Duffy, Dean G. Green’s Functions with Applications

McGraw-Hill, 1993. - 348 pages. Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. It will primarily be used by students with a background in ordinary differential equations and advanced calculus. There are two main objectives of this text. The first is to introduce the conce...

Academic Press, 1978. - 343 Pages. This book is mainly about four functions denoted by r, R, S, and 2 F 0 . The first is the gamma function, Euler's extension of the factorial function 11! to nonintegral values of 11. The other three are hypergeometric functions and embrace as special cases the functions named after Bessel, Hankel, Legendre, Gauss, Kummer, Whittaker, Jacobi, Chebyshev, Gegenbauer, Laguerre, Hermite, and others. The R function u...

Cambridge University Press 2002 169 pages This book presents a functional approach to the construction, use and approximation of Green’s function, the author discusses new solutions to problems involving particle production in crossed laser fields and non-constant electric fields. Applications to problems in potential theory and quantum field theory are covered, along with approximations for the treatment of color fluctuations in high-energy QCD...

Prentice Hall, 1987. - 532 p. This text discusses elementary partial differential equations in the engineering and physical sciences. It is suited for courses whose titles include Fourier series, orthogonal functions, or boundary value problems. It may also be used in courses on Green's functions or transform methods. Simple models (heat flow, vibrating strings and membranes) are emphasized. Equations are formulated carefully from physical princi...

Sрringer, 2005. - 512 pages. This book, dedicated to Mizan Rahman, is made up of a collection of articles on various aspects of q-series and special functions. Also, it includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject. Audience This book is intended for researchers and graduate students in special functions, algebraic combinatorics, quantum groups...

Cambridge University Press , 2011. - 232 pages. This book is ideal for engineering, physical science, and applied mathematics students and professionals who want to enhance their mathematical knowledge. Advanced Topics in Applied Mathematics covers four essential applied mathematics topics: Green's functions, Integral equations, Fourier transforms, and Laplace transforms. Also included is a useful discussion of topics such as the Wiener-Hopf me...

Walter de Gruyter, 1993. - 216 pages. Contains three chapters titled: Homogeneous Functions, Fourier Transformation, and Contact Structures; Fourier-Maslov Operators; and Applications to Differential Equations.

Publisher: Birkh?usеr, Bоston, 1988, 427 pages Authors of this book have collected the material on special functions that is most important in mathematical physics and quantum mechanics. They have not attempted to provide the most extensive collection possible of information about special functions, but have set ourselves the task of finding an exposition which, based on a unified approach, ensures the possibility of applying the theory in other...

American Mathematical Society, 2011. - 526 pages. Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems-rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the...

Society for Industrial Mathematics, 1987. - 748 pages. For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problem...