Elements Of Real Analysis

Author : Murray H. Protter
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 40,9 Mb
Release : 2006-03-29
Category : Mathematics
ISBN : 9780387227498

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Basic Elements of Real Analysis by Murray H. Protter Pdf

From the author of the highly-acclaimed "A First Course in Real Analysis" comes a volume designed specifically for a short one-semester course in real analysis. Many students of mathematics and the physical and computer sciences need a text that presents the most important material in a brief and elementary fashion. The author meets this need with such elementary topics as the real number system, the theory at the basis of elementary calculus, the topology of metric spaces and infinite series. There are proofs of the basic theorems on limits at a pace that is deliberate and detailed, backed by illustrative examples throughout and no less than 45 figures.

Author : David A. Sprecher
Publisher : Courier Corporation
Page : 357 pages
File Size : 43,9 Mb
Release : 2012-04-25
Category : Mathematics
ISBN : 9780486153254

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Elements of Real Analysis by David A. Sprecher Pdf

Classic text explores intermediate steps between basics of calculus and ultimate stage of mathematics — abstraction and generalization. Covers fundamental concepts, real number system, point sets, functions of a real variable, Fourier series, more. Over 500 exercises.

Author : Charles G. Denlinger
Publisher : Jones & Bartlett Publishers
Page : 769 pages
File Size : 46,6 Mb
Release : 2010-05-08
Category : Mathematics
ISBN : 9781449659936

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Elements of Real Analysis by Charles G. Denlinger Pdf

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.

Author : M.A. Al-Gwaiz,S.A. Elsanousi
Publisher : CRC Press
Page : 448 pages
File Size : 52,6 Mb
Release : 2006-08-21
Category : Mathematics
ISBN : 9781420011609

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Elements of Real Analysis by M.A. Al-Gwaiz,S.A. Elsanousi Pdf

Focusing on one of the main pillars of mathematics, Elements of Real Analysis provides a solid foundation in analysis, stressing the importance of two elements. The first building block comprises analytical skills and structures needed for handling the basic notions of limits and continuity in a simple concrete setting while the second component involves conducting analysis in higher dimensions and more abstract spaces. Largely self-contained, the book begins with the fundamental axioms of the real number system and gradually develops the core of real analysis. The first few chapters present the essentials needed for analysis, including the concepts of sets, relations, and functions. The following chapters cover the theory of calculus on the real line, exploring limits, convergence tests, several functions such as monotonic and continuous, power series, and theorems like mean value, Taylor's, and Darboux's. The final chapters focus on more advanced theory, in particular, the Lebesgue theory of measure and integration. Requiring only basic knowledge of elementary calculus, this textbook presents the necessary material for a first course in real analysis. Developed by experts who teach such courses, it is ideal for undergraduate students in mathematics and related disciplines, such as engineering, statistics, computer science, and physics, to understand the foundations of real analysis.

Author : M.D.Raisinghania
Publisher : S. Chand Publishing
Page : 312 pages
File Size : 44,8 Mb
Release : 2003-06-01
Category : Mathematics
ISBN : 9788121903066

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Elements of Real Anyalsis by M.D.Raisinghania Pdf

This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.

Author : Charles Denlinger
Publisher : Jones & Bartlett Learning
Page : 769 pages
File Size : 49,5 Mb
Release : 2011
Category : Mathematics
ISBN : 9780763779474

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Elements of Real Analysis by Charles Denlinger Pdf

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.

Author : Herbert S. Gaskill,P. P. Narayanaswami
Publisher : Upper Saddle River, NJ : Prentice Hall
Page : 520 pages
File Size : 41,7 Mb
Release : 1998
Category : Mathematics
ISBN : UCSC:32106014628173

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Elements of Real Analysis by Herbert S. Gaskill,P. P. Narayanaswami Pdf

Comprehensive in coverage, this book explores the principles of logic, the axioms for the real numbers, limits of sequences, limits of functions, differentiation and integration, infinite series, convergence, and uniform convergence for sequences of real-valued functions. Concepts are presented slowly and include the details of calculations as well as substantial explanations as to how and why one proceeds in the given manner.Uses the words WHY? and HOW? throughout; inviting readers to become active participants and to supply a missing argument or a simple calculation. Contains more than 1000 individual exercises. Stresses and reviews elementary algebra and symbol manipulation as essential tools for success at the kind of computations required in dealing with limiting processes.

Author : Sheldon Axler
Publisher : Springer Nature
Page : 430 pages
File Size : 44,5 Mb
Release : 2019-11-29
Category : Mathematics
ISBN : 9783030331436

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Measure, Integration & Real Analysis by Sheldon Axler Pdf

This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online. For errata and updates, visit https://measure.axler.net/

Author : Piotr Mikusiński,Jan Mikusiński
Publisher : World Scientific Publishing Company
Page : 320 pages
File Size : 55,9 Mb
Release : 2017-02-17
Category : Electronic
ISBN : 9789813202634

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An Introduction to Analysis by Piotr Mikusiński,Jan Mikusiński Pdf

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. Request Inspection Copy

Author : Efe A. Ok
Publisher : Princeton University Press
Page : 832 pages
File Size : 48,5 Mb
Release : 2011-09-05
Category : Business & Economics
ISBN : 9781400840892

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Real Analysis with Economic Applications by Efe A. Ok Pdf

There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.

Author : Nader Vakil
Publisher : Cambridge University Press
Page : 587 pages
File Size : 48,7 Mb
Release : 2011-02-17
Category : Mathematics
ISBN : 9781107002029

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Real Analysis Through Modern Infinitesimals by Nader Vakil Pdf

A coherent, self-contained treatment of the central topics of real analysis employing modern infinitesimals.

Author : Maxwell Rosenlicht
Publisher : Courier Corporation
Page : 272 pages
File Size : 51,5 Mb
Release : 2012-05-04
Category : Mathematics
ISBN : 9780486134680

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Introduction to Analysis by Maxwell Rosenlicht Pdf

Written for junior and senior undergraduates, this remarkably clear and accessible treatment covers set theory, the real number system, metric spaces, continuous functions, Riemann integration, multiple integrals, and more. 1968 edition.

Author : Omar Hijab
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 40,9 Mb
Release : 2011-03-19
Category : Mathematics
ISBN : 9781441994882

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Introduction to Calculus and Classical Analysis by Omar Hijab Pdf

This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text include: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; and There are 385 problems with all the solutions at the back of the text.

Author : William P. Ziemer
Publisher : Springer
Page : 382 pages
File Size : 44,5 Mb
Release : 2017-11-30
Category : Mathematics
ISBN : 9783319646299

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Modern Real Analysis by William P. Ziemer Pdf

This first year graduate text is a comprehensive resource in real analysis based on a modern treatment of measure and integration. Presented in a definitive and self-contained manner, it features a natural progression of concepts from simple to difficult. Several innovative topics are featured, including differentiation of measures, elements of Functional Analysis, the Riesz Representation Theorem, Schwartz distributions, the area formula, Sobolev functions and applications to harmonic functions. Together, the selection of topics forms a sound foundation in real analysis that is particularly suited to students going on to further study in partial differential equations. This second edition of Modern Real Analysis contains many substantial improvements, including the addition of problems for practicing techniques, and an entirely new section devoted to the relationship between Lebesgue and improper integrals. Aimed at graduate students with an understanding of advanced calculus, the text will also appeal to more experienced mathematicians as a useful reference.

Author : Robert G. Bartle
Publisher : Unknown
Page : 0 pages
File Size : 48,8 Mb
Release : 2006
Category : Functions of real variables
ISBN : 0470088265

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Introduction to Real Analysis by Robert G. Bartle Pdf