Neoclassical Analysis:
Calculus Closer to the Real World by Mark Burgin
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About this book :-
Neoclassical Analysis: Calculus Closer to the Real World written by
Mark Burgin
Calculus Made Easy
Neoclassical analysis extends methods of classical calculus to reflect uncertainties that arise in computations and measurements. In it, ordinary structures of analysis, that is, functions, sequences, series, and operators, are studied by means of fuzzy concepts: fuzzy limits, fuzzy continuity, and fuzzy derivatives. For example, continuous functions, which are studied in the classical analysis, become a part of the set of the fuzzy continuous functions studied in neoclassical analysis.
Aiming at representation of uncertainties and imprecision and extending the scope of the classical calculus and analysis, neoclassical analysis makes, at the same time, methods of the classical calculus more precise with respect to real life applications. Consequently, new results are obtained extending and even completing classical theorems. In addition, facilities of analytical methods for various applications also become more broad and efficient.
Neoclassical analysis is closely related to fuzzy set theory, set-valued analysis, and interval analysis.
The book presents the core of the neoclassical analysis on three levels in each chapter. At first, basic classical constructions of the conventional calculus, such as limits, continuous functions, derivatives, differentiable functions, and integrals, and their properties are considered. The next level gives an exposition of neoclassical, fuzzy extensions of the classical constructions for real functions and sequences, i.e., neoclassical analysis of real functions and sequences is constructed. The third level elevates elements of calculus from numerical functions to functions in metric and normed linear spaces and is presented at the end of the main chapters.
This facilitates reading of the book and makes it accessible to a wide range of readers. Even those who did not learn or forgot calculus can read this book as the beginning section of each chapter introduces the reader to the classical calculus. Even for those who studied calculus at a college or university, the expository section liberates such a reader from necessity to go from time to time to other sources. At the same time, mathematicians who know the classical calculus very well will be able to find many innovative information about a new, extended and more realistic calculus called neoclassical analysis.
It is possible to use this book for enhancing traditional courses of calculus for undergraduates, as well as for teaching separate courses for graduate and undergraduate students at colleges and universities.
At the same time, it is possible to use this book for teaching such courses as "Foundations of Calculus," "Real Analysis," and "Calculus" aimed at mathematically oriented students. Detailed proofs, formalized definitions of the main constructions combined with an informal exposition of the main ideas provide convenient opportunities to learn calculus in both classical and innovative form. In the educational context, those statements that are given without proofs can be used as homework and classwork problems.
Book Detail :-
Title: Neoclassical Analysis: Calculus Closer to the Real World
Edition:
Author(s): Mark Burgin
Publisher: Nova Science Pub Inc
Series:
Year: 2008
Pages: 409
Type: PDF
Language: English
ISBN: 1600219462,9781600219467,9781606926291
Country: US
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About Author :-
Author Mark Burgin is professor of Mathematics from Department of Mathematics, University of California, Los Angeles.
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Book Contents :-
Neoclassical Analysis: Calculus Closer to the Real World written by
Mark Burgin
cover the following topics.
1. Introduction
2. Fuzzy Limits
3. Fuzzy Continuous Functions
4. Fuzzy Differentiation
5. Monotone and Fuzzy Monotone Functions
6. Fuzzy Maxima and Minima of Real Functions
7. Fuzzy Integration
8. Fuzzy Dynamical Systems
9. Conclusion
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