Introduction To Analysis Of The Infinite
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Introduction To Analysis Of The Infinite
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Author : Leonhard Euler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Analysis Of The Infinite written by Leonhard Euler 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 2012-12-06 with Mathematics categories.
From the preface of the author: "...I have divided this work into two books; in the first of these I have confined myself to those matters concerning pure analysis. In the second book I have explained those thing which must be known from geometry, since analysis is ordinarily developed in such a way that its application to geometry is shown. In the first book, since all of analysis is concerned with variable quantities and functions of such variables, I have given full treatment to functions. I have also treated the transformation of functions and functions as the sum of infinite series. In addition I have developed functions in infinite series..."
An Introduction To Infinite Dimensional Analysis
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Author : Giuseppe Da Prato
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-25
An Introduction To Infinite Dimensional Analysis written by Giuseppe Da Prato 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 2006-08-25 with Mathematics categories.
Based on well-known lectures given at Scuola Normale Superiore in Pisa, this book introduces analysis in a separable Hilbert space of infinite dimension. It starts from the definition of Gaussian measures in Hilbert spaces, concepts such as the Cameron-Martin formula, Brownian motion and Wiener integral are introduced in a simple way. These concepts are then used to illustrate basic stochastic dynamical systems and Markov semi-groups, paying attention to their long-time behavior.
An Introduction To Infinite Products
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Author : Charles H. C. Little
language : en
Publisher: Springer Nature
Release Date : 2022-01-10
An Introduction To Infinite Products written by Charles H. C. Little and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-10 with Mathematics categories.
This text provides a detailed presentation of the main results for infinite products, as well as several applications. The target readership is a student familiar with the basics of real analysis of a single variable and a first course in complex analysis up to and including the calculus of residues. The book provides a detailed treatment of the main theoretical results and applications with a goal of providing the reader with a short introduction and motivation for present and future study. While the coverage does not include an exhaustive compilation of results, the reader will be armed with an understanding of infinite products within the course of more advanced studies, and, inspired by the sheer beauty of the mathematics. The book will serve as a reference for students of mathematics, physics and engineering, at the level of senior undergraduate or beginning graduate level, who want to know more about infinite products. It will also be of interest to instructors who teach courses that involve infinite products as well as mathematicians who wish to dive deeper into the subject. One could certainly design a special-topics class based on this book for undergraduates. The exercises give the reader a good opportunity to test their understanding of each section.
Analysis By Its History
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Author : Ernst Hairer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-30
Analysis By Its History written by Ernst Hairer 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 2008-05-30 with Mathematics categories.
. . . that departed from the traditional dry-as-dust mathematics textbook. (M. Kline, from the Preface to the paperback edition of Kline 1972) Also for this reason, I have taken the trouble to make a great number of drawings. (Brieskom & Knorrer, Plane algebraic curves, p. ii) . . . I should like to bring up again for emphasis . . . points, in which my exposition differs especially from the customary presentation in the text books: 1. Illustration of abstract considerations by means of figures. 2. Emphasis upon its relation to neighboring fields, such as calculus of dif ferences and interpolation . . . 3. Emphasis upon historical growth. It seems to me extremely important that precisely the prospective teacher should take account of all of these. (F. Klein 1908, Eng\. ed. p. 236) Traditionally, a rigorous first course in Analysis progresses (more or less) in the following order: limits, sets, '* continuous '* derivatives '* integration. mappings functions On the other hand, the historical development of these subjects occurred in reverse order: Archimedes Cantor 1875 Cauchy 1821 Newton 1665 . ;::: Kepler 1615 Dedekind . ;::: Weierstrass . ;::: Leibniz 1675 Fermat 1638 In this book, with the four chapters Chapter I. Introduction to Analysis of the Infinite Chapter II. Differential and Integral Calculus Chapter III. Foundations of Classical Analysis Chapter IV. Calculus in Several Variables, we attempt to restore the historical order, and begin in Chapter I with Cardano, Descartes, Newton, and Euler's famous Introductio.
Introduction To Infinite Dimensional Stochastic Analysis
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Author : Zhi-yuan Huang
language : en
Publisher: Springer Science & Business Media
Release Date : 2000
Introduction To Infinite Dimensional Stochastic Analysis written by Zhi-yuan Huang 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 2000 with Mathematics categories.
This book offers a concise introduction to the rapidly expanding field of infinite dimensional stochastic analysis. It treats Malliavin calculus and white noise analysis in a single book, presenting these two different areas in a unified setting of Gaussian probability spaces. Topics include recent results and developments in the areas of quasi-sure analysis, anticipating stochastic calculus, generalised operator theory and applications in quantum physics. A short overview on the foundations of infinite dimensional analysis is given. Audience: This volume will be of interest to researchers and graduate students whose work involves probability theory, stochastic processes, functional analysis, operator theory, mathematics of physics and abstract harmonic analysis.
Functional Analysis And Infinite Dimensional Geometry
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Author : Marián J. Fabian
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-05-25
Functional Analysis And Infinite Dimensional Geometry written by Marián J. Fabian 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 2001-05-25 with Mathematics categories.
This book introduces the reader to the basic principles of functional analysis and to areas of Banach space theory that are close to nonlinear analysis and topology. In the first part, the book develops the classical theory, including weak topologies, locally convex spaces, Schauder bases, and compact operator theory. The presentation is self-contained, including many folklore results, and the proofs are accessible to students with the usual background in real analysis and topology. The second part covers topics in convexity and smoothness, finite representability, variational principles, homeomorphisms, weak compactness and more. Several results are published here for the first time in a monograph. The text can be used in graduate courses or for independent study. It includes a large number of exercises of different levels of difficulty, accompanied by hints. The book is also directed to young researchers in functional analysis and can serve as a reference book.This is an introduction to basic principles of functional analysis and to areas of Banach space theory close to nonlinear analysis and topology. The first part, which develops the classical theory, is self-contained and features a large number of exercises containing many important results. The second part covers selected topics in the theory of Banach spaces related to smoothness and topology. It is intended to be an introduction to and complement of existing books on the subject. This text may be used in graduate courses, for independent study, or as a reference book.
A Course Of Modern Analysis
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Author : E. T. Whittaker
language : en
Publisher: Cambridge University Press
Release Date : 1927
A Course Of Modern Analysis written by E. T. Whittaker 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 1927 with Mathematics categories.
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Introduction To Analysis
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Author : Edward Gaughan
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Introduction To Analysis written by Edward Gaughan 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 2009 with Mathematics categories.
"The topics are quite standard: convergence of sequences, limits of functions, continuity, differentiation, the Riemann integral, infinite series, power series, and convergence of sequences of functions. Many examples are given to illustrate the theory, and exercises at the end of each chapter are keyed to each section."--pub. desc.
An Introduction To Classical Real Analysis
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Author : Karl R. Stromberg
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-10-10
An Introduction To Classical Real Analysis written by Karl R. Stromberg 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 2015-10-10 with Mathematics categories.
This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. One significant way in which this book differs from other texts at this level is that the integral which is first mentioned is the Lebesgue integral on the real line. There are at least three good reasons for doing this. First, this approach is no more difficult to understand than is the traditional theory of the Riemann integral. Second, the readers will profit from acquiring a thorough understanding of Lebesgue integration on Euclidean spaces before they enter into a study of abstract measure theory. Third, this is the integral that is most useful to current applied mathematicians and theoretical scientists, and is essential for any serious work with trigonometric series. The exercise sets are a particularly attractive feature of this book. A great many of the exercises are projects of many parts which, when completed in the order given, lead the student by easy stages to important and interesting results. Many of the exercises are supplied with copious hints. This new printing contains a large number of corrections and a short author biography as well as a list of selected publications of the author. This classic book is a text for a standard introductory course in real analysis, covering sequences and series, limits and continuity, differentiation, elementary transcendental functions, integration, infinite series and products, and trigonometric series. The author has scrupulously avoided any presumption at all that the reader has any knowledge of mathematical concepts until they are formally presented in the book. - See more at: http://bookstore.ams.org/CHEL-376-H/#sthash.wHQ1vpdk.dpuf
Introduction To Analysis On Graphs
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Author : Alexander Grigor’yan
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-08-23
Introduction To Analysis On Graphs written by Alexander Grigor’yan 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 2018-08-23 with Mathematics categories.
A central object of this book is the discrete Laplace operator on finite and infinite graphs. The eigenvalues of the discrete Laplace operator have long been used in graph theory as a convenient tool for understanding the structure of complex graphs. They can also be used in order to estimate the rate of convergence to equilibrium of a random walk (Markov chain) on finite graphs. For infinite graphs, a study of the heat kernel allows to solve the type problem—a problem of deciding whether the random walk is recurrent or transient. This book starts with elementary properties of the eigenvalues on finite graphs, continues with their estimates and applications, and concludes with heat kernel estimates on infinite graphs and their application to the type problem. The book is suitable for beginners in the subject and accessible to undergraduate and graduate students with a background in linear algebra I and analysis I. It is based on a lecture course taught by the author and includes a wide variety of exercises. The book will help the reader to reach a level of understanding sufficient to start pursuing research in this exciting area.