Mathematical Analysis, 2E, Tom M. Apostol
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About this book :-
Mathematical Analysis, 2E written by
Tom M. Apostol .
A glance at the table of contents will reveal that this textbook treats topics in analysis at the "Advanced Calculus" level. The aim has been to provide a development of the subject which is honest, rigorous, up to date, and, at the same time, not too pedantic. The book provides a transition from elementary calculus to advanced courses in real and complex function theory, and it introduces the reader to some of the abstract thinking that pervades modern analysis.
The second edition differs from the first in many respects. Point set topology is developed in the setting of general metric spaces as well as in Euclidean n-space, and two new chapters have been added on Lebesgue integration. The material on line integrals, vector analysis, and surface integrals has been deleted. The order of some chapters has been rearranged, many sections have been completely rewritten, and several new exercises have been added.
(Tom M. Apostol)
Book Detail :-
Title: Mathematical Analysis
Author(s): Tom M. Apostol
Publisher: Addison Wesley
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About Author :-
The author Peter J. Olver is an American mathematician whose primary research interests involve the applications of symmetry and Lie groups to differential equations. He has been a full professor at the University of Minnesota since 1985 and is currently head of their mathematics department. In 2003, Olver was one of the top 234 most cited mathematicians in the world.
In 2014, Olver became a fellow of the Society for Industrial and Applied Mathematics for "developing new geometric methods for differential equations leading to applications in fluid mechanics, elasticity, quantum mechanics, and image processing.". In addition, Olver is an elected fellow of the Institute of Physics and a fellow of the American Mathematical Society.
Olver is a prolific author, having written over 200 academic papers as of 2015. Of these, 137 have appeared or will appear in major refereed journals, 46 have appeared in conference proceedings and seven have appeared as appendices and chapters in books.
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Book Contents :-
Mathematical Analysis, 2E written by
Tom M. Apostol
cover the following topics.
1. The Real and Complex Number Systems
2. Some Basic Notions of Set Theory
3. Elements of Point Set Topology
4. Limits and Continuity
6. Functions of Bounded Variation and Rectifiable Curves
7. The Riemann-Stieltjes Integral
8. Infinite Series and Infinite Products
9. Sequences of Functions Pointwise convergence of sequences of functions
10. The Lebesgue Integral
11. Fourier Series and Fourier Integrals
12. Multivariable Differential Calculus
13. Implicit Functions and Extremum Problems
14. Multiple Riemann Integrals
15. Multiple Lebesgue Integrals
16. Cauchy's Theorem and the Residue Calculus
Index of Special Symbols
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