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In 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.
Petre P. Teodorescu is professor at the University of Bucharest and member of the Romanian Academy of Sciences. He is president of the Section of Technical Mechanics and member of GAMM (Gesellschaft f?r Angewandte Mathematik und Mechanik). He was awarded by a prize of the Romanian Academy and is member of the editorial board of several scientific publications.
Wilhelm W. Kecs is professor at the University of Petrosani and member of GAMM (Gesellschaft f?r angewandte Mathematik und Mechanik). He published a book on "Theory of distributions with applications" (in Romanian), Romanian Academy Publishing House, 2003.
Antonela Toma is professor at university "Politehnica" Bucharest. She published a monograph on Mathematical Methods in Elasticity and Viscoelasticity (in Romanian), 2004.
Table of Contents
1 INTRODUCTION TO THE THEORY OF DISTRIBUTIONS
2 INTEGRAL TRANSFORMS OF DISTRIBUTIONS
3 VARIATIONAL CALCULUS AND DIFFERENTIAL EQUATIONS IN DISTRIBUTIONS
4 REPRESENTATION IN DISTRIBUTIONS OF MECHANICAL AND PHYSICAL QUANTITIES
5 APPLICATIONS OF THE THEORY OF DISTRIBUTIONS IN MECHANICS
6 APPLICATION OF THE THEORY OF DISTRIBUTIONS TO LINEAR ELASTIC BODIES
7 APPLICATION OF THE THEORY OF DISTRIBUTIONS TO LINEAR VISCOELASTIC BODIES
8 APPLICATIONS OF THE DISTRIBUTION THEORY IN ELECTRICAL ENGINEERING
9 APPLICATIONS OF THE THEORY OF DISTRIBUTIONS IN THE STUDY OF ELASTIC BARS
10 APPLICATIONS OF THE DISTRIBUTION THEORY IN THE STUDY OF VISCOELASTIC BARS
11 APPLICATIONS OF THE DISTRIBUTION THEORY IN PHYSICS