basic real analysis

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Basic Real Analysis

Author : James S. Howland
ISBN : 9781449668525
Genre : Mathematics
File Size : 88. 66 MB
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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 : Houshang H. Sohrab
ISBN : 9780817682323
Genre : Mathematics
File Size : 62. 58 MB
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Basic Real Analysis demonstrates the richness of real analysis, giving students an introduction both to mathematical rigor and to the deep theorems and counter examples that arise from such rigor. In this modern and systematic text, all the touchstone results and fundamentals are carefully presented in a style that requires little prior familiarity with proofs or mathematical language. With its many examples, exercises and broad view of analysis, this work is ideal for senior undergraduates and beginning graduate students, either in the classroom or for self-study.

Basic Real Analysis

Author : Anthony W. Knapp
ISBN : 9780817644413
Genre : Mathematics
File Size : 69. 8 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.

Basic Real Analysis And Advanced Real Analysis Set

Author : Anthony W. Knapp
ISBN : 0817644075
Genre : Mathematics
File Size : 46. 4 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.

A Basic Course In Real Analysis

Author : Ajit Kumar
ISBN : 9781482216370
Genre : Mathematics
File Size : 21. 1 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.

Basic Elements Of Real Analysis

Author : Murray H. Protter
ISBN : 9780387227498
Genre : Mathematics
File Size : 90. 45 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.

Advanced Real Analysis

Author : Anthony W. Knapp
ISBN : 0817644423
Genre : Mathematics
File Size : 78. 10 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

Principles Of Real Analysis

Author : Charalambos D. Aliprantis
ISBN : 9780128015025
Genre : Mathematics
File Size : 22. 73 MB
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This major textbook on real analysis is now available in a corrected and slightly amended reprint. It covers the basic theory of integration in a clear, well-organized manner using an imaginative and highly practical synthesis of the 'Daniell method' and the measure-theoretic approach. It is the ideal text for senior undergraduate and first-year graduate courses in real analysis, assuming student familiarity with advanced calculus and basic algebraic concepts.

Fourier Analysis And Nonlinear Partial Differential Equations

Author : Hajer Bahouri
ISBN : 3642168302
Genre : Mathematics
File Size : 66. 18 MB
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In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.

Concise Introduction To Basic Real Analysis

Author : Hemen Dutta
ISBN : 1138612464
Genre :
File Size : 52. 67 MB
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This book provides an introduction to basic topics in Real Analysis and makes the subject easily understandable to all learners. It is for those that are involved with Real Analysis in disciplines such as mathematics, engineering, technology, and other physical sciences. This book will provide a good balance while dealing with the basic and essential topics enabling a learner to digest more advanced topics easily. It includes many examples and end of chapter exercises including hints for solution in several critical cases. It is ideal for students, instructors, as well as those doing research in areas requiring basic knowledge of Real Analysis. A reader having advanced knowledge of Real Analysis should also find the book useful to refresh his/her basic knowledge of Real Analysis. Features Includes basic and essential topics of real analysis Adopts a Reasonable approach to make the subject digestible to all learners Contains lots of solved examples and exercise at the end of each chapter Presents a quick review of the fundamentals of set theory Covers the real number system Discusses the basic concepts of metric spaces and complete metric spaces

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