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Author : Jean Dieudonné
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 9783663077688
Total Pages : 446 pages
Book Rating : 4.0/5 (776 download)
Download or read book Grundzüge der modernen Analysis written by Jean Dieudonné and published by Vieweg+Teubner Verlag. This book was released on 2013-10-03 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Jean Alexandre Dieudonné
Publisher : Vieweg+Teubner Verlag
ISBN 13 : 9783528182908
Total Pages : 0 pages
Book Rating : 4.1/5 (829 download)
Download or read book Grundzüge der modernen Analysis written by Jean Alexandre Dieudonné and published by Vieweg+Teubner Verlag. This book was released on 1972-01-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Das vorliegende Bueh entstand aus Vorlesungen, die fUr Studenten mit ab gesehlossenem Grundstudium oder auBergewohnlieh fortgesehrittene Studenten 1 niederer Studienjahre ) bestimmt waren. Diese Vorlesungen, die ieh in den Jahren 1956-57 an der Northwestern University gehalten habe, verfolgten einen doppelten Zweek: Sie soUten die notwendigen elementaren Hilfsmittel fiir ein Studium aller Zweige der modernen Mathematik bereitstelIen, in denen die "Ana lysis" eine Rolle spielt (d. h. praktiseh aller Zweige, eventueU mit Ausnahme der mathematisehen Logik und der reinen Algebra), und sie soUten den Studenten mit dem Gebraueh des grundlegenden mathematisehen Werkzeugs unserer Zeit - der axiomatischen Methode - vertraut machen (mit der er wiihrend seiner Grundausbildung katllI, wenn iiberhaupt, in Beriihrung gekommen sein diidte). Es wird dem Leser sehr bald auffalIen, daB ich iiberall den begrifllichen Aspekt betont habe, wiihrend der rechnerische Aspekt, der das Hauptanliegen der klassi schen Analysis war (vgl. [27]), zuriicktritt. Das gilt nicht nur fiir den Text, sondern aueh fUr die meisten Aufgaben. Es wurden verhiiltnismiiBig viele Aufgaben ein gearbeitet, urn den Text zu ergiinzen und auf interessante Weiterentwicklungen hinzuweisen. Gleiehzeitig geben die Aufgaben dem Studenten eine Gelegenheit zu priifen, inwieweit er den dargebotenen Stoff verstanden hat.
Author : Niels Jacob
Publisher : World Scientific Publishing Company
ISBN 13 : 9814689106
Total Pages : 768 pages
Book Rating : 4.8/5 (146 download)
Download or read book A Course in Analysis written by Niels Jacob and published by World Scientific Publishing Company. This book was released on 2015-08-18 with total page 768 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis. Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions. Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers. Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.
Author : E. Zeidler
Publisher : Springer Science & Business Media
ISBN 13 : 1461245664
Total Pages : 1007 pages
Book Rating : 4.4/5 (612 download)
Download or read book Nonlinear Functional Analysis and its Applications written by E. Zeidler and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 1007 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fourth of a five-volume exposition of the main principles of nonlinear functional analysis and its applications to the natural sciences, economics, and numerical analysis. The presentation is self-contained and accessible to the non-specialist, and topics covered include applications to mechanics, elasticity, plasticity, hydrodynamics, thermodynamics, statistical physics, and special and general relativity including cosmology. The book contains a detailed physical motivation of the relevant basic equations and a discussion of particular problems which have played a significant role in the development of physics and through which important mathematical and physical insight may be gained. It combines classical and modern ideas to build a bridge between the language and thoughts of physicists and mathematicians. Many exercises and a comprehensive bibliography complement the text.
Author : Paolo Ciatti
Publisher : World Scientific
ISBN 13 : 9812811052
Total Pages : 460 pages
Book Rating : 4.8/5 (128 download)
Download or read book Topics in Mathematical Analysis written by Paolo Ciatti and published by World Scientific. This book was released on 2008 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This volume consists of a series of lecture notes on mathematical analysis. The contributors have been selected on the basis of both their outstanding scientific level and their clarity of exposition. Thus, the present collection is particularly suited to young researchers and graduate students. Through this volume, the editors intend to provide the reader with material otherwise difficult to find and written in a manner which is also accessible to nonexperts."--BOOK JACKET.
Author : Niels Jacob
Publisher : World Scientific
ISBN 13 : 9811215510
Total Pages : 854 pages
Book Rating : 4.8/5 (112 download)
Download or read book Course In Analysis, A - Vol V: Functional Analysis, Some Operator Theory, Theory Of Distributions written by Niels Jacob and published by World Scientific. This book was released on 2020-01-22 with total page 854 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is an advanced textbook and a reference text in functional analysis in the wide sense. It provides advanced undergraduate and graduate students with a coherent introduction to the field, i.e. the basic principles, and leads them to more demanding topics such as the spectral theorem, Choquet theory, interpolation theory, analysis of operator semigroups, Hilbert-Schmidt operators and Hille-Tamarkin operators, topological vector spaces and distribution theory, fundamental solutions, or the Schwartz kernel theorem.All topics are treated in great detail and the text provided is suitable for self-studying the subject. This is enhanced by more than 270 problems solved in detail. At the same time the book is a reference text for any working mathematician needing results from functional analysis, operator theory or the theory of distributions.Embedded as Volume V in the Course of Analysis, readers will have a self-contained treatment of a key area in modern mathematics. A detailed list of references invites to further studies.
Author : Michael Matthes
Publisher : Logos Verlag Berlin GmbH
ISBN 13 : 3832532781
Total Pages : 191 pages
Book Rating : 4.8/5 (325 download)
Download or read book Numerical Analysis of Nonlinear Partial Differential-algebraic Equations written by Michael Matthes and published by Logos Verlag Berlin GmbH. This book was released on 2012 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: Various mathematical models in many application areas give rise to systems of so called partial or abstract differential-algebraic equations (ADAEs). A substantial mathematical treatment of nonlinear ADAEs is still at an initial stage.In this thesis two approaches for treating nonlinear ADAEs are presented. The first one represents an extension of an approach by Tischendorf for the treatment of a specific class of linear ADAEs to the nonlinear case. It is based on the Galerkin approach and the theory of monotone operators for evolution equations. Unique solvability of the ADAE and strong convergence of the Galerkin solutions is proven. Furthermore it is shown that this class of ADAEs has Perturbation Index 1 and at most ADAE Index 1. In the second approach we formulate two prototypes of coupled systems where a semi-explicit differential-algebraic equation is coupled to an infinite dimensional algebraic operator equation or an evolution equation. For both prototypes unique solvability, strong convergence of Galerkin solutions and a Perturbation Index 1 result is shown. Both prototypes can be applied to concrete coupled systems in circuit simulation relying on a new global solvability result for the nonlinear equations of the Modified Nodal Analysis under suitable topological assumptions.
Author : Yu.M. Berezansky
Publisher : Springer Science & Business Media
ISBN 13 : 9401717583
Total Pages : 494 pages
Book Rating : 4.4/5 (17 download)
Download or read book Harmonic Analysis in Hypercomplex Systems written by Yu.M. Berezansky and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: First works related to the topics covered in this book belong to J. Delsarte and B. M. Le vitan and appeared since 1938. In these works, the families of operators that generalize usual translation operators were investigated and the corresponding harmonic analysis was constructed. Later, starting from 1950, it was noticed that, in such constructions, an important role is played by the fact that the kernels of the corresponding convolutions of functions are nonnegative and by the properties of the normed algebras generated by these convolutions. That was the way the notion of hypercomplex system with continu ous basis appeared. A hypercomplex system is a normed algebra of functions on a locally compact space Q-the "basis" of this hypercomplex system. Later, similar objects, hypergroups, were introduced, which have complex-valued measures on Q as elements and convolution defined to be essentially the convolution of functionals and dual to the original convolution (if measures are regarded as functionals on the space of continuous functions on Q). However, until 1991, the time when this book was written in Russian, there were no monographs containing fundamentals of the theory (with an exception of a short section in the book by Yu. M. Berezansky and Yu. G. Kondratiev [BeKo]). The authors wanted to give an introduction to the theory and cover the most important subsequent results and examples.
Author : Achim Feldmeier
Publisher : CRC Press
ISBN 13 : 1000610004
Total Pages : 355 pages
Book Rating : 4.0/5 (6 download)
Download or read book Introduction to Arnold’s Proof of the Kolmogorov–Arnold–Moser Theorem written by Achim Feldmeier and published by CRC Press. This book was released on 2022-07-08 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREM This book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Features • Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics. • Covers all aspects of Arnold’s proof, including those often left out in more general or simplifi ed presentations. • Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).
Author : WILLS
Publisher : Birkhäuser
ISBN 13 : 3034857659
Total Pages : 399 pages
Book Rating : 4.0/5 (348 download)
Download or read book Contributions to Geometry written by WILLS and published by Birkhäuser. This book was released on 2013-11-11 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the time from June 28-July 1, 1978, representatives of different branches of geometry met in Siegen for discussion of and reports on current problems. In particular, the survey lectures, presented by well known geometers, gave nonspecialists the welcome opportunity to learn about the questions posed, the methods used and the results obtained in different areas of the field of geometry. The research areas represented at the meeting in Siegen are reflected in the list of participants and their contributions: Ranging from geometric convexity and related topics to differential geometry and kinematics. The foundations of geometry, an area well established in Germany, was also represented. It is a pleasure to thank all the lecturers as well as other participants in the Geometry Symposium for their contribution to the success of the meeting. We also thank the "Minister fUr Wissenschaft und Forschung des Landes Nordrhein-Westfalen" and the University of Siegen for their generous support which helped make the Symposium so successful. In order to make the contributions and results of the Symposium accessible to the general public, the publication of a proceedings volume was planned. The idea was to give a summary of a wide spectrum of research in geometr- through survey articles and original research papers.
Author : Ludwig Arnold
Publisher : Springer Science & Business Media
ISBN 13 : 3662128780
Total Pages : 590 pages
Book Rating : 4.6/5 (621 download)
Download or read book Random Dynamical Systems written by Ludwig Arnold and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.
Author : Niels Jacob
Publisher : Imperial College Press
ISBN 13 : 1860945686
Total Pages : 506 pages
Book Rating : 4.8/5 (69 download)
Download or read book Pseudo Differential Operators & Markov Processes: Markov processes and applications written by Niels Jacob and published by Imperial College Press. This book was released on 2001 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work covers two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups. In addition, Dirichlet forms are treated.
Author :
Publisher :
ISBN 13 : 1783260246
Total Pages : pages
Book Rating : 4.7/5 (832 download)
Download or read book Pseudo Differential Operators and Markov Processes written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : J. Dieudonne
Publisher : Hesperides Press
ISBN 13 : 1443724262
Total Pages : 412 pages
Book Rating : 4.4/5 (437 download)
Download or read book Foundations of Modern Analysis written by J. Dieudonne and published by Hesperides Press. This book was released on 2008-11 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: FOUNDATIONS OFMODERN ANALYSISEnlarged and Corrected PrintingJ. DIEUDONNEThis book is the first volume of a treatise which will eventually consist offour volumes. It is also an enlarged and corrected printing, essentiallywithout changes, of my Foundations of Modern Analysis, published in1960. Many readers, colleagues, and friends have urged me to write a sequelto that book, and in the end I became convinced that there was a place fora survey of modern analysis, somewhere between the minimum tool kitof an elementary nature which I had intended to write, and specialistmonographs leading to the frontiers of research. My experience of teachinghas also persuaded me that the mathematical apprentice, after taking the firststep of Foundations, needs further guidance and a kind of general birdseyeview of his subject before he is launched onto the ocean of mathematicalliterature or set on the narrow path of his own topic of research.Thus I have finally been led to attempt to write an equivalent, for themathematicians of 1970, of what the Cours dAnalyse of Jordan, Picard, and Goursat were for mathematical students between 1880 and 1920.It is manifestly out of the question to attempt encyclopedic coverage, andcertainly superfluous to rewrite the works of N. Bourbaki. I have thereforebeen obliged to cut ruthlessly in order to keep within limits comparable tothose of the classical treatises. I have opted for breadth rather than depth, inthe opinion that it is better to show the reader rudiments of many branchesof modern analysis rather than to provide him with a complete and detailedexposition of a small number of topics.Experience seems to show that the student usually finds a new theorydifficult tograsp at a first reading. He needs to return to it several times beforehe becomes really familiar with it and can distinguish for himself whichare the essential ideas and which results are of minor importance, and onlythen will he be able to apply it intelligently. The chapters of this treatise arevi PREFACE TO THE ENLARGED AND CORRECTED PRINTINGtherefore samples rather than complete theories: indeed, I have systematically tried not to be exhaustive. The works quoted in the bibliography willalways enable the reader to go deeper into any particular theory.However, I have refused to distort the main ideas of analysis by presentingthem in too specialized a form, and thereby obscuring their power andgenerality. It gives a false impression, for example, if differential geometryis restricted to two or three dimensions, or if integration is restricted to Lebesgue measure, on the pretext of making these subjects more accessible orintuitive.On the other hand I do not believe that the essential content of the ideasinvolved is lost, in a first study, by restricting attention to separable metrizabletopological spaces. The mathematicians of my own generation were certainlyright to banish, hypotheses of countability wherever they were not needed: thiswas the only way to get a clear understanding.
Author : Immanuel M. Bomze
Publisher : Springer Science & Business Media
ISBN 13 : 1475726007
Total Pages : 350 pages
Book Rating : 4.4/5 (757 download)
Download or read book Developments in Global Optimization written by Immanuel M. Bomze and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks. The collection of papers in this book indicates the diverse applicability of global optimization. Furthermore, various algorithmic, theoretical developments and computational studies are presented. Audience: All researchers and students working in mathematical programming.
Author :
Publisher :
ISBN 13 :
Total Pages : 822 pages
Book Rating : 4.:/5 (43 download)
Download or read book Reviews in Global Analysis, 1980-86 as Printed in Mathematical Reviews written by and published by . This book was released on 1988 with total page 822 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Wolfgang Tutschke
Publisher : Springer Science & Business Media
ISBN 13 : 3662099438
Total Pages : 189 pages
Book Rating : 4.6/5 (62 download)
Download or read book Solution of Initial Value Problems in Classes of Generalized Analytic Functions written by Wolfgang Tutschke and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of the present book is to solve initial value problems in classes of generalized analytic functions as well as to explain the functional-analytic background material in detail. From the point of view of the theory of partial differential equations the book is intend ed to generalize the classicalCauchy-Kovalevskayatheorem, whereas the functional-analytic background connected with the method of successive approximations and the contraction-mapping principle leads to the con cept of so-called scales of Banach spaces: 1. The method of successive approximations allows to solve the initial value problem du CTf = f(t,u), (0. 1) u(O) = u , (0. 2) 0 where u = u(t) ist real o. r vector-valued. It is well-known that this method is also applicable if the function u belongs to a Banach space. A completely new situation arises if the right-hand side f(t,u) of the differential equation (0. 1) depends on a certain derivative Du of the sought function, i. e. , the differential equation (0,1) is replaced by the more general differential equation du dt = f(t,u,Du), (0. 3) There are diff. erential equations of type (0. 3) with smooth right-hand sides not possessing any solution to say nothing about the solvability of the initial value problem (0,3), (0,2), Assume, for instance, that the unknown function denoted by w is complex-valued and depends not only on the real variable t that can be interpreted as time but also on spacelike variables x and y, Then the differential equation (0.
