Zorich V.A. Mathematical Analysis II

2nd Edition. — Springer, 2016. — 729 p. — (Universitext). — ISBN: 3662489910.Science has not stood still in the years since the first English edition of this book was published. For example, Fermat’s last theorem has been proved, the Poincaré conjecture is now a theorem, and the Higgs boson has been discovered. Other events in science, while not directly related to the contents of a textbook in classical mathematical analysis, have indirectly led the author to learn something new, to think over something familiar, or to extend his knowledge and understanding. All of this additional knowledge and understanding end up being useful even when one speaks about something apparently completely unrelated.
In addition to the original Russian edition, the book has been published in English, German, and Chinese. Various attentive multilingual readers have detected many errors in the text. Luckily, these are local errors, mostly misprints. They have assuredly all been corrected in this new edition.Continuous Mappings (General Theory)
Differential Calculus from a More General Point of View
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 the Basic Operations of Analysis on Series and Families of Functions
Integrals Depending on a Parameter
Fourier Series and the Fourier Transform
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)
Appendixes
Series as a Tool (Introductory Lecture)
Change of Variables in Multiple Integrals (Deduction and First Discussion of the Change of Variables Formula)
Multidimensional Geometry and Functions of a Very Large Number of Variables (Concentration of Measures and Laws of Large Numbers)
Operators of Field Theory in Curvilinear Coordinates
Modern Formula of Newton–Leibniz and the Unity of Mathematics (Final Survey)