Analysis I: Integral Representations and Asymptotic Methods: 13 (Encyclopaedia of Mathematical Sciences) - Tapa blanda

 
9783642647864: Analysis I: Integral Representations and Asymptotic Methods: 13 (Encyclopaedia of Mathematical Sciences)
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ISBN 10: 3642647863 ISBN 13: 9783642647864
Editorial: Springer, 2011

Sinopsis

Infinite series, and their analogues-integral representations, became funda­ mental tools in mathematical analysis, starting in the second half of the seven­ teenth century. They have provided the means for introducing into analysis all o( the so-called transcendental functions, including those which are now called elementary (the logarithm, exponential and trigonometric functions). With their help the solutions of many differential equations, both ordinary and partial, have been found. In fact the whole development of mathematical analysis from Newton up to the end of the nineteenth century was in the closest way connected with the development of the apparatus of series and integral representations. Moreover, many abstract divisions of mathematics (for example, functional analysis) arose and were developed in order to study series. In the development of the theory of series two basic directions can be singled out. One is the justification of operations with infmite series, the other is the creation oftechniques for using series in the solution of mathematical and applied problems. Both directions have developed in parallel Initially progress in the first direction was significantly smaller, but, in the end, progress in the second direction has always turned out to be of greater difficulty.

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Reseña del editor

Infinite series, and their analogues-integral representations, became funda­ mental tools in mathematical analysis, starting in the second half of the seven­ teenth century. They have provided the means for introducing into analysis all o( the so-called transcendental functions, including those which are now called elementary (the logarithm, exponential and trigonometric functions). With their help the solutions of many differential equations, both ordinary and partial, have been found. In fact the whole development of mathematical analysis from Newton up to the end of the nineteenth century was in the closest way connected with the development of the apparatus of series and integral representations. Moreover, many abstract divisions of mathematics (for example, functional analysis) arose and were developed in order to study series. In the development of the theory of series two basic directions can be singled out. One is the justification of operations with infmite series, the other is the creation oftechniques for using series in the solution of mathematical and applied problems. Both directions have developed in parallel Initially progress in the first direction was significantly smaller, but, in the end, progress in the second direction has always turned out to be of greater difficulty.

Reseña del editor

The major achievements of mathematical analysis from Newton and Euler to modern applications of mathematics in physical sciences, engineering and other areas are presented in this volume. Its three parts cover the methods of analysis: representation methods, asymptotic methods and transform methods. The authors - the well-known analysts M.A. Evgrafov and M.V. Fedoryuk - have not simply presented a compendium of techniques but have stressed throughout the underlying unity of the various methods. The fundamental ideas are clearly presented and illustrated with interesting and non-trivial examples. References, together with guides to the literature, are provided for those readers who wish to go further.

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Editorial
Springer
Año de publicación
2011
Idioma
Inglés
ISBN 10 
3642647863
ISBN 13 
9783642647864
Encuadernación
Tapa blanda
Número de páginas
252
Editor
Gamkrelidze Revaz V.
Contacto del fabricante
no disponible
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Otras ediciones populares con el mismo título

9780387170084: Analysis I: Integral Representations and Asymptotic Methods: 001 (Encyclopaedia of Mathematical Sciences)

Edición Destacada

ISBN 10:  0387170081 ISBN 13:  9780387170084
Editorial: Springer Verlag, 1989
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