Essential Real Analysis
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Essential Real Analysis
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Author : Michael Field
language : en
Publisher: Springer
Release Date : 2017-11-06
Essential Real Analysis written by Michael Field and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-06 with Mathematics categories.
This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.
Basic Real Analysis
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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-04
Basic Real Analysis written by Anthony W. Knapp 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 2007-10-04 with Mathematics categories.
Systematically develop the concepts and tools that are vital to every mathematician, whether pure or applied, aspiring or established A comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics Included throughout are many examples and hundreds of problems, and a separate 55-page section gives hints or complete solutions for most.
Elements Of Real Analysis
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Author : Charles Denlinger
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2011
Elements Of Real Analysis written by Charles Denlinger and has been published by Jones & Bartlett Learning this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
A student-friendly guide to learning all the important ideas of elementary real analysis, this resource is based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors.
Core Concepts In Real Analysis
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Author : Roshan Trivedi
language : en
Publisher: Educohack Press
Release Date : 2025-02-20
Core Concepts In Real Analysis written by Roshan Trivedi 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.
"Core Concepts in Real Analysis" is a comprehensive book that delves into the fundamental concepts and applications of real analysis, a cornerstone of modern mathematics. Written with clarity and depth, this book serves as an essential resource for students, educators, and researchers seeking a rigorous understanding of real numbers, functions, limits, continuity, differentiation, integration, sequences, and series. The book begins by laying a solid foundation with an exploration of real numbers and their properties, including the concept of infinity and the completeness of the real number line. It then progresses to the study of functions, emphasizing the importance of continuity and differentiability in analyzing mathematical functions. One of the book's key strengths lies in its treatment of limits and convergence, providing clear explanations and intuitive examples to help readers grasp these foundational concepts. It covers topics such as sequences and series, including convergence tests and the convergence of power series. The approach to differentiation and integration is both rigorous and accessible, offering insights into the calculus of real-valued functions and its applications in various fields. It explores techniques for finding derivatives and integrals, as well as the relationship between differentiation and integration through the Fundamental Theorem of Calculus. Throughout the book, readers will encounter real-world applications of real analysis, from physics and engineering to economics and computer science. Practical examples and exercises reinforce learning and encourage critical thinking. "Core Concepts in Real Analysis" fosters a deeper appreciation for the elegance and precision of real analysis while equipping readers with the analytical tools needed to tackle complex mathematical problems. Whether used as a textbook or a reference guide, this book offers a comprehensive journey into the heart of real analysis, making it indispensable for anyone interested in mastering this foundational branch of mathematics.
Real Analysis Theory Of Measure And Integration 3rd Edition
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Author : James J Yeh
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-06-11
Real Analysis Theory Of Measure And Integration 3rd Edition written by James J Yeh and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-11 with Mathematics categories.
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped. The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.The book is also very helpful to graduate students in statistics and electrical engineering, two disciplines that apply measure theory.
Advanced Real Analysis
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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-07-27
Advanced Real Analysis written by Anthony W. Knapp 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 2005-07-27 with Mathematics categories.
* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician
Real Analysis
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Author : Daniel W. Cunningham
language : en
Publisher: CRC Press
Release Date : 2021-01-19
Real Analysis written by Daniel W. Cunningham and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-19 with Mathematics categories.
Typically, undergraduates see real analysis as one of the most difficult courses that a mathematics major is required to take. The main reason for this perception is twofold: Students must comprehend new abstract concepts and learn to deal with these concepts on a level of rigor and proof not previously encountered. A key challenge for an instructor of real analysis is to find a way to bridge the gap between a student’s preparation and the mathematical skills that are required to be successful in such a course. Real Analysis: With Proof Strategies provides a resolution to the "bridging-the-gap problem." The book not only presents the fundamental theorems of real analysis, but also shows the reader how to compose and produce the proofs of these theorems. The detail, rigor, and proof strategies offered in this textbook will be appreciated by all readers. Features Explicitly shows the reader how to produce and compose the proofs of the basic theorems in real analysis Suitable for junior or senior undergraduates majoring in mathematics.
Essential Mathematics For Economics
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Author : Alexis Akira Toda
language : en
Publisher: CRC Press
Release Date : 2024-10-08
Essential Mathematics For Economics written by Alexis Akira Toda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-08 with Business & Economics categories.
Essential Mathematics for Economics covers mathematical topics that are essential for economic analysis in a concise but rigorous fashion. The book covers selected topics such as linear algebra, real analysis, convex analysis, constrained optimization, dynamic programming, and numerical analysis in a single volume. The book is entirely self-contained, and almost all propositions are proved. Features Replete with exercises and illuminating examples Suitable as a primary text for an advanced undergraduate or postgraduate course on mathematics for economics Basic linear algebra and real analysis are the only prerequisites. Supplementary materials such as Matlab codes, teaching slides etc. are posted on the book website https://github.com/alexisakira/EME.
Basic Real Analysis
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Author : Howland
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2009-09-21
Basic Real Analysis written by Howland and has been published by Jones & Bartlett Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-21 with Mathematics categories.
Ideal for the one-semester undergraduate course, Basic Real Analysis is intended for students who have recently completed a traditional calculus course and proves the basic theorems of Single Variable Calculus in a simple and accessible manner. It gradually builds upon key material as to not overwhelm students beginning the course and becomes more rigorous as they progresses. Optional appendices on sets and functions, countable and uncountable sets, and point set topology are included for those instructors who wish include these topics in their course. The author includes hints throughout the text to help students solve challenging problems. An online instructor's solutions manual is also available.
The Real Numbers And Real Analysis
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Author : Ethan D. Bloch
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-05-14
The Real Numbers And Real Analysis written by Ethan D. Bloch 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 2011-05-14 with Mathematics categories.
This text is a rigorous, detailed introduction to real analysis that presents the fundamentals with clear exposition and carefully written definitions, theorems, and proofs. It is organized in a distinctive, flexible way that would make it equally appropriate to undergraduate mathematics majors who want to continue in mathematics, and to future mathematics teachers who want to understand the theory behind calculus. The Real Numbers and Real Analysis will serve as an excellent one-semester text for undergraduates majoring in mathematics, and for students in mathematics education who want a thorough understanding of the theory behind the real number system and calculus.