DescriptionIn this comprehensive monograph, the authors apply modern mathematical methods to the study of mechanical and physical phenomena or techniques in acoustics, optics, and electrostatics, where classical mathematical tools fail.
They present a general method of approaching problems, pointing out different aspects and difficulties that may occur. With respect to the theory of distributions, only the results and the principle theorems are given as well as some mathematical results. The book also systematically deals with a large number of applications to problems of general Newtonian mechanics, as well as to problems pertaining to the mechanics of deformable solids and physics. Special attention is placed upon the introduction of corresponding mathematical models.
Addressed to a wide circle of readers who use mathematical methods in their work: applied mathematicians, engineers in various branches, as well as physicists, while also benefiting students in various fields.
1 Introduction to the Distribution Theory 1
2 Integral Transforms of Distributions 113
3 Variational Calculus and Differential Equations in Distributions 151
4 Representation in Distributions of Mechanical and Physical Quantities 201
5 Applications of the Distribution Theory in Mechanics 241
6 Applications of the Distribution Theory to the Mechanics of the Linear Elastic Bodies 253
7 Applications of the Distribution Theory of Linear Viscoelastic Bodies 273
8 Applications of the Distribution Theory in Electrical Engineering 285
9 Applications of the Distribution Theory in the Study of Elastic Bars 301
10 Applications of the Distribution Theory in the Study of Viscoelastic Bars 343
11 Applications of the Distribution Theory in Physics 365