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A Nonlinear Theory of Generalized Functions: 1421 (Lecture Notes in Mathematics, 1421) - Tapa blanda

Biagioni, Hebe A.

 
9783540524083: A Nonlinear Theory of Generalized Functions: 1421 (Lecture Notes in Mathematics, 1421)
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ISBN 10: 3540524088 ISBN 13: 9783540524083
Editorial: Springer, 1990

Sinopsis

This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.

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Reseña del editor

This book provides a simple introduction to a nonlinear theory of generalized functions introduced by J.F. Colombeau, which gives a meaning to any multiplication of distributions. This theory extends from pure mathematics (it presents a faithful generalization of the classical theory of C? functions and provides a synthesis of most existing multiplications of distributions) to physics (it permits the resolution of ambiguities that appear in products of distributions), passing through the theory of partial differential equations both from the theoretical viewpoint (it furnishes a concept of weak solution of pde's leading to existence-uniqueness results in many cases where no distributional solution exists) and the numerical viewpoint (it introduces new and efficient methods developed recently in elastoplasticity, hydrodynamics and acoustics). This text presents basic concepts and results which until now were only published in article form. It is in- tended for mathematicians but, since the theory and applications are not dissociated it may also be useful for physicists and engineers. The needed prerequisites for its reading are essentially reduced to the classical notions of differential calculus and the theory of integration over n-dimensional euclidean spaces.

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Editorial
Springer
Año de publicación
1990
Idioma
Inglés
ISBN 10 
3540524088
ISBN 13 
9783540524083
Encuadernación
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Número de páginas
232
Contacto del fabricante
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Otras ediciones populares con el mismo título

9780387524085: A Nonlinear Theory of Generalized Functions (Lecture Notes in Mathematics)

Edición Destacada

ISBN 10:  0387524088 ISBN 13:  9780387524085
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