Mathematical analysis, 2

This two-volume work by V.A.Zorich on Mathematical Analysis constitutes a thorough first course in real analysis, leading from the most elementary facts about real numbers to such advanced topics as differential forms on manifolds, asymptotic methods, Fourier, Laplace, and Legendre transforms, and elliptic functions. With masterful exposition, the author provides a smooth, gradual transition from each topic to the next, so that the slope never feels too steep for the reader. Making use of Cartan's concept of a filter base, the author disperses the fog of epsilons and deltas that have always made the crucial subject of limits a barrier for the nonmathematical specialist. As a result, the major theorems of differentiation and integrationreveal their essential unity in a nearly painless manner. The clarity of the exposition is matched by a wealth of instructive exercises and fresh applications to areas seldom touched on in real analysis books, many of which are taken from physics and technology. TOC:Prefaces.- 9 Continuous Mappings (General Theory).- 10 Differential Calculus from a General Viewpoint.- 11 Multiple Integrals.- 12 Surfaces and Differential Forms in Rn.- 13 Line and Surface Integrals.- 14 The Elements of Vector Analysis and Field Theory.- 15 Integration of Differential Forms on Manifolds.- 16 Uniform Convergence and the Basic Operations of Analysis.- 17 Integrals Depending on a Parameter.- 18 Fourier Series and the Fourier Transform.- 19 Asymptotic Expansions.- Some Problems from the Midterm Examinations.- Examination Topics.- References.- Subject Index.- Name Index

Angaben zum Objekt

• Standort: Deutsche Nationalbibliothek Frankfurt am Main
• ISBN: 9783540406334 ; 3540406336
• Umfang: XV, 681 S.
• Sprache: Deutsch
• Anmerkungen: graph. Darst.

Verweise und Beziehungen

• Erschienen in: Mathematical analysis

Klassifikation und Themen

• Klassifikation: Mathematik

Beteiligte, Orts- und Zeitangaben

• Ereignis: Veröffentlichung
• (wo): Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo
• (wer): Springer
• (wann): (2004)
• Urheber: Zorič, Vladimir A.

Weitere Informationen

• Inhaltsverzeichnis: https://d-nb.info/968515479/04
• Rechteinformation: Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
• Letzte Aktualisierung: 11.06.2025, 13:41 MESZ