Mathematical analysis, 1

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.- 1. Some General Mathematical Concepts and Notation.- 2. The Real Numbers.- 3. Limits.- 4. Continuous Functions.- 5. Differential Calculus.- 6. Integration.- 7. Functions of Several Variables.- 8. Differential Calculus in Several Variables.- Some Problems from the Midterm Examinations.- Examination Topics.- References.- Subject Index.- Name Index

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• ISBN: 9783540403869 ; 3540403868
• Extent: XVIII, 574 S.
• Language: Deutsch
• Notes: graph. Darst.

References and Relationships

• Bibliographic citation: Mathematical analysis

Classification and Topics

• Classification: Mathematik

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Berlin, Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo
• (who): Springer
• (when): (2004)
• Creator: Zorič, Vladimir A.

Further information

• Table of contents: https://d-nb.info/968515584/04
• Rights: Bei diesem Objekt liegt nur das Inhaltsverzeichnis digital vor. Der Zugriff darauf ist unbeschränkt möglich.
• Last update: 11.03.2025, 11:55 AM CET