New Generalized Functions and Multiplication of Distributions

New Generalized Functions and Multiplication of Distributions PDF

Author: J.F. Colombeau

Publisher: Elsevier

Published: 2000-04-01

Total Pages: 374

ISBN-13: 9780080871950

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This volume presents a new mathematical theory of generalized functions, more general than Distribution Theory, giving a rigorous mathematical sense to any product of a finite number of distributions and to heuristic computations of Quantum Field Theory. Although the physical motivations are emphasized, the book is also addressed to mathematicians with no knowledge of physics. This work opens a new domain of research in both pure and applied mathematics.

Multiplication of Distributions

Multiplication of Distributions PDF

Author: Jean F. Colombeau

Publisher: Springer

Published: 2006-11-15

Total Pages: 193

ISBN-13: 3540475109

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This book presents recent and very elementary developments of a theory of multiplication of distributions in the field of explicit and numerical solutions of systems of PDEs of physics (nonlinear elasticity, elastoplasticity, hydrodynamics, multifluid flows, acoustics). The prerequisites are kept to introductory calculus level so that the book remains accessible at the same time to pure mathematicians (as a smoothand somewhat heuristic introdcution to this theory) and to applied mathematicians, numerical engineers and theoretical physicists (as a tool to treat problems involving products of distributions).

Distributions

Distributions PDF

Author: J.J. Duistermaat

Publisher: Springer Science & Business Media

Published: 2010-08-09

Total Pages: 445

ISBN-13: 0817646752

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This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.

Mathematical Methods in Engineering

Mathematical Methods in Engineering PDF

Author: Nuno Miguel Fonseca Ferreira

Publisher: Springer

Published: 2014-08-18

Total Pages: 311

ISBN-13: 9400771835

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This book presents a careful selection of the contributions presented at the Mathematical Methods in Engineering (MME10) International Symposium, held at the Polytechnic Institute of Coimbra- Engineering Institute of Coimbra (IPC/ISEC), Portugal, October 21-24, 2010. The volume discusses recent developments about theoretical and applied mathematics toward the solution of engineering problems, thus covering a wide range of topics, such as: Automatic Control, Autonomous Systems, Computer Science, Dynamical Systems and Control, Electronics, Finance and Economics, Fluid Mechanics and Heat Transfer, Fractional Mathematics, Fractional Transforms and Their Applications, Fuzzy Sets and Systems, Image and Signal Analysis, Image Processing, Mechanics, Mechatronics, Motor Control and Human Movement Analysis, Nonlinear Dynamics, Partial Differential Equations, Robotics, Acoustics, Vibration and Control, and Wavelets.

Theory of Distributions

Theory of Distributions PDF

Author: Svetlin G. Georgiev

Publisher: Springer

Published: 2015-07-13

Total Pages: 218

ISBN-13: 3319195271

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This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This book, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.

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