Green's Functions with Applications

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Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical applications in physics rather than the practical means of finding Green's functions for applications in engineering and the sciences.

Green's Functions with Applications systematically presents the various methods of deriving these useful functions. It leads readers through the process of developing Green's functions for ordinary and partial differential equations. In addition to exploring the classical problems involving the wave, heat, and Helmholtz equations, the book includes special sections on leaky modes, water waves, and absolute/convective instability.

The author gives special attention to the numerical evaluation of Green's functions. By illustrating many of the functions in the text and problem sets, he helps readers develop an intuition about the behavior of Green's function in certain problems. He also considers the questions of the computational efficiency and possible methods for accelerating the process.

With its wealth of examples and problems drawn from the literature, this book provides a treasure-trove of methods to construct and compute Green's functions. It is the most exhaustive source book of Green's functions yet available and the only one designed specifically for engineering and scientific applications.

Booknews

Realizing that based on his own experiences utilizing Green's functions alone and in conjunction with numerical solvers, he had his own ideas about how to present the material, Duffy (physics and astronomy, Howard U., Washington, D.C.) provides applied scientists and engineers with a systematic reference to the various methods available for deriving a Green's function. His goal was to create the most exhaustive source book on practical aspects of the function, so he describes every possible analytic technique rather than theory. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Since its introduction in 1828, using Green's functions has become a fundamental mathematical technique for solving boundary value problems. Most treatments, however, focus on its theory and classical applications in physics rather than the practical means of finding Green's functions for applications in engineering and the sciences. Green's Functions with Applications systematically presents the various methods of deriving these useful functions. It leads readers through the process of developing Green's functions for ordinary and partial differential equations. In addition to exploring the classical problems involving the wave, heat, and Helmholtz equations, the book includes special sections on leaky modes, water waves, and absolute/convective instability. The author gives special attention to the numerical evaluation of Green's functions. By illustrating many of the functions in the text and problem sets, he helps readers develop an intuition about the behavior of Green's function in certain problems. He also considers the questions of the computational efficiency and possible methods for accelerating the process. With its wealth of examples and problems drawn from the literature, this book provides a treasure-trove of methods to construct and compute Green's functions. It is the most exhaustive source book of Green's functions yet available and the only one designed specifically for engineering and scientific applications. Content: Some background material -- Green's functions for ordinary differential equations -- Green's functions for the wave equations -- Green's functions for the heat equation -- Green's function for the Helmholtz equation -- Appendix A: The Fourier transform -- Appendix B: The Laplace transform -- Appendix C: Bessel functions -- Appendix D: Relationship between solutions of Helmholtz's and Laplace's equations in cylindrical and spherical coordinates Since their introduction in 1828, Green's functions have become a fundamental mathematical technique for solving boundary-value problems. This book presents the various methods for deriving these functions and leads readers through the process of developing Green's functions for ordinary and partial differential equations. This text systematically presents the various methods of deriving Green's functions and leads readers through the process of developing Green's functions for ordinary and partial differential equations. It includes sections on leaky modes, water waves, and absolute/convective instability One of the fundamental problems of field theory is the construction of solutions to linear differential equations when there is a specified source and the differential equation must satisfy certain boundary conditions.