Differentiation Of Real Functions
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Differentiation Of Real Functions
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Author : A. M. Bruckner
language : en
Publisher: Springer
Release Date : 2006-11-15
Differentiation Of Real Functions written by A. M. Bruckner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Differentiation Of Real Functions
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Author : Andrew M. Bruckner
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Differentiation Of Real Functions written by Andrew M. Bruckner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Topics related to the differentiation of real functions have received considerable attention during the last few decades. This book provides an efficient account of the present state of the subject. Bruckner addresses in detail the problems that arise when dealing with the class $\Delta '$ of derivatives, a class that is difficult to handle for a number of reasons. Several generalized forms of differentiation have assumed importance in the solution of various problems. Some generalized derivatives are excellent substitutes for the ordinary derivative when the latter is not known to exist; others are not. Bruckner studies generalized derivatives and indicates 'geometric' conditions that determine whether or not a generalized derivative will be a good substitute for the ordinary derivative. There are a number of classes of functions closely linked to differentiation theory, and these are examined in some detail.The book unifies many important results from the literature as well as some results not previously published. The first edition of this book, which was current through 1976, has been referenced by most researchers in this subject. This second edition contains a new chapter dealing with most of the important advances between 1976 and 1993.
A Second Course On Real Functions
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Author : A. C. M. van Rooij
language : en
Publisher: Cambridge University Press
Release Date : 1982-03-25
A Second Course On Real Functions written by A. C. M. van Rooij and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-03-25 with Mathematics categories.
When considering a mathematical theorem one ought not only to know how to prove it but also why and whether any given conditions are necessary. All too often little attention is paid to to this side of the theory and in writing this account of the theory of real functions the authors hope to rectify matters. They have put the classical theory of real functions in a modern setting and in so doing have made the mathematical reasoning rigorous and explored the theory in much greater depth than is customary. The subject matter is essentially the same as that of ordinary calculus course and the techniques used are elementary (no topology, measure theory or functional analysis). Thus anyone who is acquainted with elementary calculus and wishes to deepen their knowledge should read this.
Hypernumbers And Extrafunctions
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Author : Mark Burgin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-05-16
Hypernumbers And Extrafunctions written by Mark Burgin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-16 with Mathematics categories.
“Hypernumbers and Extrafunctions” presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for solving some problems in probability theory, which is also important for contemporary physics. This book introduces a new theory that includes the theory of distributions as a subtheory, providing more powerful tools for mathematics and its applications. Specifically, it makes it possible to solve PDE for which it is proved that they do not have solutions in distributions. Also illustrated in this text is how this new theory allows the differentiation and integration of any real function. This text can be used for enhancing traditional courses of calculus for undergraduates, as well as for teaching a separate course for graduate students.
Real Analysis
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Author : Brian S. Thomson
language : en
Publisher: ClassicalRealAnalysis.com
Release Date : 2008
Real Analysis written by Brian S. Thomson and has been published by ClassicalRealAnalysis.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This is the second edition of a graduate level real analysis textbook formerly published by Prentice Hall (Pearson) in 1997. This edition contains both volumes. Volumes one and two can also be purchased separately in smaller, more convenient sizes.
Complex Analysis
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Author : Shashank Tiwari
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Complex Analysis written by Shashank Tiwari and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.
"Complex Analysis: Advanced Concepts" delves into the intricate world of complex numbers and functions, offering a thorough exploration of their properties and applications. The book begins with a detailed examination of basic concepts, covering arithmetic operations, geometric interpretations, and the fundamental theorem of algebra. It then progresses to advanced topics such as complex functions, differentiation, integration, and series. One of the book's notable strengths lies in its clear and concise explanations, accompanied by numerous examples and exercises to reinforce understanding. Readers are guided through theorems and proofs, gaining insight into the elegance and power of complex analysis. The book also highlights the relevance of complex analysis in various fields, including physics, engineering, and economics. Applications such as potential theory, fluid dynamics, and signal processing are explored, demonstrating the subject's practical significance. Whether used as a textbook for students or a reference for professionals, "Complex Analysis: Advanced Concepts" offers a valuable resource for mastering the intricacies of this essential branch of mathematics. Its comprehensive coverage and accessible style make it an indispensable addition to any mathematician's library.
Mean Value Theorems And Functional Equations
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Author : Thomas Riedel
language : en
Publisher: World Scientific
Release Date : 1998-10-30
Mean Value Theorems And Functional Equations written by Thomas Riedel and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-10-30 with Mathematics categories.
This book takes a comprehensive look at mean value theorems and their connection with functional equations. Besides the traditional Lagrange and Cauchy mean value theorems, it covers the Pompeiu and the Flett mean value theorems as well as extension to higher dimensions and the complex plane. Furthermore the reader is introduced to the field of functional equations through equations that arise in connection with the many mean value theorems discussed.
Mathematical Analysis
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Author : Elias Zakon
language : en
Publisher: The Trillia Group
Release Date : 2004-05
Mathematical Analysis written by Elias Zakon and has been published by The Trillia Group this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-05 with Mathematics categories.
The Calculus Of Complex Functions
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Author : William Johnston
language : en
Publisher: American Mathematical Society
Release Date : 2022-04-01
The Calculus Of Complex Functions written by William Johnston and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-04-01 with Mathematics categories.
The book introduces complex analysis as a natural extension of the calculus of real-valued functions. The mechanism for doing so is the extension theorem, which states that any real analytic function extends to an analytic function defined in a region of the complex plane. The connection to real functions and calculus is then natural. The introduction to analytic functions feels intuitive and their fundamental properties are covered quickly. As a result, the book allows a surprisingly large coverage of the classical analysis topics of analytic and meromorphic functions, harmonic functions, contour integrals and series representations, conformal maps, and the Dirichlet problem. It also introduces several more advanced notions, including the Riemann hypothesis and operator theory, in a manner accessible to undergraduates. The last chapter describes bounded linear operators on Hilbert and Banach spaces, including the spectral theory of compact operators, in a way that also provides an excellent review of important topics in linear algebra and provides a pathway to undergraduate research topics in analysis. The book allows flexible use in a single semester, full-year, or capstone course in complex analysis. Prerequisites can range from only multivariate calculus to a transition course or to linear algebra or real analysis. There are over one thousand exercises of a variety of types and levels. Every chapter contains an essay describing a part of the history of the subject and at least one connected collection of exercises that together comprise a project-level exploration.
Introduction To Statistical Limit Theory
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Author : Alan M. Polansky
language : en
Publisher: CRC Press
Release Date : 2011-01-07
Introduction To Statistical Limit Theory written by Alan M. Polansky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-07 with Mathematics categories.
Helping students develop a good understanding of asymptotic theory, Introduction to Statistical Limit Theory provides a thorough yet accessible treatment of common modes of convergence and their related tools used in statistics. It also discusses how the results can be applied to several common areas in the field.The author explains as much of the