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Neoclassical Analysis: Calculus Closer to the Real World
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Authors: Mark Burgin (Univ. of California, Los Angeles) 
Book Description:
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 calculus from numerical functions to functions in metric and normed linear spaces and is presented at the end of each of the main chapters.

Table of Contents:

Chapter 1 - Introduction; pp. 1-57

Chapter 2 - Fuzzy Limits; pp. 59-159

Chapter 3 - Fuzzy Continuous Functions; pp. 161-227

Chapter 4 - Fuzzy Differentiation; pp. 229-268

Chapter 5 - Monotone and Fuzzy Monotone Functions; pp. 269-280

Chapter 6 - Fuzzy Maxima and Minima of Real Functions; pp. 281-296

Chapter 7 - Fuzzy Integration; pp. 297-316

Chapter 8 - Fuzzy Dynamical Systems; pp. 317-333

Chapter 9 - Conclusion; pp. 335-341


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   Binding: Hardcover
   Pub. Date: 2008 1st Quarter
   ISBN: 1-60021-946-2
   Status: AV
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
AV Available
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Neoclassical Analysis: Calculus Closer to the Real World