Concepts Of Real Analysis
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Concepts Of Real Analysis
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Author : R.D. Sarma
language : en
Publisher: Sultan Chand & Sons
Release Date : 2022-11-01
Concepts Of Real Analysis written by R.D. Sarma and has been published by Sultan Chand & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-01 with Education categories.
Concepts of Real Analysis is a student friendly text book on real analysis, a topic taught as part of the undergraduate mathematics syllabus of pass and honours courses of all Indian universities. All the relevant topics of real analysis such as real numbers, sequences and series, limit, continuity, derivatives, Riemann Integration, improper integration, sequence and series of functions, power series etc. are covered in a lucid manner in the book. Each concept is explained with the help of solved examples. Remarks are provided whenever special attention is required about some aspects of a definition or of a result. Diagrams and graphs are provided for further comprehension of a topic or a result, whenever felt necessary. Illustrative examples are provided at the end of each topic, which is followed by exercises. Overall, it is a complete-in-itself book on real analysis, suitable for students and teachers alike. Salient Features 1. Covers the entire syllabus of Real Analysis taught in the undergraduate level courses including B.Sc. (H), B.A. (Prog.), and B.Sc. (Prog.) of all Indian Universities. 2. Written in simple language. 3. Emphasis on logical, step-by-step development of proofs. 4. More than 450 solved examples and 50 diagrams. 5. Sufficient explanations are provided for the concepts introduced and results provided. 6. Remarks are provided to highlight any special aspect of a definition or a result, which might go unnoticed by the readers. 7. Student-friendly approach. 8. Appendix is added to provide the basics for curve tracing.
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.
Concepts Of Real Analysis
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Author : C. A. Hayes
language : en
Publisher: John Wiley & Sons
Release Date : 1964-01-15
Concepts Of Real Analysis written by C. A. Hayes and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1964-01-15 with Mathematics categories.
Elements Of Real Analysis
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Author : Denlinger
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2010-05-08
Elements Of Real Analysis written by Denlinger 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 2010-05-08 with Mathematics categories.
Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage. In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.
An Introduction To Real Analysis
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Author : Derek G. Ball
language : en
Publisher: Elsevier
Release Date : 2014-05-17
An Introduction To Real Analysis written by Derek G. Ball and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-17 with Mathematics categories.
An Introduction to Real Analysis presents the concepts of real analysis and highlights the problems which necessitate the introduction of these concepts. Topics range from sets, relations, and functions to numbers, sequences, series, derivatives, and the Riemann integral. This volume begins with an introduction to some of the problems which are met in the use of numbers for measuring, and which provide motivation for the creation of real analysis. Attention then turns to real numbers that are built up from natural numbers, with emphasis on integers, rationals, and irrationals. The chapters that follow explore the conditions under which sequences have limits and derive the limits of many important sequences, along with functions of a real variable, Rolle's theorem and the nature of the derivative, and the theory of infinite series and how the concepts may be applied to decimal representation. The book also discusses some important functions and expansions before concluding with a chapter on the Riemann integral and the problem of area and its measurement. Throughout the text the stress has been upon concepts and interesting results rather than upon techniques. Each chapter contains exercises meant to facilitate understanding of the subject matter. This book is intended for students in colleges of education and others with similar needs.
Real Analysis
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Author :
language : en
Publisher: Ram Prasad Publications(R.P.H.)
Release Date :
Real Analysis written by and has been published by Ram Prasad Publications(R.P.H.) this book supported file pdf, txt, epub, kindle and other format this book has been release on with Juvenile Fiction categories.
• Introductory Concepts 1. Axiomatic Study of Real Numbers (Completeness Property in R, Archimedian Property, Countable and Uncountable Sets) 2. Neighborhood, Interior Points, Limit Points, Open and Closed Sets, Derived Sets, Dense Sets, Perfect Sets, Bolzano-Weierstrass Theorem 3. Sequences of Real Numbers, Sub-Sequences, Bounded and Monotonic Sequences, Convergent Sequences, Cauchy's Theorems on Limits, Cauchy's General Principle of Convergence 4. Uniform Convergence of Sequences and Series of Functions, Weierstrass M-Test, Abel's and Dirichlet's Tests 5. Sequential Continuity, Boundedness and Intermediate Value Properties of Continuous Functions, Uniform Continuity, Meaning of Sign of Derivative, Darboux Theorem 6. Limit and Continuity of Functions of Two Variables 7. Taylor's Theorem for Functions of Two Variables 8. Maxima and Minima of Functions of Three Variables, Lagrange's Method of Undetermined Multipliers 9. Riemann Integral, Integrability of Continuous and Monotonic Function, the Fundamental Theorem of Integral Calculus, Mean Value Theorems of Integral Calculus 10.The Riemann-Stieltjes Integral 11. Improper Integrals and their Convergence, Comparison Test, µ-test, Abel's Test, Dirichlet's Test 12. Metric Spaces, Neighborhoods, Interior Points, Limit Points, Open and Closed Sets, Subspaces 13. Convergent and Cauchy Sequences, Completeness, Cantor's Intersection Theorem
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.
Real Analysis
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Author : A. Shabazz
language : en
Publisher: Trafford Publishing
Release Date : 2006
Real Analysis written by A. Shabazz and has been published by Trafford Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Education categories.
You should not be intimidated by advanced calculus. It is just another logical subject, which can be tamed by a systematic, logical approach. This textbook proves it.
Real Analysis
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Author : Miklós Laczkovich
language : en
Publisher: Springer
Release Date : 2015-10-08
Real Analysis written by Miklós Laczkovich and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-08 with Mathematics categories.
Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable — systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated. In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.
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.