Research Topics In Analysis Volume Ii
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Research Topics In Analysis Volume I
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Author : Shouchuan Hu
language : en
Publisher: Birkhäuser
Release Date : 2022-11-30
Research Topics In Analysis Volume I written by Shouchuan Hu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-30 with Mathematics categories.
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Research Topics In Analysis Volume Ii
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Author : Shouchuan Hu
language : en
Publisher: Birkhäuser
Release Date : 2024-10-14
Research Topics In Analysis Volume Ii written by Shouchuan Hu and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-14 with Mathematics categories.
This book, the second of two volumes, presents significant applications for understanding modern analysis. It empowers young researchers with key techniques and applications to explore various subfields of this broad subject and introduces relevant frameworks for immediate deployment. The applications list begins with Degree Theory, a useful tool for studying nonlinear equations. Chapter 2 deals with Fixed Point Theory, and Chapter 3 introduces Critical Point Theory. Chapter 4 presents the main spectral properties of linear, nonlinear, anisotropic, and double-phase differential operators. Chapter 5 covers semilinear and nonlinear elliptic equations with different boundary conditions, while Chapter 6 addresses dynamic systems monitored by ordinary and partial differential equations. Chapter 7 delves into optimal control problems, and Chapter 8 discusses some economic models, providing a brief presentation of Game Theory and Nash equilibrium. By offering a clear and comprehensive overview of modern analysis tools and applications, this work can greatly benefit mature graduate students seeking research topics, as well as experienced researchers interested in this vast and rich field of mathematics.
Research Topics In Analysis Volume I
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Author : Shouchuan Hu
language : en
Publisher: Springer Nature
Release Date : 2022-11-29
Research Topics In Analysis Volume I written by Shouchuan Hu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-29 with Mathematics categories.
This book, which is the first of two volumes, presents, in a unique way, some of the most relevant research tools of modern analysis. This work empowers young researchers with all the necessary techniques to explore the various subfields of this broad subject, and introduces relevant frameworks where these tools can be immediately deployed. Volume I starts with the foundations of modern analysis. The first three chapters are devoted to topology, measure theory, and functional analysis. Chapter 4 offers a comprehensive analysis of the main function spaces, while Chapter 5 covers more concrete subjects, like multivariate analysis, which are closely related to applications and more difficult to find in compact form. Chapter 6 deals with smooth and non-smooth calculus of functions; Chapter 7 introduces certain important classes of nonlinear operators; and Chapter 8 complements the previous three chapters with topics of variational analysis. Each chapter of this volume finishes with a list of problems – handy for understanding and self-study – and historical notes that give the reader a more vivid picture of how the theory developed. Volume II consists of various applications using the tools and techniques developed in this volume. By offering a clear and wide picture of the tools and applications of modern analysis, this work can be of great benefit not only to mature graduate students seeking topics for research, but also to experienced researchers with an interest in this vast and rich field of mathematics.
Basic Analysis Ii
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Author : Jiri Lebl
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-05-09
Basic Analysis Ii written by Jiri Lebl and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-09 with categories.
Version 2.0. The second volume of Basic Analysis, a first course in mathematical analysis. This volume is the second semester material for a year-long sequence for advanced undergraduates or masters level students. This volume started with notes for Math 522 at University of Wisconsin-Madison, and then was heavily revised and modified for teaching Math 4153/5053 at Oklahoma State University. It covers differential calculus in several variables, line integrals, multivariable Riemann integral including a basic case of Green's Theorem, and topics on power series, Arzelà-Ascoli, Stone-Weierstrass, and Fourier Series. See http://www.jirka.org/ra/ Table of Contents (of this volume II): 8. Several Variables and Partial Derivatives 9. One Dimensional Integrals in Several Variables 10. Multivariable Integral 11. Functions as Limits
Handbook Of Multivalued Analysis
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Author : Shouchuan Hu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-21
Handbook Of Multivalued Analysis written by Shouchuan Hu 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 2013-11-21 with Mathematics categories.
In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.
Methodological Approaches To Stem Education Research Volume 2
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Author : Peta J. White
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2021-08-27
Methodological Approaches To Stem Education Research Volume 2 written by Peta J. White and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-27 with Reference categories.
The COVID-19 pandemic has likely changed the mathematics, health and environmental education research landscape in profound and long-lasting ways. As such, more than ever, there is a need to creatively and critically think about how we design research and for what purposes. This necessitates a considered and robust discussion about educational research theory, method, and methodology to ensure that our research continues to impact practice in valuable ways. This book maps out some of these key challenges and opportunities as we collectively enter a post-COVID-19 world in which method and methodology need to be appreciated as much as research findings. Topics explored here range from big-picture issues in STEM Education research, through perspectives on design-based research, to questions of analysis, complexity, the Delphi method, and ethical dilemmas.
Problems And Theorems In Analysis
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Author : Georg Polya
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Problems And Theorems In Analysis written by Georg Polya 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 2013-03-14 with Mathematics categories.
Handbook Of Applied And Abstract Analysis Volume Ii
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Author : Charlin Chester
language : en
Publisher:
Release Date : 2015-02-13
Handbook Of Applied And Abstract Analysis Volume Ii written by Charlin Chester and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-13 with Mathematical analysis categories.
This book is a guide to all those researching new theories in the field of mathematics. It encircles the latest researches, theories and concepts in the field of classical analysis, linear and nonlinear functional analysis, ordinary and partial differential equations, etc. The aim of this book is to provide current and crucial developments and become a researcher's guide in the area of abstract and applied analysis.
Sharpening Mathematical Analysis Skills
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Author : Alina Sîntămărian
language : en
Publisher: Springer Nature
Release Date : 2021-10-25
Sharpening Mathematical Analysis Skills written by Alina Sîntămărian and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.
This book gathers together a novel collection of problems in mathematical analysis that are challenging and worth studying. They cover most of the classical topics of a course in mathematical analysis, and include challenges presented with an increasing level of difficulty. Problems are designed to encourage creativity, and some of them were especially crafted to lead to open problems which might be of interest for students seeking motivation to get a start in research. The sets of problems are comprised in Part I. The exercises are arranged on topics, many of them being preceded by supporting theory. Content starts with limits, series of real numbers and power series, extending to derivatives and their applications, partial derivatives and implicit functions. Difficult problems have been structured in parts, helping the reader to find a solution. Challenges and open problems are scattered throughout the text, being an invitation to discover new original methods for proving known results and establishing new ones. The final two chapters offer ambitious readers splendid problems and two new proofs of a famous quadratic series involving harmonic numbers. In Part II, the reader will find solutions to the proposed exercises. Undergraduate students in mathematics, physics and engineering, seeking to strengthen their skills in analysis, will most benefit from this work, along with instructors involved in math contests, individuals who want to enrich and test their knowledge in analysis, and anyone willing to explore the standard topics of mathematical analysis in ways that aren’t commonly seen in regular textbooks.
Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science
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Author : Isaac Pesenson
language : en
Publisher: Birkhäuser
Release Date : 2017-08-09
Recent Applications Of Harmonic Analysis To Function Spaces Differential Equations And Data Science written by Isaac Pesenson and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-09 with Mathematics categories.
The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.