Foundations Of Mathematical Analysis
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Foundations Of Mathematical Analysis
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Author : Richard Johnsonbaugh
language : en
Publisher: Courier Corporation
Release Date : 2002-01-01
Foundations Of Mathematical Analysis written by Richard Johnsonbaugh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-01-01 with Mathematics categories.
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises. 1981 edition. Includes 34 figures.
Foundations Of Mathematical Analysis
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Author : Saminathan Ponnusamy
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-17
Foundations Of Mathematical Analysis written by Saminathan Ponnusamy 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 2011-12-17 with Mathematics categories.
Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-contained textbook consists of eleven chapters, which are further divided into sections and subsections. Each section includes a careful selection of special topics covered that will serve to illustrate the scope and power of various methods in real analysis. The exposition is developed with thorough explanations, motivating examples, exercises, and illustrations conveying geometric intuition in a pleasant and informal style to help readers grasp difficult concepts. Foundations of Mathematical Analysis is intended for undergraduate students and beginning graduate students interested in a fundamental introduction to the subject. It may be used in the classroom or as a self-study guide without any required prerequisites.
Foundations Of Real And Abstract Analysis
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Author : Douglas S. Bridges
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Foundations Of Real And Abstract Analysis written by Douglas S. Bridges 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 2006-04-06 with Mathematics categories.
A complete course on metric, normed, and Hilbert spaces, including many results and exercises seldom found in texts on analysis at this level. The author covers an unusually wide range of material in a clear and concise format, including elementary real analysis, Lebesgue integration on R, and an introduction to functional analysis. The book begins with a fast-paced course on real analysis, followed by an introduction to the Lebesgue integral. This provides a reference for later chapters as well as a preparation for students with only the typical sequence of undergraduate calculus courses as prerequisites. Other features include a chapter introducing functional analysis, the Hahn-Banach theorem and duality, separation theorems, the Baire Category Theorem, the Open Mapping Theorem and their consequences, and unusual applications. Of special interest are the 750 exercises, many with guidelines for their solutions, applications and extensions of the main propositions and theorems, pointers to new branches of the subject, and difficult challenges for the very best students.
Real Analysis Foundations
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Author : Sergei Ovchinnikov
language : en
Publisher: Springer Nature
Release Date : 2021-02-16
Real Analysis Foundations written by Sergei Ovchinnikov and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-16 with Mathematics categories.
This textbook explores the foundations of real analysis using the framework of general ordered fields, demonstrating the multifaceted nature of the area. Focusing on the logical structure of real analysis, the definitions and interrelations between core concepts are illustrated with the use of numerous examples and counterexamples. Readers will learn of the equivalence between various theorems and the completeness property of the underlying ordered field. These equivalences emphasize the fundamental role of real numbers in analysis. Comprising six chapters, the book opens with a rigorous presentation of the theories of rational and real numbers in the framework of ordered fields. This is followed by an accessible exploration of standard topics of elementary real analysis, including continuous functions, differentiation, integration, and infinite series. Readers will find this text conveniently self-contained, with three appendices included after the main text, covering an overview of natural numbers and integers, Dedekind's construction of real numbers, historical notes, and selected topics in algebra. Real Analysis: Foundations is ideal for students at the upper-undergraduate or beginning graduate level who are interested in the logical underpinnings of real analysis. With over 130 exercises, it is suitable for a one-semester course on elementary real analysis, as well as independent study.
Foundations Of Analysis
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Author : Joseph L. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Foundations Of Analysis written by Joseph L. Taylor 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 2012 with Mathematics categories.
Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.
Foundations Of Mathematical Analysis
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Author : J. K. Truss
language : en
Publisher: Oxford University Press
Release Date : 1997
Foundations Of Mathematical Analysis written by J. K. Truss and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Foundations of Mathematical Analysis covers a wide variety of topics that will be of great interest to students of pure mathematics or mathematics and philosophy. Aimed principally at graduate and advanced undergraduate students, its primary goal is to discuss the fundamental number systems, N, Z, Q, R, and C, in the context of the branches of mathematics for which they form a starting point; for example, a study of the natural numbers leads on to logic (via Gödel's theorems), and of the real numbers (as constructed by Cauchy) to metric spaces and topology. The author offers a refreshingly original and accessible approach, presenting standard material in new ways and incorporating less mainstream topics such as long real and rational lines and the p-adic numbers. With a discussion of constructivism and independence questions, including Suslin's problem and the continuum hypothesis, the author completes a wide-ranging consideration of the development of mathematics from the very beginning, concentrating on the foundational issues particularly related to analysis.
Foundations Of Mathematical Analysis
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Author : Richard Johnsonbaugh
language : en
Publisher: Courier Corporation
Release Date : 2012-09-11
Foundations Of Mathematical Analysis written by Richard Johnsonbaugh and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-11 with Mathematics categories.
Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
Handbook Of Analysis And Its Foundations
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Author : Eric Schechter
language : en
Publisher: Academic Press
Release Date : 1996-10-24
Handbook Of Analysis And Its Foundations written by Eric Schechter and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-10-24 with Mathematics categories.
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/
The Development Of The Foundations Of Mathematical Analysis From Euler To Riemann
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Author : I. Grattan-Guinness
language : en
Publisher:
Release Date : 1970
The Development Of The Foundations Of Mathematical Analysis From Euler To Riemann written by I. Grattan-Guinness and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.
Foundations Of Modern Analysis
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Author : Avner Friedman
language : en
Publisher: Courier Corporation
Release Date : 1982-01-01
Foundations Of Modern Analysis written by Avner Friedman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982-01-01 with Mathematics categories.
Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.