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Calculus On Normed Vector Spaces

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Calculus On Normed Vector Spaces

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Author : Rodney Coleman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-07-25

Calculus On Normed Vector Spaces written by Rodney Coleman 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 2012-07-25 with Mathematics categories.

This book serves as an introduction to calculus on normed vector spaces at a higher undergraduate or beginning graduate level. The prerequisites include basic calculus and linear algebra, as well as a certain mathematical maturity. All the important topology and functional analysis topics are introduced where necessary. In its attempt to show how calculus on normed vector spaces extends the basic calculus of functions of several variables, this book is one of the few textbooks to bridge the gap between the available elementary texts and high level texts. The inclusion of many non-trivial applications of the theory and interesting exercises provides motivation for the reader.

Convex Functional Analysis

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Author : Andrew J. Kurdila
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-03-30

Convex Functional Analysis written by Andrew J. Kurdila 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 2006-03-30 with Science categories.

This volume is dedicated to the fundamentals of convex functional analysis. It presents those aspects of functional analysis that are extensively used in various applications to mechanics and control theory. The purpose of the text is essentially two-fold. On the one hand, a bare minimum of the theory required to understand the principles of functional, convex and set-valued analysis is presented. Numerous examples and diagrams provide as intuitive an explanation of the principles as possible. On the other hand, the volume is largely self-contained. Those with a background in graduate mathematics will find a concise summary of all main definitions and theorems.

Calculus In Vector Spaces Revised Expanded

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Author : Lawrence Corwin
language : en
Publisher: Routledge
Release Date : 2017-11-22

Calculus In Vector Spaces Revised Expanded written by Lawrence Corwin and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.

Calculus in Vector Spaces addresses linear algebra from the basics to the spectral theorem and examines a range of topics in multivariable calculus. This second edition introduces, among other topics, the derivative as a linear transformation, presents linear algebra in a concrete context based on complementary ideas in calculus, and explains differential forms on Euclidean space, allowing for Green's theorem, Gauss's theorem, and Stokes's theorem to be understood in a natural setting. Mathematical analysts, algebraists, engineers, physicists, and students taking advanced calculus and linear algebra courses should find this book useful.

Analysis In Vector Spaces

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Author : Mustafa A. Akcoglu
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09

Analysis In Vector Spaces written by Mustafa A. Akcoglu 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 2011-09-09 with Mathematics categories.

A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined withrelated computational methods are essential to understanding nearlyall areas of quantitative science. Analysis in Vector Spacespresents the central results of this classic subject throughrigorous arguments, discussions, and examples. The book aims tocultivate not only knowledge of the major theoretical results, butalso the geometric intuition needed for both mathematicalproblem-solving and modeling in the formal sciences. The authors begin with an outline of key concepts, terminology,and notation and also provide a basic introduction to set theory,the properties of real numbers, and a review of linear algebra. Anelegant approach to eigenvector problems and the spectral theoremsets the stage for later results on volume and integration.Subsequent chapters present the major results of differential andintegral calculus of several variables as well as the theory ofmanifolds. Additional topical coverage includes: Sets and functions Real numbers Vector functions Normed vector spaces First- and higher-order derivatives Diffeomorphisms and manifolds Multiple integrals Integration on manifolds Stokes' theorem Basic point set topology Numerous examples and exercises are provided in each chapter toreinforce new concepts and to illustrate how results can be appliedto additional problems. Furthermore, proofs and examples arepresented in a clear style that emphasizes the underlying intuitiveideas. Counterexamples are provided throughout the book to warnagainst possible mistakes, and extensive appendices outline theconstruction of real numbers, include a fundamental result aboutdimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra andsingle variable calculus, Analysis in Vector Spaces is anexcellent book for a second course in analysis for mathematics,physics, computer science, and engineering majors at theundergraduate and graduate levels. It also serves as a valuablereference for further study in any discipline that requires a firmunderstanding of mathematical techniques and concepts.

Calculus In Vector Spaces Without Norm

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Author : A. Frölicher
language : en
Publisher: Springer
Release Date : 2006-11-15

Calculus In Vector Spaces Without Norm written by A. Frölicher and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Advanced Calculus Revised Edition

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Author : Lynn Harold Loomis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-26

Advanced Calculus Revised Edition written by Lynn Harold Loomis 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 2014-02-26 with Mathematics categories.

An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.

Fundamental Concepts In Modern Analysis

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Author : Vagn Lundsgaard Hansen
language : en
Publisher: World Scientific
Release Date : 1999

Fundamental Concepts In Modern Analysis written by Vagn Lundsgaard Hansen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.

Many advanced mathematical disciplines, such as dynamical systems, calculus of variations, differential geometry and the theory of Lie groups, have a common foundation in general topology and calculus in normed vector spaces. In this book, mathematically inclined engineering students are offered an opportunity to go into some depth with fundamental notions from mathematical analysis that are not only important from a mathematical point of view but also occur frequently in the more theoretical parts of the engineering sciences. The book should also appeal to university students in mathematics and in the physical sciences.

Calculus In Vector Spaces Second Edition Revised Expanded

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Author : Lawrence Corwin
language : en
Publisher: CRC Press
Release Date : 1994-12-08

Calculus In Vector Spaces Second Edition Revised Expanded written by Lawrence Corwin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-08 with Mathematics categories.

Classical Analysis On Normed Spaces

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Author : Tsoy-Wo Ma
language : en
Publisher: World Scientific
Release Date : 1995

Classical Analysis On Normed Spaces written by Tsoy-Wo Ma and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.

This book provides an elementary introduction to the classical analysis on normed spaces, paying special attention to nonlinear topics such as fixed points, calculus and ordinary differential equations. It is aimed at beginners who want to get through the basic material as soon as possible and then move on to do their own research immediately. It assumes only general knowledge in finite-dimensional linear algebra, simple calculus and elementary complex analysis. Since the treatment is self-contained with sufficient details, even an undergraduate with mathematical maturity should have no problem working through it alone. Various chapters can be integrated into parts of a Master degree program by course work organized by any regional university. Restricted to finite-dimensional spaces rather than normed spaces, selected chapters can be used for a course in advanced calculus. Engineers and physicists may find this book a handy reference in classical analysis.

Advanced Calculus Of Several Variables

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Author : C. H. Edwards
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Advanced Calculus Of Several Variables written by C. H. Edwards and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.

Calculus On Normed Vector Spaces

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