Topics In Classical And Modern Analysis
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Classical And Modern Numerical Analysis
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Author : Azmy S. Ackleh
language : en
Publisher: CRC Press
Release Date : 2009-07-20
Classical And Modern Numerical Analysis written by Azmy S. Ackleh and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-20 with Mathematics categories.
Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o
A Course Of Modern Analysis
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Author : E. T. Whittaker
language : en
Publisher: Cambridge University Press
Release Date : 1927
A Course Of Modern Analysis written by E. T. Whittaker and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1927 with Mathematics categories.
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Introduction To Classical And Modern Analysis And Their Application To Group Representation Theory
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Author : Debabrata Basu
language : en
Publisher: World Scientific
Release Date : 2011
Introduction To Classical And Modern Analysis And Their Application To Group Representation Theory written by Debabrata Basu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Science categories.
This book is suitable for use in any graduate course on analytical methods and their application to representation theory. Each concept is developed with special emphasis on lucidity and clarity. The book also shows the direct link of Cauchy?Pochhammer theory with the Hadamard?Reisz?Schwartz?Gel'fand et al. regularization. The flaw in earlier works on the Plancheral formula for the universal covering group of SL(2, R) is pointed out and rectified. This topic appears here for the first time in the correct form.Existing treatises are essentially magnum opus of the experts, intended for other experts in the field. This book, on the other hand, is unique insofar as every chapter deals with topics in a way that differs remarkably from traditional treatment. For example, Chapter 3 presents the Cauchy?Pochhammer theory of gamma, beta and zeta function in a form which has not been presented so far in any treatise of classical analysis.
Integration And Modern Analysis
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Author : John J. Benedetto
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-08
Integration And Modern Analysis written by John J. Benedetto 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 2010-01-08 with Mathematics categories.
This textbook and treatise begins with classical real variables, develops the Lebesgue theory abstractly and for Euclidean space, and analyzes the structure of measures. The authors' vision of modern real analysis is seen in their fascinating historical commentary and perspectives with other fields. There are comprehensive treatments of the role of absolute continuity, the evolution of the Riesz representation theorem to Radon measures and distribution theory, weak convergence of measures and the Dieudonné–Grothendieck theorem, modern differentiation theory, fractals and self-similarity, rearrangements and maximal functions, and surface and Hausdorff measures. There are hundreds of illuminating exercises, and extensive, focused appendices on functional and Fourier analysis. The presentation is ideal for the classroom, self-study, or professional reference.
A Concrete Approach To Classical Analysis
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Author : Marian Muresan
language : en
Publisher: Springer Science & Business Media
Release Date : 2015-09-16
A Concrete Approach To Classical Analysis written by Marian Muresan 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 2015-09-16 with Mathematics categories.
Mathematical analysis offers a solid basis for many achievements in applied mathematics and discrete mathematics. This new textbook is focused on differential and integral calculus, and includes a wealth of useful and relevant examples, exercises, and results enlightening the reader to the power of mathematical tools. The intended audience consists of advanced undergraduates studying mathematics or computer science. The author provides excursions from the standard topics to modern and exciting topics, to illustrate the fact that even first or second year students can understand certain research problems. The text has been divided into ten chapters and covers topics on sets and numbers, linear spaces and metric spaces, sequences and series of numbers and of functions, limits and continuity, differential and integral calculus of functions of one or several variables, constants (mainly pi) and algorithms for finding them, the W - Z method of summation, estimates of algorithms and of certain combinatorial problems. Many challenging exercises accompany the text. Most of them have been used to prepare for different mathematical competitions during the past few years. In this respect, the author has maintained a healthy balance of theory and exercises.
An Illustrative Introduction To Modern Analysis
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Author : Nikolaos Katzourakis
language : en
Publisher: CRC Press
Release Date : 2018-01-02
An Illustrative Introduction To Modern Analysis written by Nikolaos Katzourakis and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-01-02 with Mathematics categories.
Aimed primarily at undergraduate level university students, An Illustrative Introduction to Modern Analysis provides an accessible and lucid contemporary account of the fundamental principles of Mathematical Analysis. The themes treated include Metric Spaces, General Topology, Continuity, Completeness, Compactness, Measure Theory, Integration, Lebesgue Spaces, Hilbert Spaces, Banach Spaces, Linear Operators, Weak and Weak* Topologies. Suitable both for classroom use and independent reading, this book is ideal preparation for further study in research areas where a broad mathematical toolbox is required.
Classical Fourier Analysis
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Author : Loukas Grafakos
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-18
Classical Fourier Analysis written by Loukas Grafakos 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 2008-09-18 with Mathematics categories.
The primary goal of this text is to present the theoretical foundation of the field of Fourier analysis. This book is mainly addressed to graduate students in mathematics and is designed to serve for a three-course sequence on the subject. The only prerequisite for understanding the text is satisfactory completion of a course in measure theory, Lebesgue integration, and complex variables. This book is intended to present the selected topics in some depth and stimulate further study. Although the emphasis falls on real variable methods in Euclidean spaces, a chapter is devoted to the fundamentals of analysis on the torus. This material is included for historical reasons, as the genesis of Fourier analysis can be found in trigonometric expansions of periodic functions in several variables. While the 1st edition was published as a single volume, the new edition will contain 120 pp of new material, with an additional chapter on time-frequency analysis and other modern topics. Asa result, the book is now being published in 2 separate volumes, the first volume containing the classical topics (Lp Spaces, Littlewood-Paley Theory, Smoothness, etc...), the second volume containing the modern topics (weighted inequalities, wavelets, atomic decomposition, etc...). From a review of the first edition: “Grafakos’s book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA Online
Invitation To Classical Analysis
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Author : Peter Duren
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Invitation To Classical Analysis written by Peter Duren 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 Education categories.
This book gives a rigorous treatment of selected topics in classical analysis, with many applications and examples. The exposition is at the undergraduate level, building on basic principles of advanced calculus without appeal to more sophisticated techniques of complex analysis and Lebesgue integration. Among the topics covered are Fourier series and integrals, approximation theory, Stirling's formula, the gamma function, Bernoulli numbers and polynomials, the Riemann zeta function, Tauberian theorems, elliptic integrals, ramifications of the Cantor set, and a theoretical discussion of differential equations including power series solutions at regular singular points, Bessel functions, hypergeometric functions, and Sturm comparison theory. Preliminary chapters offer rapid reviews of basic principles and further background material such as infinite products and commonly applied inequalities. This book is designed for individual study but can also serve as a text for second-semester courses in advanced calculus. Each chapter concludes with an abundance of exercises. Historical notes discuss the evolution of mathematical ideas and their relevance to physical applications. Special features are capsule scientific biographies of the major players and a gallery of portraits. Although this book is designed for undergraduate students, others may find it an accessible source of information on classical topics that underlie modern developments in pure and applied mathematics.
Excursions In Classical Analysis
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Author : Hongwei Chen
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-12-31
Excursions In Classical Analysis written by Hongwei Chen 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 2010-12-31 with Mathematics categories.
Excursions in Classical Analysis will introduce students to advanced problem solving and undergraduate research in two ways: it will provide a tour of classical analysis, showcasing a wide variety of problems that are placed in historical context, and it will help students gain mastery of mathematical discovery and proof. The [Author]; presents a variety of solutions for the problems in the book. Some solutions reach back to the work of mathematicians like Leonhard Euler while others connect to other beautiful parts of mathematics. Readers will frequently see problems solved by using an idea that, at first glance, might not even seem to apply to that problem. Other solutions employ a specific technique that can be used to solve many different kinds of problems. Excursions emphasizes the rich and elegant interplay between continuous and discrete mathematics by applying induction, recursion, and combinatorics to traditional problems in classical analysis. The book will be useful in students' preparations for mathematics competitions, in undergraduate reading courses and seminars, and in analysis courses as a supplement. The book is also ideal for self study, since the chapters are independent of one another and may be read in any order.
Classical And Discrete Functional Analysis With Measure Theory
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Author : Martin Buntinas
language : en
Publisher: Cambridge University Press
Release Date : 2022-01-20
Classical And Discrete Functional Analysis With Measure Theory written by Martin Buntinas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-20 with Mathematics categories.
This advanced undergraduate/beginning graduate text covers measure theory and discrete aspects of functional analysis, with 760 exercises.