Topics In Mathematical Analysis
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Advanced Topics In Mathematical Analysis
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Author : Michael Ruzhansky
language : en
Publisher: CRC Press
Release Date : 2019-01-08
Advanced Topics In Mathematical Analysis written by Michael Ruzhansky and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Mathematics categories.
Advanced Topics in Mathematical Analysis is aimed at researchers, graduate students, and educators with an interest in mathematical analysis, and in mathematics more generally. The book aims to present theory, methods, and applications of the selected topics that have significant, useful relevance to contemporary research.
Topics In Contemporary Mathematical Analysis And Applications
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Author : Hemen Dutta
language : en
Publisher: CRC Press
Release Date : 2020-12-22
Topics In Contemporary Mathematical Analysis And Applications written by Hemen Dutta and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-22 with Mathematics categories.
Topics in Contemporary Mathematical Analysis and Applications encompasses several contemporary topics in the field of mathematical analysis, their applications, and relevancies in other areas of research and study. The readers will find developments concerning the topics presented to a reasonable extent with various new problems for further study. Each chapter carefully presents the related problems and issues, methods of solutions, and their possible applications or relevancies in other scientific areas. Aims at enriching the understanding of methods, problems, and applications Offers an understanding of research problems by presenting the necessary developments in reasonable details Discusses applications and uses of operator theory, fixed-point theory, inequalities, bi-univalent functions, functional equations, and scalar-objective programming, and presents various associated problems and ways to solve such problems This book is written for individual researchers, educators, students, and department libraries.
A Concise Approach To Mathematical Analysis
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Author : Mangatiana A. Robdera
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-27
A Concise Approach To Mathematical Analysis written by Mangatiana A. Robdera 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 2011-06-27 with Mathematics categories.
A Concise Approach to Mathematical Analysis introduces the undergraduate student to the more abstract concepts of advanced calculus. The main aim of the book is to smooth the transition from the problem-solving approach of standard calculus to the more rigorous approach of proof-writing and a deeper understanding of mathematical analysis. The first half of the textbook deals with the basic foundation of analysis on the real line; the second half introduces more abstract notions in mathematical analysis. Each topic begins with a brief introduction followed by detailed examples. A selection of exercises, ranging from the routine to the more challenging, then gives students the opportunity to practise writing proofs. The book is designed to be accessible to students with appropriate backgrounds from standard calculus courses but with limited or no previous experience in rigorous proofs. It is written primarily for advanced students of mathematics - in the 3rd or 4th year of their degree - who wish to specialise in pure and applied mathematics, but it will also prove useful to students of physics, engineering and computer science who also use advanced mathematical techniques.
Mathematical Analysis And Applications
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Author : Michael Ruzhansky
language : en
Publisher: John Wiley & Sons
Release Date : 2018-04-11
Mathematical Analysis And Applications written by Michael Ruzhansky and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-11 with Mathematics categories.
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Topics In Mathematical Analysis And Applications
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2014-10-13
Topics In Mathematical Analysis And Applications written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-13 with Mathematics categories.
This volume presents significant advances in a number of theories and problems of Mathematical Analysis and its applications in disciplines such as Analytic Inequalities, Operator Theory, Functional Analysis, Approximation Theory, Functional Equations, Differential Equations, Wavelets, Discrete Mathematics and Mechanics. The contributions focus on recent developments and are written by eminent scientists from the international mathematical community. Special emphasis is given to new results that have been obtained in the above mentioned disciplines in which Nonlinear Analysis plays a central role. Some review papers published in this volume will be particularly useful for a broader readership in Mathematical Analysis, as well as for graduate students. An attempt is given to present all subjects in this volume in a unified and self-contained manner, to be particularly useful to the mathematical community.
Mathematical Analysis
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Author : Andrew Browder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Analysis written by Andrew Browder 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 is a textbook suitable for a year-long course in analysis at the ad vanced undergraduate or possibly beginning-graduate level. It is intended for students with a strong background in calculus and linear algebra, and a strong motivation to learn mathematics for its own sake. At this stage of their education, such students are generally given a course in abstract algebra, and a course in analysis, which give the fundamentals of these two areas, as mathematicians today conceive them. Mathematics is now a subject splintered into many specialties and sub specialties, but most of it can be placed roughly into three categories: al gebra, geometry, and analysis. In fact, almost all mathematics done today is a mixture of algebra, geometry and analysis, and some of the most in teresting results are obtained by the application of analysis to algebra, say, or geometry to analysis, in a fresh and surprising way. What then do these categories signify? Algebra is the mathematics that arises from the ancient experiences of addition and multiplication of whole numbers; it deals with the finite and discrete. Geometry is the mathematics that grows out of spatial experience; it is concerned with shape and form, and with measur ing, where algebra deals with counting.
Topics In Mathematical Analysis And Differential Geometry
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Author : Nicolas K. Laos
language : en
Publisher: World Scientific
Release Date : 1998
Topics In Mathematical Analysis And Differential Geometry written by Nicolas K. Laos and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
This book studies the interplay between mathematical analysis and differential geometry as well as the foundations of these two fields. The development of a unified approach to topological vector spaces, differential geometry and algebraic and differential topology of function manifolds led to the broad expansion of global analysis. This book serves as a self-contained reference on both the prerequisites for further study and the recent research results which have played a decisive role in the advancement of global analysis.
Real Mathematical Analysis
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Author : Charles Chapman Pugh
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-19
Real Mathematical Analysis written by Charles Chapman Pugh 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 2013-03-19 with Mathematics categories.
Was plane geometry your favorite math course in high school? Did you like proving theorems? Are you sick of memorizing integrals? If so, real analysis could be your cup of tea. In contrast to calculus and elementary algebra, it involves neither formula manipulation nor applications to other fields of science. None. It is pure mathematics, and I hope it appeals to you, the budding pure mathematician. Berkeley, California, USA CHARLES CHAPMAN PUGH Contents 1 Real Numbers 1 1 Preliminaries 1 2 Cuts . . . . . 10 3 Euclidean Space . 21 4 Cardinality . . . 28 5* Comparing Cardinalities 34 6* The Skeleton of Calculus 36 Exercises . . . . . . . . 40 2 A Taste of Topology 51 1 Metric Space Concepts 51 2 Compactness 76 3 Connectedness 82 4 Coverings . . . 88 5 Cantor Sets . . 95 6* Cantor Set Lore 99 7* Completion 108 Exercises . . . 115 x Contents 3 Functions of a Real Variable 139 1 Differentiation. . . . 139 2 Riemann Integration 154 Series . . 179 3 Exercises 186 4 Function Spaces 201 1 Uniform Convergence and CO[a, b] 201 2 Power Series . . . . . . . . . . . . 211 3 Compactness and Equicontinuity in CO . 213 4 Uniform Approximation in CO 217 Contractions and ODE's . . . . . . . . 228 5 6* Analytic Functions . . . . . . . . . . . 235 7* Nowhere Differentiable Continuous Functions . 240 8* Spaces of Unbounded Functions 248 Exercises . . . . . 251 267 5 Multivariable Calculus 1 Linear Algebra . . 267 2 Derivatives. . . . 271 3 Higher derivatives . 279 4 Smoothness Classes . 284 5 Implicit and Inverse Functions 286 290 6* The Rank Theorem 296 7* Lagrange Multipliers 8 Multiple Integrals . .
Mathematical Analysis For Engineers
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Author : Bernard Dacorogna
language : en
Publisher: World Scientific Publishing Company
Release Date : 2012-06-18
Mathematical Analysis For Engineers written by Bernard Dacorogna and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-18 with Mathematics categories.
This book follows an advanced course in analysis (vector analysis, complex analysis and Fourier analysis) for engineering students, but can also be useful, as a complement to a more theoretical course, to mathematics and physics students. The first three parts of the book represent the theoretical aspect and are independent of each other. The fourth part gives detailed solutions to all exercises that are proposed in the first three parts. Foreword Foreword (71 KB) Sample Chapter(s) Chapter 1: Differential Operators of Mathematical Physics (272 KB) Chapter 9: Holomorphic functions and Cauchy–Riemann equations (248 KB) Chapter 14: Fourier series (281 KB) Request Inspection Copy Contents: Vector Analysis:Differential Operators of Mathematical PhysicsLine IntegralsGradient Vector FieldsGreen TheoremSurface IntegralsDivergence TheoremStokes TheoremAppendixComplex Analysis:Holomorphic Functions and Cauchy–Riemann EquationsComplex IntegrationLaurent SeriesResidue Theorem and ApplicationsConformal MappingFourier Analysis:Fourier SeriesFourier TransformLaplace TransformApplications to Ordinary Differential EquationsApplications to Partial Differential EquationsSolutions to the Exercises:Differential Operators of Mathematical PhysicsLine IntegralsGradient Vector FieldsGreen TheoremSurface IntegralsDivergence TheoremStokes TheoremHolomorphic Functions and Cauchy–Riemann EquationsComplex IntegrationLaurent SeriesResidue Theorem and ApplicationsConformal MappingFourier SeriesFourier TransformLaplace TransformApplications to Ordinary Differential EquationsApplications to Partial Differential Equations Readership: Undergraduate students in analysis & differential equations, complex analysis, civil, electrical and mechanical engineering.
Topics In Mathematical Analysis
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Author : Augustin Louis Baron Cauchy
language : en
Publisher: World Scientific
Release Date : 1989
Topics In Mathematical Analysis written by Augustin Louis Baron Cauchy and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
This volume aims at surveying and exposing the main ideas and principles accumulated in a number of theories of Mathematical Analysis. The underlying methodological principle is to develop a unified approach to various kinds of problems. In the papers presented, outstanding research scientists discuss the present state of the art and the broad spectrum of topics in the theory.