basic real analysis

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Basic Real Analysis

Author : Houshang H. Sohrab
ISBN : 9781493918416
Genre : Mathematics
File Size : 88. 14 MB
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This expanded second edition presents the fundamentals and touchstone results of real analysis in full rigor, but in a style that requires little prior familiarity with proofs or mathematical language. The text is a comprehensive and largely self-contained introduction to the theory of real-valued functions of a real variable. The chapters on Lebesgue measure and integral have been rewritten entirely and greatly improved. They now contain Lebesgue’s differentiation theorem as well as his versions of the Fundamental Theorem(s) of Calculus. With expanded chapters, additional problems, and an expansive solutions manual, Basic Real Analysis, Second Edition is ideal for senior undergraduates and first-year graduate students, both as a classroom text and a self-study guide. Reviews of first edition: The book is a clear and well-structured introduction to real analysis aimed at senior undergraduate and beginning graduate students. The prerequisites are few, but a certain mathematical sophistication is required. ... The text contains carefully worked out examples which contribute motivating and helping to understand the theory. There is also an excellent selection of exercises within the text and problem sections at the end of each chapter. In fact, this textbook can serve as a source of examples and exercises in real analysis. —Zentralblatt MATH The quality of the exposition is good: strong and complete versions of theorems are preferred, and the material is organised so that all the proofs are of easily manageable length; motivational comments are helpful, and there are plenty of illustrative examples. The reader is strongly encouraged to learn by doing: exercises are sprinkled liberally throughout the text and each chapter ends with a set of problems, about 650 in all, some of which are of considerable intrinsic interest. —Mathematical Reviews [This text] introduces upper-division undergraduate or first-year graduate students to real analysis.... Problems and exercises abound; an appendix constructs the reals as the Cauchy (sequential) completion of the rationals; references are copious and judiciously chosen; and a detailed index brings up the rear. —CHOICE Reviews

Basic Real Analysis

Author : James S. Howland
ISBN : 9781449668525
Genre : Mathematics
File Size : 62. 51 MB
Format : PDF
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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.

Basic Real Analysis

Author : Anthony W. Knapp
ISBN : 9780817644413
Genre : Mathematics
File Size : 27. 75 MB
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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.

A Basic Course In Real Analysis

Author : Ajit Kumar
ISBN : 9781482216370
Genre : Mathematics
File Size : 44. 94 MB
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Based on the authors’ combined 35 years of experience in teaching, A Basic Course in Real Analysis introduces students to the aspects of real analysis in a friendly way. The authors offer insights into the way a typical mathematician works observing patterns, conducting experiments by means of looking at or creating examples, trying to understand the underlying principles, and coming up with guesses or conjectures and then proving them rigorously based on his or her explorations. With more than 100 pictures, the book creates interest in real analysis by encouraging students to think geometrically. Each difficult proof is prefaced by a strategy and explanation of how the strategy is translated into rigorous and precise proofs. The authors then explain the mystery and role of inequalities in analysis to train students to arrive at estimates that will be useful for proofs. They highlight the role of the least upper bound property of real numbers, which underlies all crucial results in real analysis. In addition, the book demonstrates analysis as a qualitative as well as quantitative study of functions, exposing students to arguments that fall under hard analysis. Although there are many books available on this subject, students often find it difficult to learn the essence of analysis on their own or after going through a course on real analysis. Written in a conversational tone, this book explains the hows and whys of real analysis and provides guidance that makes readers think at every stage.

Advanced Real Analysis

Author : Anthony W. Knapp
ISBN : 0817644423
Genre : Mathematics
File Size : 71. 69 MB
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* 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

Basic Real Analysis And Advanced Real Analysis Set

Author : Anthony W. Knapp
ISBN : 0817644075
Genre : Mathematics
File Size : 30. 3 MB
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Basic Real Analysis and Advanced Real Analysis systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics. Key topics and features: * The development proceeds from the particular to the general, often introducing examples well before a theory that incorporates them * Incorporates, in the text and especially in the problems, material in which real analysis is used in algebra, in topology, in complex analysis, in probability, in differential geometry, and in applied mathematics of various kinds * The texts include many examples and hundreds of problems, and each provides a lengthy separate section giving hints or complete solutions for most of the problems Because they focus on what every young mathematician needs to know about real analysis, the books are ideal both as course texts and for self-study, especially for graduate students preparing for qualifying examinations. Their scope and approach will appeal to instructors and professors in nearly all areas of pure mathematics, as well as applied mathematicians working in analytic areas such as statistics, mathematical physics, and differential equations. Indeed, their clarity and breadth make them a welcome addition to the personal library of every mathematician.

Basic Elements Of Real Analysis

Author : Murray H. Protter
ISBN : 9780387227498
Genre : Mathematics
File Size : 59. 2 MB
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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.

Introduction To Real Analysis

Author : John D. DePree
ISBN : STANFORD:36105032426202
Genre : Mathematics
File Size : 51. 13 MB
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Assuming minimal background on the part of students, this text gradually develops the principles of basic real analysis and presents the background necessary to understand applications used in such disciplines as statistics, operations research, and engineering. The text presents the first elementary exposition of the gauge integral and offers a clear and thorough introduction to real numbers, developing topics in n-dimensions, and functions of several variables. Detailed treatments of Lagrange multipliers and the Kuhn-Tucker Theorem are also presented. The text concludes with coverage of important topics in abstract analysis, including the Stone-Weierstrass Theorem and the Banach Contraction Principle.

Real Analysis

Author : Karunakaran
ISBN : 9789332506640
Genre :
File Size : 47. 22 MB
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Real Analysis is designed for an undergraduate course on mathematics. It covers the basic material that every graduate student should know in the classical theory of functions of real variables, measures, limits and continuity. This text book offers readability, practicality and flexibility. It presents fundamental theorems and ideas from a practical viewpoint, showing students the motivation behind mathematics and enabling them to construct their own proofs.

Introductory Real Analysis

Author : A. N. Kolmogorov
ISBN : 9780486134741
Genre : Mathematics
File Size : 71. 37 MB
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Comprehensive, elementary introduction to real and functional analysis covers basic concepts and introductory principles in set theory, metric spaces, topological and linear spaces, linear functionals and linear operators, more. 1970 edition.

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