Mathematical Analysis – Tom Apostol – 2nd Edition


In this new edition, of a more modern spirit than the first excellent one, one can repeat the praise that was made previously: its precise and rigorous style, in a program balanced but sufficiently broad, gives character of basic text.
It contains topics such as the of real and numbers; Some basic notions of set theory; Elements of topology in sets of points; Limits and continuity; Derivatives; of bounded variation and rectifiable curves; The Riemann-Stieltjes integral; Infinite series and infinite products; Inheritance of functions; The Lebesgue integral; series and Fourier integrals; Differential of several variables. Implicit and extreme problems; of Riemann; Multiple Lebesgue integrals; Cauchy’s theorem and residual calculus.

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Table of Contents

The system of real numbers and complex numbers
Some Basics of Set Theory
Topology elements in point sets
Limits and continuity
Functions of bounded variation and rectifiable curves
The Riemann Stieltjes Integral
Infinite series and infinite products
Functional successions
The Lebesgue integral
Fourier series and Fourier integrals
Implicit functions and extreme problems
The inverse function theorem
Conditioned End Issues
Multiple Lebesgue integrals
Cauchy Theorem and Residual Calculus

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