An Introduction To Analysis
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An Introduction To Analysis
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Author : Robert C. Gunning
language : en
Publisher: Princeton University Press
Release Date : 2018-03-20
An Introduction To Analysis written by Robert C. Gunning and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-20 with Mathematics categories.
An essential undergraduate textbook on algebra, topology, and calculus An Introduction to Analysis is an essential primer on basic results in algebra, topology, and calculus for undergraduate students considering advanced degrees in mathematics. Ideal for use in a one-year course, this unique textbook also introduces students to rigorous proofs and formal mathematical writing--skills they need to excel. With a range of problems throughout, An Introduction to Analysis treats n-dimensional calculus from the beginning—differentiation, the Riemann integral, series, and differential forms and Stokes's theorem—enabling students who are serious about mathematics to progress quickly to more challenging topics. The book discusses basic material on point set topology, such as normed and metric spaces, topological spaces, compact sets, and the Baire category theorem. It covers linear algebra as well, including vector spaces, linear mappings, Jordan normal form, bilinear mappings, and normal mappings. Proven in the classroom, An Introduction to Analysis is the first textbook to bring these topics together in one easy-to-use and comprehensive volume. Provides a rigorous introduction to calculus in one and several variables Introduces students to basic topology Covers topics in linear algebra, including matrices, determinants, Jordan normal form, and bilinear and normal mappings Discusses differential forms and Stokes's theorem in n dimensions Also covers the Riemann integral, integrability, improper integrals, and series expansions
An Introduction To Analysis
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Author : Gerald Bilodeau
language : en
Publisher: Jones & Bartlett Learning
Release Date : 2010
An Introduction To Analysis written by Gerald Bilodeau 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 2010 with Mathematics categories.
This book presents a concise and sharpley focused introduction to the basic concepts of analysis - from the development of real numbers through uniform convergences of a sequence of functions - and includes coverage both of the analysis of functions of more than one variable and of differential equations. Examples and figures are used extensively to assist the reader in understanding the concepts and then applying them.
An Introduction To Analysis
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Author : James R. Kirkwood
language : en
Publisher: CRC Press
Release Date : 2021-08-15
An Introduction To Analysis written by James R. Kirkwood and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-15 with Mathematics categories.
The third edition of this widely popular textbook is authored by a master teacher. This book provides a mathematically rigorous introduction to analysis of realvalued functions of one variable. This intuitive, student-friendly text is written in a manner that will help to ease the transition from primarily computational to primarily theoretical mathematics. The material is presented clearly and as intuitive as possible while maintaining mathematical integrity. The author supplies the ideas of the proof and leaves the write-up as an exercise. The text also states why a step in a proof is the reasonable thing to do and which techniques are recurrent. Examples, while no substitute for a proof, are a valuable tool in helping to develop intuition and are an important feature of this text. Examples can also provide a vivid reminder that what one hopes might be true is not always true. Features of the Third Edition: Begins with a discussion of the axioms of the real number system. The limit is introduced via sequences. Examples motivate what is to come, highlight the need for hypothesis in a theorem, and make abstract ideas more concrete. A new section on the Cantor set and the Cantor function. Additional material on connectedness. Exercises range in difficulty from the routine "getting your feet wet" types of problems to the moderately challenging problems. Topology of the real number system is developed to obtain the familiar properties of continuous functions. Some exercises are devoted to the construction of counterexamples. The author presents the material to make the subject understandable and perhaps exciting to those who are beginning their study of abstract mathematics. Table of Contents Preface Introduction The Real Number System Sequences of Real Numbers Topology of the Real Numbers Continuous Functions Differentiation Integration Series of Real Numbers Sequences and Series of Functions Fourier Series Bibliography Hints and Answers to Selected Exercises Index Biography James R. Kirkwood holds a Ph.D. from University of Virginia. He has authored fifteen, published mathematics textbooks on various topics including calculus, real analysis, mathematical biology and mathematical physics. His original research was in mathematical physics, and he co-authored the seminal paper in a topic now called Kirkwood-Thomas Theory in mathematical physics. During the summer, he teaches real analysis to entering graduate students at the University of Virginia. He has been awarded several National Science Foundation grants. His texts, Elementary Linear Algebra, Linear Algebra, and Markov Processes, are also published by CRC Press.
An Introduction To Analysis
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Author : Jan Mikusiński
language : en
Publisher:
Release Date : 2017
An Introduction To Analysis written by Jan Mikusiński and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017 with categories.
An Introduction To Analysis
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Author : Piotr Mikusinski
language : en
Publisher: World Scientific Publishing Company
Release Date : 2017
An Introduction To Analysis written by Piotr Mikusinski 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 2017 with Calculus categories.
The book contains a rigorous exposition of calculus of a single real variable. It covers the standard topics of an introductory analysis course, namely, functions, continuity, differentiability, sequences and series of numbers, sequences and series of functions, and integration. A direct treatment of the Lebesgue integral, based solely on the concept of absolutely convergent series, is presented, which is a unique feature of a textbook at this level. The standard material is complemented by topics usually not found in comparable textbooks, for example, elementary functions are rigorously defined and their properties are carefully derived and an introduction to Fourier series is presented as an example of application of the Lebesgue integral.The text is for a post-calculus course for students majoring in mathematics or mathematics education. It will provide students with a solid background for further studies in analysis, deepen their understanding of calculus, and provide sound training in rigorous mathematical proof.
An Introduction To Analysis
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Author : Gerald G. Bilodeau
language : en
Publisher: Jones & Bartlett Publishers
Release Date : 2009-07-28
An Introduction To Analysis written by Gerald G. Bilodeau 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 2009-07-28 with Mathematics categories.
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An Introduction To Mathematical Analysis
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Author : Robert A. Rankin
language : en
Publisher: Elsevier
Release Date : 2014-07-10
An Introduction To Mathematical Analysis written by Robert A. Rankin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.
International Series of Monographs on Pure and Applied Mathematics, Volume 43: An Introduction to Mathematical Analysis discusses the various topics involved in the analysis of functions of a single real variable. The title first covers the fundamental idea and assumptions in analysis, and then proceeds to tackling the various areas in analysis, such as limits, continuity, differentiability, integration, convergence of infinite series, double series, and infinite products. The book will be most useful to undergraduate students of mathematical analysis.
Analysis With An Introduction To Proof
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Author : Steven R. Lay
language : en
Publisher: Pearson
Release Date : 2015-12-03
Analysis With An Introduction To Proof written by Steven R. Lay and has been published by Pearson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-03 with Mathematics categories.
This is the eBook of the printed book and may not include any media, website access codes, or print supplements that may come packaged with the bound book. For courses in undergraduate Analysis and Transition to Advanced Mathematics. Analysis with an Introduction to Proof, Fifth Edition helps fill in the groundwork students need to succeed in real analysis—often considered the most difficult course in the undergraduate curriculum. By introducing logic and emphasizing the structure and nature of the arguments used, this text helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable, student-oriented, and teacher- friendly.
An Introduction To Mathematical Analysis
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Author : Herbert Stanley Bear
language : en
Publisher:
Release Date : 1997
An Introduction To Mathematical Analysis written by Herbert Stanley Bear and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
An Introduction to Mathematical Analysis provides detailed explanations and exhaustive proofs, and follows an axiomatic approach to presenting the material. The text assumes that the student has little background in mathematical analysis; therefore, the initial pace is slowed down. The proofs are formal, complete, and augmented by an informal and heuristic explanation. The author presents the subject in clear and evocative language, and includes treatment of the Lebesgue integral, a topic not usually found in texts of this level. Mathematical problems are included throughout the text and are designed to get the student involved at every stage. Key Features: * All the information introduced is proved by axioms * Extensive proofs are formal and complete * Includes a novel treatment of the Lebesgue Integral * Emphasis on developing proofs helps students acquire skills essential to subsequent courses
Analysis
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Author : Richard Beals
language : en
Publisher: Cambridge University Press
Release Date : 2004-09-13
Analysis written by Richard Beals 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 2004-09-13 with Mathematics categories.
This book is an extensive introductory text to mathematical analysis for graduate students and advanced undergraduates, complete with 500 exercises and numerous examples.