Linear Partial Differential Equations for Scientists and Engineers

Description

One of the most fundamental and active areas in mathematics, the theory of partial differential equations (PDEs) is essential in the modeling of natural phenomena. PDEs have a wide range of interesting and important applications in every branch of applied mathematics, physics, and engineering, including fluid dynamics, elasticity, and optics. This significantly expanded fourth edition is designed as an introduction to the theory and applications of linear PDEs. The authors provide fundamental concepts, underlying principles, a wide range of applications, and various methods of solutions to PDEs. In addition to essential standard material on the subject, the book contains new material that is not usually covered in similar texts and reference books, including conservation laws, the spherical wave equation, the cylindrical wave equation, higher-dimensional boundary-value problems, the finite element method, fractional partial differential equations, and nonlinear partial differential equations with applications. Key features include: * Applications to a wide variety of physical problems in numerous interdisciplinary areas * Over 900 worked examples and exercises dealing with problems in fluid mechanics, gas dynamics, optics, plasma physics, elasticity, biology, and chemistry * Historical comments on partial differential equations * Solutions and hints to selected exercises * A comprehensive bibliography—comprised of many standard texts and reference books, as well as a set of selected classic and recent papers—for readers interested in learning more about the modern treatment of the subject Linear Partial Differential Equations for Scientists and Engineers, Fourth Edition will primarily serve as a textbook for the first two courses in PDEs, or in a course on advanced engineering mathematics. The book may also be used as a reference for graduate students, researchers, and professionals in modern applied mathematics, mathematical physics, and engineering. Readers will gain a solid mathematical background in PDEs, sufficient to start interdisciplinary collaborative research in a variety of fields. Also by L. Debnath: Nonlinear Partial Differential Equations for Scientists and Engineers, Second Edition, ISBN 0-8176-4323-0.   Linear Partial Differential Equations for Scientists and Engineers......Page 2 Contents......Page 7 Preface to the Fourth Edition......Page 13 Preface to the Third Edition......Page 17 1 Introduction......Page 21 2 First-Order, Quasi-Linear Equations and Method of Characteristics......Page 47 3 Mathematical Models......Page 83 4 Classification of Second-Order Linear Equations......Page 111 5 The Cauchy Problem and Wave Equations......Page 137 6 Fourier Series and Integrals with Applications......Page 187 7 Method of Separation of Variables......Page 251 8 Eigenvalue Problems and Special Functions......Page 293 9 Boundary-Value Problems and Applications......Page 349 10 Higher-Dimensional Boundary-Value Problems......Page 381 11 Green’s Functions and Boundary-Value Problems......Page 427 12 Integral Transform Methods with Applications......Page 459 13 Nonlinear Partial Differential Equations with Applications......Page 555 14 Numerical and Approximation Methods......Page 621 15 Tables of Integral Transforms......Page 701 Answers and Hints to Selected Exercises......Page 717 Appendix: Some Special Functions and Their Properties......Page 769 Bibliography......Page 780 Index......Page 790