This book describes mathematical techniques for integral transforms in a detailed but concise manner. The techniques are subsequently applied to the standard partial differential equations, such as the Laplace equation, the wave equation and elasticity equations. Green's functions for beams, plates and acoustic media are also shown, along with their mathematical derivations. The Cagniard-de Hoop method for double inversion is described in detail and 2D and 3D elastodynamic problems are treated in full.

This new edition explains in detail how to introduce the branch cut for the multi-valued square root function. Further, an exact closed form Green's function for torsional waves is presented, as well as an application technique of the complex integral, which includes the square root function and an application technique of the complex integral.

A valuable reference book for engineers Includes full descriptions of the Cagniard-de Hoop technique and the branch cut for square root functions Employs a unified mathematical technique as the solution method for the fundamental partial differential equations Includes supplementary material: sn.pub/extras

Autorentext

Professor Watanabe is retired professor (2012) of mechanical engineering; he is active member of the advisory board of Acta Mechanica and has already co-edited a book at Springer

Inhalt
Definition of integral transforms and distributions.- Green's functions for Laplace and wave equations.- Green's dyadic for an isotropic elastic solid.- Acoustic wave in an uniform flow.- Green's functions for beam and plate.- Cagniard de Hoop technique.- Miscellaneous Green's functions.- Exercises.