Examples and Theorems in Analysis

Author: Peter Walker

Publisher: Springer Science & Business Media

ISBN: 085729380X

Category: Mathematics

Page: 287

View: 8204

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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.
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Basic Real Analysis

Author: Houshang H. Sohrab

Publisher: Springer Science & Business Media

ISBN: 9780817642112

Category: Mathematics

Page: 559

View: 2494

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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.
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CounterExamples

From Elementary Calculus to the Beginnings of Analysis

Author: Andrei Bourchtein,Ludmila Bourchtein

Publisher: CRC Press

ISBN: 1482246686

Category: Mathematics

Page: 362

View: 9345

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This book provides a one-semester undergraduate introduction to counterexamples in calculus and analysis. It helps engineering, natural sciences, and mathematics students tackle commonly made erroneous conjectures. The book encourages students to think critically and analytically, and helps to reveal common errors in many examples.In this book, the
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Real and Functional Analysis

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461208971

Category: Mathematics

Page: 580

View: 6277

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This book is meant as a text for a first-year graduate course in analysis. In a sense, it covers the same topics as elementary calculus but treats them in a manner suitable for people who will be using it in further mathematical investigations. The organization avoids long chains of logical interdependence, so that chapters are mostly independent. This allows a course to omit material from some chapters without compromising the exposition of material from later chapters.
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Functional Analysis

Author: P. K. Jain,Khalil Ahmad,Om P. Ahuja

Publisher: New Age International

ISBN: 9788122408010

Category: Functional analysis

Page: 326

View: 2033

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The Book Is Intended To Serve As A Textbook For An Introductory Course In Functional Analysis For The Senior Undergraduate And Graduate Students. It Can Also Be Useful For The Senior Students Of Applied Mathematics, Statistics, Operations Research, Engineering And Theoretical Physics. The Text Starts With A Chapter On Preliminaries Discussing Basic Concepts And Results Which Would Be Taken For Granted Later In The Book. This Is Followed By Chapters On Normed And Banach Spaces, Bounded Linear Operators, Bounded Linear Functionals. The Concept And Specific Geometry Of Hilbert Spaces, Functionals And Operators On Hilbert Spaces And Introduction To Spectral Theory. An Appendix Has Been Given On Schauder Bases.The Salient Features Of The Book Are: * Presentation Of The Subject In A Natural Way * Description Of The Concepts With Justification * Clear And Precise Exposition Avoiding Pendantry * Various Examples And Counter Examples * Graded Problems Throughout Each ChapterNotes And Remarks Within The Text Enhances The Utility Of The Book For The Students.
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Mathematical Analysis

Author: S. C. Malik,Savita Arora

Publisher: New Age International

ISBN: 9788122403237

Category: Mathematical analysis

Page: 903

View: 3386

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The Book Is Intended To Serve As A Text In Analysis By The Honours And Post-Graduate Students Of The Various Universities. Professional Or Those Preparing For Competitive Examinations Will Also Find This Book Useful.The Book Discusses The Theory From Its Very Beginning. The Foundations Have Been Laid Very Carefully And The Treatment Is Rigorous And On Modem Lines. It Opens With A Brief Outline Of The Essential Properties Of Rational Numbers And Using Dedekinds Cut, The Properties Of Real Numbers Are Established. This Foundation Supports The Subsequent Chapters: Topological Frame Work Real Sequences And Series, Continuity Differentiation, Functions Of Several Variables, Elementary And Implicit Functions, Riemann And Riemann-Stieltjes Integrals, Lebesgue Integrals, Surface, Double And Triple Integrals Are Discussed In Detail. Uniform Convergence, Power Series, Fourier Series, Improper Integrals Have Been Presented In As Simple And Lucid Manner As Possible And Fairly Large Number Solved Examples To Illustrate Various Types Have Been Introduced.As Per Need, In The Present Set Up, A Chapter On Metric Spaces Discussing Completeness, Compactness And Connectedness Of The Spaces Has Been Added. Finally Two Appendices Discussing Beta-Gamma Functions, And Cantors Theory Of Real Numbers Add Glory To The Contents Of The Book.
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How to Think about Analysis

Author: Lara Alcock

Publisher: Oxford University Press, USA

ISBN: 0198723539

Category: Mathematics

Page: 246

View: 3398

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Analysis is a core subject in most undergraduate mathematics degrees. It is elegant, clever and rewarding to learn, but it is hard. Even the best students find it challenging, and those who are unprepared often find it incomprehensible at first. This book aims to ensure that no student need be unprepared.
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Real Analysis and Probability

Author: R. M. Dudley

Publisher: Cambridge University Press

ISBN: 9780521007542

Category: Mathematics

Page: 555

View: 4679

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This classic graduate textbook offers a clear exposition of modern probability theory and of the interplay between the properties of metric spaces and probability measures. The comprehensive historical notes have been further amplified for this new edition, and a number of new exercises have been added, together with hints for solution.
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