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Analysis: From Concepts to Applications (Universitext)
by Jean-Paul PenotThis textbook covers the main results and methods of real analysis in a single volume. Taking a progressive approach to equations and transformations, this book starts with the very foundations of real analysis (set theory, order, convergence, and measure theory) before presenting powerful results that can be applied to concrete problems. In addition to classical results of functional analysis, differential calculus and integration, Analysis discusses topics such as convex analysis, dissipative operators and semigroups which are often absent from classical treatises. Acknowledging that analysis has significantly contributed to the understanding and development of the present world, the book further elaborates on techniques which pervade modern civilization, including wavelets in information theory, the Radon transform in medical imaging and partial differential equations in various mechanical and physical phenomena. Advanced undergraduate and graduate students, engineers as well as practitioners wishing to familiarise themselves with concepts and applications of analysis will find this book useful. With its content split into several topics of interest, the book's style and layout make it suitable for use in several courses, while its self-contained character makes it appropriate for self-study.
Analysis: Grundlagen, Differentiation, Integrationstheorie, Differentialgleichungen, Variationsmethoden, Funktionenräume, Darstellungssätze
by Friedrich SauvignyDieses Lehrbuch behandelt Lehrinhalte der Analysis für die ersten drei Semester des Bachelor-Studiums der Mathematik, Physik und Informatik. Es bietet eine moderne Darstellung der Differential- und Integralrechnung für Funktionen in einer und mehreren reellen sowie einer komplexen Variablen. Elementare Funktionen werden über komplexe Potenzreihen definiert und die Logarithmusfunktion auf ihrer Riemannschen Fläche betrachtet. Nachdem die eindimensionale Integration mittels reeller und komplexer Stammfunktionen durchgeführt ist, wird über uneigentliche n-dimensionale Riemannsche Integrale die Integration auf Mannigfaltigkeiten mit Differentialformen vorgestellt. Mit dem Lebesgueschen Integral und dessen Maßtheorie wird der Banachraum der p-fach integrablen Funktionen eingeführt. Für gewöhnliche Differentialgleichungen werden Existenz-, Eindeutigkeits- und Stabilitätsfragen beantwortet. In einem Kapitel zur Variationsrechnung wird über Geodätische der n-dimensionale Riemannsche Raum präsentiert. Ferner wird das Stieltjes-Integral mit BV-Belegungsfunktionen behandelt und die Differentiation absolut stetiger Funktionen durchgeführt. Schließlich wird der stetige Dualraum zum Lebesgueraum der p-fach integrablen Funktionen über den Rieszschen Darstellungssatz bestimmt.
Analysis
by Norbert SteinmetzDas Buch wendet sich sowohl an Studierende aller mathematischen Fachrichtungen und mathematisch interessierte Studierende der Physik als auch an Dozentinnen und Dozenten, die den Aufbau ihres ersten Analysiskurses noch vor sich haben oder Anregungen für ihre Vorlesungen suchen. Inhalt und Form sind entstanden und vielfach erprobt in immer wieder kritisch veränderten und angepassten 3-semestrigen Analysiskursen. Etwa 2/3 des Buches decken die Erfordernisse einer 2-semestrigen Grundvorlesung Analysis ab, wohingegen das restliche Drittel Elemente der Fourieranalysis, der Differentialgeometrie, der gewöhnlichen Differentialgleichungen und der Funktionentheorie behandeln, Themen, denen eigenständige Vorlesungen auch weiterhin zu wünschen sind. Zu den Besonderheiten zählen die parallele und miteinander verzahnte Einführung des Riemann- und Lebesgueintegrals, die Einbettung einfacher Elemente der komplexen in die reelle Analysis, ausgedehnte Anwendungen – von der Heisenbergschen Unschärferelation über die Lösung der Wärmeleitungsgleichung bis hin zur Black-Scholes-Formel – sowie die Darstellung der Methode von Ostrogradski und des Dixon-Beweises der allgemeinen Cauchyschen Integralformel. Dass an verschiedenen Stellen die eingefahrenen Pfade verlassen wurden, wird der kundigen Leserschaft nicht verborgen bleiben. Die Frage „abstrakt oder anschaulich-verständlich“ wird konsequent zugunsten des letzteren entschieden. Die Übungsaufgaben sind in den laufenden Text eingebaut in der Hoffnung, dass sie so mehr Beachtung finden. Schließlich vermitteln die historischen Anmerkungen und Kurzbiographien einen Eindruck davon, wie die Analysis sich entwickelt hat und wer wesentlich an dieser Entwicklung beteiligt war.
Analysis – Grundlagen und Exkurse: Mehrdimensionale Integralrechnung und ihre Anwendungen
by Adrian Hirn Christian WeißIn diesem Lehrbuch wird der moderne Lebesguesche Integralbegriff ausf#65533;hrlich entwickelt und auf eine vielf#65533;ltige Klasse von geometrischen Objekten, sogenannte Untermannigfaltigkeiten, #65533;bertragen. Der vorliegende zweite Band richtet den Fokus st#65533;rker auf h#65533;here Dimensionen und stellt zusammen mit dem ersten Band eine umfassende Einf#65533;hrung in die Analysis dar. Die mathematischen Grundlagen werden durch zahlreiche *-Kapitel erweitert, welche die Beziehungen der erlernten Inhalte zu anderen Teilgebieten der Mathematik aufzeigen und die Bedeutung der Analysis f#65533;r praktische Anwendungen verdeutlichen. Dar#65533;ber hinaus enth#65533;lt dieses Buch mehr als 50 #65533;bungsaufgaben inklusive L#65533;sungen, sodass es sich sehr gut f#65533;r Pr#65533;fungsvorbereitungen und zum Selbststudium eignet.
Analysis – Grundlagen und Exkurse: Grundprinzipien der Differential- und Integralrechnung
by Adrian Hirn Christian WeißIn diesem Lehrbuch wird der moderne Lebesguesche Integralbegriff ausf#65533;hrlich entwickelt und auf eine vielf#65533;ltige Klasse von geometrischen Objekten, sogenannte Untermannigfaltigkeiten, #65533;bertragen. Der vorliegende zweite Band richtet den Fokus st#65533;rker auf h#65533;here Dimensionen und stellt zusammen mit dem ersten Band eine umfassende Einf#65533;hrung in die Analysis dar. Die mathematischen Grundlagen werden durch zahlreiche *-Kapitel erweitert, welche die Beziehungen der erlernten Inhalte zu anderen Teilgebieten der Mathematik aufzeigen und die Bedeutung der Analysis f#65533;r praktische Anwendungen verdeutlichen. Dar#65533;ber hinaus enth#65533;lt dieses Buch mehr als 50 #65533;bungsaufgaben inklusive L#65533;sungen, sodass es sich sehr gut f#65533;r Pr#65533;fungsvorbereitungen und zum Selbststudium eignet.
Analysis 1: Ein zuverlässiger und verständlicher Begleiter für Studium und Prüfung
by Martin Brokate Johannes Zimmer Florian LindemannZiel dieses Lehrbuchs ist es, das Material des ersten Semesters eines Vorlesungszyklus zur Analysis prägnant und verständlich darzustellen und darüber hinaus Ausblicke und Ergänzungen zu geben, die den Stoff lebendig werden lassen. Besonderer Wert wird auf die Motivation der zu behandelnden Themen gelegt. Zu Beginn des Buchs wird die mathematische Denkweise, insbesondere Beweistechniken und axiomatisches Vorgehen, ausführlich eingeführt. Dieses Buch basiert auf Vorlesungen, die regelmäßig und seit vielen Jahren an der TU München abgehalten werden. Zahlreiche Abbildungen veranschaulichen die behandelten Konzepte und Ideen. Zudem ermöglicht dieses Lehrbuch den Zugriff auf mehr als 250 interaktive Aufgaben in der Springer Nature Flashcards-App, mit denen Wissen und Verständnis überprüft werden kann – hervorragend geeignet auch zur Prüfungsvorbereitung.
Analysis 1: Differential- und Integralrechnung einer Veränderlichen (Grundkurs Mathematik)
by Otto Forster Florian LindemannDieses fest etablierte Lehrbuch begleitet Studierende der Mathematik, Physik und Informatik seit über vier Jahrzehnten durch die Analysis des ersten Semesters. Es gelangt in systematischer Weise, aber ohne zu große Abstraktionen, einfach und verständlich zu den grundlegenden Begriffen (Konvergenz von Folgen und Reihen, Stetigkeit, Differentiation, Riemannsches Integral) und illustriert sie mit zahlreichen Beispielen. Die numerische Seite der Analysis wird an verschiedenen Stellen beleuchtet, um den Grenzwertbegriff konkreter zu machen. Das Buch schließt mit zwei Kapiteln über Taylor- und Fourier-Reihen, in denen alle bis dahin gelernten Techniken zum Einsatz kommen. Jedes Kapitel enthält Übungsaufgaben zum Vertiefen der Inhalte. Für die vorliegende Auflage wurde der Text einschließlich aller Abbildungen erneut überarbeitet. Darüber hinaus ergänzen nun elektronische Flashcards das Buch: Diese per App zugänglichen Verständnisfragen unterstützen den Lernprozess und eignen sich auch sehr gut zur Prüfungsvorbereitung.
Analysis and Algebra on Differentiable Manifolds: A Workbook for Students and Teachers (Problem Books in Mathematics)
by Ihor V. Mykytyuk Jaime Muñoz Masqué Pedro M. GadeaThis is the second edition of this best selling problem book for students, now containing over 400 completely solved exercises on differentiable manifolds, Lie theory, fibre bundles and Riemannian manifolds. The exercises go from elementary computations to rather sophisticated tools. Many of the definitions and theorems used throughout are explained in the first section of each chapter where they appear. A 56-page collection of formulae is included which can be useful as an aide-mémoire, even for teachers and researchers on those topics. In this 2nd edition: * 76 new problems * a section devoted to a generalization of Gauss' Lemma * a short novel section dealing with some properties of the energy of Hopf vector fields * an expanded collection of formulae and tables * an extended bibliography Audience This book will be useful to advanced undergraduate and graduate students of mathematics, theoretical physics and some branches of engineering with a rudimentary knowledge of linear and multilinear algebra.
Analysis and Applied Mathematics: Extended Abstracts of the 2022 Joint Seminar (Trends in Mathematics #6)
by Allaberen Ashyralyev Michael Ruzhansky Makhmud A. SadybekovThis book presents extended abstracts of the Analysis and Applied Mathematics seminar organized jointly by Bahçeşehir University, Istanbul, Turkey, Ghent Analysis & PDE Center, Ghent University, Ghent, Belgium and the Institute Mathematics & Math. Modeling, Almaty, Kazakhstan. The book is of value to professional mathematicians as well as advanced students in the fields of analysis and applied mathematics. The goal of the seminar is to provide a forum for researchers and scientists from different regions to communicate their recent developments and to present their original results in various fields of analysis and applied mathematics. All of the articles contain new results and are peer-reviewed. The volume reflects the latest developments in the area of analysis and applied mathematics and their interdisciplinary applications.
Analysis and Approximation of Contact Problems with Adhesion or Damage (Chapman & Hall/CRC Pure and Applied Mathematics)
by Mircea Sofonea Weimin Han Meir ShillorResearch into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor carefully selected several models and thoroughly study them in Analysis and Approximation of Contact P
Analysis and Approximation of Rare Events: Representations and Weak Convergence Methods (Probability Theory and Stochastic Modelling #94)
by Amarjit Budhiraja Paul DupuisThis book presents broadly applicable methods for the large deviation and moderate deviation analysis of discrete and continuous time stochastic systems. A feature of the book is the systematic use of variational representations for quantities of interest such as normalized logarithms of probabilities and expected values. By characterizing a large deviation principle in terms of Laplace asymptotics, one converts the proof of large deviation limits into the convergence of variational representations. These features are illustrated though their application to a broad range of discrete and continuous time models, including stochastic partial differential equations, processes with discontinuous statistics, occupancy models, and many others. The tools used in the large deviation analysis also turn out to be useful in understanding Monte Carlo schemes for the numerical approximation of the same probabilities and expected values. This connection is illustrated through the design and analysis of importance sampling and splitting schemes for rare event estimation. The book assumes a solid background in weak convergence of probability measures and stochastic analysis, and is suitable for advanced graduate students, postdocs and researchers.
Analysis and Control for Fractional-order Systems
by Yonggui Kao Yue Cao Changhong Wang Hongwei XiaThis book focuses on the applications of various types of fractional-order differential equations. The authors present their latest research results. This book for the first time introduces the concept of general fractional chaotic systems and their synchronisation, investigates the synchronisation of a fractional coupled reaction-diffusion system using a sliding mode control approach, and considers the impacts of fear and prey escape on a fractional-order prey-predator system with Beddington-DeAngelis functional response. Authors believe that these recent research results can promote the applications of fractional-order differential equations in diverse areas. The book will be attractive to researchers in various fields of mathematics, biomathematics and engineering. Graduate students in related fields may also find this book useful.
Analysis and Control of Boolean Networks: A Semi-tensor Product Approach (Communications and Control Engineering)
by Hongsheng Qi Daizhan Cheng Zhiqiang LiAnalysis and Control of Boolean Networks presents a systematic new approach to the investigation of Boolean control networks. The fundamental tool in this approach is a novel matrix product called the semi-tensor product (STP). Using the STP, a logical function can be expressed as a conventional discrete-time linear system. In the light of this linear expression, certain major issues concerning Boolean network topology - fixed points, cycles, transient times and basins of attractors - can be easily revealed by a set of formulae. This framework renders the state-space approach to dynamic control systems applicable to Boolean control networks. The bilinear-systemic representation of a Boolean control network makes it possible to investigate basic control problems including controllability, observability, stabilization, disturbance decoupling etc.
Analysis and Control of Coupled Neural Networks with Reaction-Diffusion Terms
by Tingwen Huang Jin-Liang Wang Huai-Ning Wu Shun-Yan RenThis book introduces selected recent findings on the analysis and control of dynamical behaviors for coupled reaction-diffusion neural networks. It presents novel research ideas and essential definitions concerning coupled reaction-diffusion neural networks, such as passivity, adaptive coupling, spatial diffusion coupling, and the relationship between synchronization and output strict passivity. Further, it gathers research results previously published in many flagship journals, presenting them in a unified form. As such, the book will be of interest to all university researchers and graduate students in Engineering and Mathematics who wish to study the dynamical behaviors of coupled reaction-diffusion neural networks.
Analysis and Control of Finite-Valued Systems
by Haitao Li Guodong Zhao Peilian GuoA comprehensive work in finite-value systems that covers the latest achievements using the semi-tensor product method, on various kinds of finite-value systems. These results occupy the highest position in the analysis and control of this field. It not only covers all aspects of research in finite-value systems, but also presents the mathematical derivation for each conclusion in depth. The book contains examples to provide a better understanding of the practical applications of finite-value systems. It will serve as a textbook for graduate students of Cybernetics, Mathematical, and Biology, and a reference for readers interested in the theory of finite-value systems.
Analysis and Control of Output Synchronization for Complex Dynamical Networks
by Jin-Liang Wang Huai-Ning Wu Tingwen Huang Shun-Yan RenThis book introduces recent results on output synchronization of complex dynamical networks with single and multiple weights. It discusses novel research ideas and a number of definitions in complex dynamical networks, such as H-Infinity output synchronization, adaptive coupling weights, multiple weights, the relationship between output strict passivity and output synchronization. Furthermore, it methodically edits the research results previously published in various flagship journals and presents them in a unified form. The book is of interest to university researchers and graduate students in engineering and mathematics who wish to study output synchronization of complex dynamical networks.
Analysis and Data-Based Reconstruction of Complex Nonlinear Dynamical Systems: Using the Methods of Stochastic Processes (Understanding Complex Systems)
by M. Reza Rahimi TabarThis book focuses on a central question in the field of complex systems: Given a fluctuating (in time or space), uni- or multi-variant sequentially measured set of experimental data (even noisy data), how should one analyse non-parametrically the data, assess underlying trends, uncover characteristics of the fluctuations (including diffusion and jump contributions), and construct a stochastic evolution equation?Here, the term "non-parametrically" exemplifies that all the functions and parameters of the constructed stochastic evolution equation can be determined directly from the measured data.The book provides an overview of methods that have been developed for the analysis of fluctuating time series and of spatially disordered structures. Thanks to its feasibility and simplicity, it has been successfully applied to fluctuating time series and spatially disordered structures of complex systems studied in scientific fields such as physics, astrophysics, meteorology, earth science, engineering, finance, medicine and the neurosciences, and has led to a number of important results.The book also includes the numerical and analytical approaches to the analyses of complex time series that are most common in the physical and natural sciences. Further, it is self-contained and readily accessible to students, scientists, and researchers who are familiar with traditional methods of mathematics, such as ordinary, and partial differential equations.The codes for analysing continuous time series are available in an R package developed by the research group Turbulence, Wind energy and Stochastic (TWiSt) at the Carl von Ossietzky University of Oldenburg under the supervision of Prof. Dr. Joachim Peinke. This package makes it possible to extract the (stochastic) evolution equation underlying a set of data or measurements.
Analysis and Design for Fuzzy Systems
by Changhong Wang Xiao Xu Yonggui Kao Hongwei XiaThis book proposes analysis and design techniques for fuzzy systems using adaptive technology, event triggering mechanism, sampling control technology, and sliding mode control technology. The book covers stochastic stability, finite-time boundedness, actuator failure problems, fault-tolerant control, asynchronous control, and adaptive sliding mode control for uncertain fuzzy systems. The topic of fault-tolerant control will be of particular interest to readers because: (i) the internal hardware components of the system may age and fail to a greater or lesser extent; (ii) the external environment may suddenly change. With illustrations and tables, readers can easily follow the didactic approach and apply the methods to their own research. This book will be of particular interest to researchers and graduate students in control engineering and applied mathematics who are interested in the latest developments in fuzzy systems.
Analysis and Design of Delayed Neural Networks (Intelligent Control and Learning Systems #19)
by Xin Wang Yu Xue Xian Zhang Yantao WangThis book provides a direct method based on system solutions to address the problems related to the analysis and control of delayed neural networks. The method proposed in this book is important for the following reasons: It does not involve the construct of any Lyapunov-Krasovskii functional (LKF), which overcomes the difficulty in constructing an appropriate and effective LKF; It can provide more simpler sufficient conditions, and hence it possesses less computational complexity; It can result in delay-dependent global exponential stability criteria that can used to give the decay rate estimation of the state; It is suitable for analysis and design problems of most system models with (multiple) delays after a small modification. The book is divided into 11 chapters, and focuses on the analysis and design problems related to delayed neural networks. It is written for graduate students and research level mathematicians and is suitable for postgraduates or as a reference.
Analysis and Design of Discrete Part Production Lines (Springer Optimization and Its Applications #31)
by Diomidis Spinellis Chrissoleon T. Papadopoulos Michael J. Vidalis Michael E. O'KellyThis book provides a complete overview of production systems and describes the best approaches to analyze their performance. Written by experts in the field, this work also presents numerous techniques that can be used to describe, model, and optimize the performance of various types of production lines. The book is intended for researchers, production managers, and graduate students in industrial, mechanical, and systems engineering.
Analysis and Design of Markov Jump Systems with Complex Transition Probabilities (Studies in Systems, Decision and Control #54)
by Peng Shi Lixian Zhang Ting Yang Yanzheng ZhuThe bookaddresses the control issues such as stability analysis, control synthesis andfilter design of Markov jump systems with the above three types of TPs, andthus is mainly divided into three parts. Part I studies the Markov jump systemswith partially unknown TPs. Different methodologies with different conservatismfor the basic stability and stabilization problems are developed and compared. Then the problems of state estimation, the control of systems with time-varyingdelays, the case involved with both partially unknown TPs and uncertain TPs ina composite way are also tackled. Part II deals with the Markov jump systemswith piecewise homogeneous TPs. Methodologies that can effectively handlecontrol problems in the scenario are developed, including the one coping withthe asynchronous switching phenomenon between the currently activated systemmode and the controller/filter to be designed. Part III focuses on the Markov jumpsystems with memory TPs. The concept of σ-mean square stability is proposedsuch that the stability problem can be solved via a finite number ofconditions. The systems involved with nonlinear dynamics (described via theTakagi-Sugeno fuzzy model) are also investigated. Numerical and practicalexamples are given to verify the effectiveness of the obtained theoreticalresults. Finally, some perspectives and future works are presented to concludethe book.
Analysis and Design of Nonlinear Systems in the Frequency Domain (Springer Theses)
by Yunpeng ZhuThis book focuses on the development of three novel approaches to build up a framework for the frequency domain analysis and design of nonlinear systems. The concepts are derived from Volterra series representation of nonlinear systems which are described by nonlinear difference or differential equations. Occupying the middle ground between traditional linear approaches and more complex nonlinear system theories, the book will help readers to have a good start to analyse and exploit the nonlinearities. Analysis and Design of Nonlinear Systems in the Frequency Domain provides clear illustrations and examples at the beginning and the end of each chapter, respectively, making it of interest to both academics and practicing engineers.
Analysis and Design of Singular Markovian Jump Systems
by Guoliang Wang Qingling Zhang Xinggang YanThis monograph is an up-to-date presentation of the analysis and design of singular Markovian jump systems (SMJSs) in which the transition rate matrix of the underlying systems is generally uncertain, partially unknown and designed. The problems addressed include stability, stabilization, H∞ control and filtering, observer design, and adaptive control. applications of Markov process are investigated by using Lyapunov theory, linear matrix inequalities (LMIs), S-procedure and the stochastic Barbalat's Lemma, among other techniques. Features of the book include: · study of the stability problem for SMJSs with general transition rate matrices (TRMs); · stabilization for SMJSs by TRM design, noise control, proportional-derivative and partially mode-dependent control, in terms of LMIs with and without equation constraints; · mode-dependent and mode-independent H∞ control solutions with development of a type of disordered controller; · observer-based controllers of SMJSs in which both the designed observer and controller are either mode-dependent or mode-independent; · consideration of robust H∞ filtering in terms of uncertain TRM or filter parameters leading to a method for totally mode-independent filtering · development of LMI-based conditions for a class of adaptive state feedback controllers with almost-certainly-bounded estimated error and almost-certainly-asymptotically-stable corres ponding closed-loop system states · applications of Markov process on singular systems with norm bounded uncertainties and time-varying delays Analysis and Design of Singular Markovian Jump Systems contains valuable reference material for academic researchers wishing to explore the area. The contents are also suitable for a one-semester graduate course.
Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi (Springer Proceedings in Mathematics & Statistics #127)
by Ali Baklouti Aziz El Kacimi Sadok Kallel Nordine MirThis book includes selected papers presented at the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) conference, held in memory of Mohammed Salah Baouendi, a most renowned figure in the field of several complex variables, who passed away in 2011. All research articles were written by leading experts, some of whom are prize winners in the fields of complex geometry, algebraic geometry and analysis. The book offers a valuable resource for all researchers interested in recent developments in analysis and geometry.
The Analysis and Geometry of Hardy's Inequality
by Alexander A. Balinsky W. Desmond Evans Roger T. LewisThis volume presents advances that have been made over recent decades in areas of research featuring Hardy's inequality and related topics. The inequality and its extensions and refinements are not only of intrinsic interest but are indispensable tools in many areas of mathematics and mathematical physics. Hardy inequalities on domains have a substantial role and this necessitates a detailed investigation of significant geometric properties of a domain and its boundary. Other topics covered in this volume are Hardy- Sobolev-Maz'ya inequalities; inequalities of Hardy-type involving magnetic fields; Hardy, Sobolev and Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich inequality. The Analysis and Geometry of Hardy's Inequality provides an up-to-date account of research in areas of contemporary interest and would be suitable for a graduate course in mathematics or physics. A good basic knowledge of real and complex analysis is a prerequisite.