Mathematical Analysis II

Vladimir A. Zorich - Collection Universitext

682 pages, parution le 28/11/2003

Ajouter à une liste

Indisponible

Résumé

Mathematical Analysis vol. II

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 integration reveal 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.

Written for:
undergraduate students (beginners) in mathematics and physics

Continuous Mappings (General Theory)
Differential Calculus from a General Viewpoint
Multiple Integrals
Surfaces and Differential Forms in Rn
Line and Surface Integrals
Elements of Vector Analysis and Field Theory
Integration of Differential Forms on Manifolds
Uniform Convergence and Basic Operations of Analysis
Integrals Depending on a Parameter
Fourier Series and the Fourier Transform
Asymptotic Expansions
Topics and Questions for Midterm Examinations
Examination Topics
References
Index of Basic Notation
Subject Index
Name Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Vladimir A. Zorich
Collection	Universitext
Parution	28/11/2003
Nb. de pages	682
Format	16,5 x 24
Couverture	Broché
Poids	1150g
Intérieur	Noir et Blanc
EAN13	9783540406334