8 : Separation of Variables Method - p. Page 246 21. Chapter 9 : Separation of Variables Method—Circular and Spherical Regions - p. Page 307 22. Chapter 10 : Integral Transform Methods - p. Page 344 23. Chapter 11 : The Finite Difference Method - p. Page 364 24. Chapter 12 : Cartesian Tensors - p. Page 393 25. Chapter 13 : Tensor Analysis - p. Page 432 26. Bibliography - p. Page 460 27. Index - p. Page 460
