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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.

Engineering. --- Appl.Mathematics/Computational Methods of Engineering. --- Theoretical and Applied Mechanics. --- Integral Transforms, Operational Calculus. --- Integral Transforms. --- Engineering mathematics. --- Mechanics, applied. --- Ingénierie --- Mathématiques de l'ingénieur --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Applied Mathematics --- Civil Engineering --- Integral transforms. --- Green's functions. --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Transform calculus --- Operational calculus. --- Applied mathematics. --- Mechanics. --- Mechanics, Applied. --- Integral equations --- Transformations (Mathematics) --- Differential equations --- Potential theory (Mathematics) --- Mathematical and Computational Engineering. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Engineering --- Engineering analysis --- Mathematical analysis --- Mathematics --- Operational calculus --- Electric circuits --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Mathematical analysis. --- Mathematical and Computational Engineering Applications. --- Engineering Mechanics. --- Integral Transforms and Operational Calculus. --- Data processing. --- 517.1 Mathematical analysis