Examples and Theorems in Analysis

Author: Peter Walker

Publisher: Springer Science & Business Media

ISBN: 085729380X

Category: Mathematics

Page: 287

View: 6028

DOWNLOAD NOW »

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.
Release

Basic Real Analysis

Author: Houshang H. Sohrab

Publisher: Springer Science & Business Media

ISBN: 0817682325

Category: Mathematics

Page: 559

View: 2983

DOWNLOAD NOW »

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.
Release

Mathematical Analysis

Author: S. C. Malik,Savita Arora

Publisher: New Age International

ISBN: 9788122403237

Category: Mathematical analysis

Page: 903

View: 4344

DOWNLOAD NOW »

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.
Release

Real and Functional Analysis

Author: Serge Lang

Publisher: Springer Science & Business Media

ISBN: 1461208971

Category: Mathematics

Page: 580

View: 1632

DOWNLOAD NOW »

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.
Release

Functional Analysis

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

Publisher: New Age International

ISBN: 9788122408010

Category: Functional analysis

Page: 326

View: 9953

DOWNLOAD NOW »

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.
Release

The Implicit Function Theorem

History, Theory, and Applications

Author: Steven George Krantz,Harold R. Parks

Publisher: Springer Science & Business Media

ISBN: 9780817642853

Category: Mathematics

Page: 163

View: 5779

DOWNLOAD NOW »

The implicit function theorem is part of the bedrock of mathematical analysis and geometry. Finding its genesis in eighteenth century studies of real analytic functions and mechanics, the implicit and inverse function theorems have now blossomed into powerful tools in the theories of partial differential equations, differential geometry, and geometric analysis. There are many different forms of the implicit function theorem, including (i) the classical formulation for C^k functions, (ii) formulations in other function spaces, (iii) formulations for non- smooth functions, (iv) formulations for functions with degenerate Jacobian. Particularly powerful implicit function theorems, such as the Nash--Moser theorem, have been developed for specific applications (e.g., the imbedding of Riemannian manifolds). All of these topics, and many more, are treated in the present volume. The history of the implicit function theorem is a lively and complex story, and is intimately bound up with the development of fundamental ideas in analysis and geometry. This entire development, together with mathematical examples and proofs, is recounted for the first time here. It is an exciting tale, and it continues to evolve. "The Implicit Function Theorem" is an accessible and thorough treatment of implicit and inverse function theorems and their applications. It will be of interest to mathematicians, graduate/advanced undergraduate students, and to those who apply mathematics. The book unifies disparate ideas that have played an important role in modern mathematics. It serves to document and place in context a substantial body of mathematical ideas.
Release

Differential and Integral Calculus

Author: Richard Courant

Publisher: John Wiley & Sons

ISBN: 9780471608424

Category: Mathematics

Page: 640

View: 3536

DOWNLOAD NOW »

Now available in a low-priced paperback edition! Written by one of the foremost mathematicians of the 20th century, this text remains the only modern treatment to successfully integrate principles of analysis into first-year calculus. Further, Courant's treatment introduces the differential and integral calculus simultaneously, emphasizing the central point of the calculus, namely, the connection between definite integral, indefinite integral, and derivative. Exposition exhibits the close connection between analysis and its applications, making this text appropriate for students of mathematics, or of science and engineering. Courant makes the subject easier to grasp by giving proofs step-by-step, and by developing the intuition that gave rise to the calculus and guides its use today.
Release

Real Analysis and Probability

Author: R. M. Dudley

Publisher: Cambridge University Press

ISBN: 9780521007542

Category: Mathematics

Page: 555

View: 3832

DOWNLOAD NOW »

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.
Release