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Mathematical analysis (functions of one variable), part 1-2 - G.E.. Shilov

 
Title: Mathematical analysis (functions of one variable), part 1-2
Author: G.E.. Shilov
Category: Mathematics
Type: The Book
Date: 12.01.2009 13:12:55
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Description: The book is a textbook at the rate of mathematical analysis. It is not a textbook and should not be official programmes course of mathematical analysis, although formally the basic knowledge of analysis is not intended. The book is designed primarily for students who are already familiar with the elements of differential and integral calculus and wish to deepen their knowledge. In chapter 13. 1 gives an axiomatic construction of the theory of real numbers. In chapter 13. 2 sets out the elements of theory of sets and theory of mathematical structures. Ch. 3 is devoted to metric spaces. In chapter 13. 4 is being constructed a general theory of limits, using a simplified scheme of filter Cartan. In chapter 13. 5 examines the concept of continuity and studied elementary transcendental functions. In chapter 13. 6 presents the theory of series of numerical and functional. Ch. 7-8 actually devoted to differential calculus, and ch. 9-the integral calculus. Ch. 10 introduces the reader to the theory of analytic functions; its methods are used, in particular, in ch. 11 of improper integrals.
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