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

Evgrafov, M.; Fedoryuk, M.

Hardcover

ISBN 10: 3540170081 ISBN 13: 9783540170082

Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1989

Über diesen Titel

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.

Details zur Ausgabe

• Verlag: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Erscheinungsdatum: 1989
• ISBN 10: 3540170081
• ISBN 13: 9783540170082
• Einband: Tapa dura
• Sprache: Englisch
• Anzahl der Seiten: 238