Mathematical analysis II / Vladimir A. Zorich.

Includes bibliographical references and indexes.

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 Elements of Vector Analysis and Field Theory.-
15 Integration of Differential Forms on Manifolds.-
16 Uniform Convergence and Basic Operations of Analysis.-
17 Integrals Depending on a Parameter.-
18 Fourier Series and the Fourier Transform.-
19 Asymptotic Expansions.-
Topics and Questions for Midterm Examinations.-
Examination Topics.-
Examination Problems (Series and Integrals Depending on a Parameter).-
Intermediate Problems (Integral Calculus of Several Variables).- Appendices:
A Series as a Tool (Introductory Lecture).-
B Change of Variables in Multiple Integrals.-
C Multidimensional Geometry and Functions of a Very Large Number of Variables.-
D Operators of Field Theory in Curvilinear Coordinates.-
E Modern Formula of Newton-Leibniz.-
References.- Index of Basic Notation.-
Subject Index.- Name Index.

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis.