Examples And Theorems In Analysis

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Examples And Theorems In Analysis

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Author : Peter Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Examples And Theorems In Analysis written by Peter Walker 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 2012-12-06 with Mathematics categories.

This book adopts a practical, example-led approach to mathematical analysis that shows both the usefulness and limitations of the results. A number of applications show what the subject is about and what can be done with it; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems.

Examples And Theorems In Analysis

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Author : Walker
language : en
Publisher:
Release Date : 2009-10-01

Examples And Theorems In Analysis written by Walker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-01 with categories.

Examples And Theorems In Analysis

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Author : Peter Walker
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-12

Examples And Theorems In Analysis written by Peter Walker 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 2003-12-12 with Mathematics categories.

This book adopts a practical, example-led approach to mathematical analysis that shows both the usefulness and limitations of the results. A number of applications show what the subject is about and what can be done with it; the applications in Fourier theory, distributions and asymptotics show how the results may be put to use. Exercises at the end of each chapter, of varying levels of difficulty, develop new ideas and present open problems.

Theorems And Counterexamples In Mathematics

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Author : Bernard R. Gelbaum
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Theorems And Counterexamples In Mathematics written by Bernard R. Gelbaum 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 2012-12-06 with Mathematics categories.

The gratifying response to Counterexamples in analysis (CEA) was followed, when the book went out of print, by expressions of dismay from those who were unable to acquire it. The connection of the present volume with CEA is clear, although the sights here are set higher. In the quarter-century since the appearance of CEA, mathematical education has taken some large steps reflected in both the undergraduate and graduate curricula. What was once taken as very new, remote, or arcane is now a well-established part of mathematical study and discourse. Consequently the approach here is designed to match the observed progress. The contents are intended to provide graduate and ad vanced undergraduate students as well as the general mathematical public with a modern treatment of some theorems and examples that constitute a rounding out and elaboration of the standard parts of algebra, analysis, geometry, logic, probability, set theory, and topology. The items included are presented in the spirit of a conversation among mathematicians who know the language but are interested in some of the ramifications of the subjects with which they routinely deal. Although such an approach might be construed as demanding, there is an extensive GLOSSARY jlNDEX where all but the most familiar notions are clearly defined and explained. The object ofthe body of the text is more to enhance what the reader already knows than to review definitions and notations that have become part of every mathematician's working context.

Lectures On Real Analysis

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Author : J. Yeh
language : en
Publisher: World Scientific
Release Date : 2000

Lectures On Real Analysis written by J. Yeh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

The theory of the Lebesgue integral is a main pillar in the foundation of modern analysis and its applications, including probability theory. This volume shows how and why the Lebesgue integral is such a universal and powerful concept. The lines of development of the theory are made clear by the order in which the main theorems are presented. Frequent references to earlier theorems made in the proofs emphasize the interdependence of the theorems and help to show how the various definitions and theorems fit together. Counter-examples are included to show why a hypothesis in a theorem cannot be dropped. The book is based upon a course on real analysis which the author has taught. It is particularly suitable for a one-year course at the graduate level. Precise statements and complete proofs are given for every theorem, with no obscurity left. For this reason the book is also suitable for self-study.

Complex Analysis

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Author : John Stalker
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03

Complex Analysis written by John Stalker 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 2009-10-03 with Mathematics categories.

All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.

Introduction To Analysis

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Author : Hidefumi Katsuura
language : en
Publisher: Springer
Release Date : 2024-09-15

Introduction To Analysis written by Hidefumi Katsuura and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-15 with Mathematics categories.

This book focuses on the theoretical aspects of calculus. The book begins with a chapter on set theory before thoroughly discussing real numbers, then moves onto sequences, series, and their convergence. The author explains why an understanding of real numbers is essential in order to create a foundation for studying analysis. Since the Cantor set is elusive to many, a section is devoted to binary/ternary numbers and the Cantor set. The book then moves on to continuous functions, differentiations, integrations, and uniform convergence of sequences of functions. An example of a nontrivial uniformly Cauchy sequence of functions is given. The author defines each topic, identifies important theorems, and includes many examples throughout each chapter. The book also provides introductory instruction on proof writing, with an emphasis on how to execute a precise writing style.

Basic Real Analysis

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Author : Houshang H. Sohrab
language : en
Publisher: Springer
Release Date : 2014-11-15

Basic Real Analysis written by Houshang H. Sohrab and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-15 with Mathematics categories.

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

Foundations Of Analysis

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Author : Joseph L. Taylor
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Foundations Of Analysis written by Joseph L. Taylor and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

Foundations of Analysis has two main goals. The first is to develop in students the mathematical maturity and sophistication they will need as they move through the upper division curriculum. The second is to present a rigorous development of both single and several variable calculus, beginning with a study of the properties of the real number system. The presentation is both thorough and concise, with simple, straightforward explanations. The exercises differ widely in level of abstraction and level of difficulty. They vary from the simple to the quite difficult and from the computational to the theoretical. Each section contains a number of examples designed to illustrate the material in the section and to teach students how to approach the exercises for that section. --Book cover.

Advanced Real Analysis

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Author : Anthony W. Knapp
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-07-11

Advanced 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 2008-07-11 with Mathematics categories.

* 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