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Calculus On Normed Vector Spaces

Author: Rodney Coleman
Publisher: Springer Science & Business Media
ISBN: 1461438942
Size: 24.15 MB
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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.

The Calculus Of Variations

Author: Bruce van Brunt
Publisher: Springer Science & Business Media
ISBN: 0387216979
Size: 49.78 MB
Format: PDF, ePub, Mobi
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Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.

An Introduction To Banach Space Theory

Author: Robert E. Megginson
Publisher: Springer Science & Business Media
ISBN: 1461206030
Size: 42.26 MB
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Preparing students for further study of both the classical works and current research, this is an accessible text for students who have had a course in real and complex analysis and understand the basic properties of L p spaces. It is sprinkled liberally with examples, historical notes, citations, and original sources, and over 450 exercises provide practice in the use of the results developed in the text through supplementary examples and counterexamples.

A Taste Of Topology

Author: Volker Runde
Publisher: Springer Science & Business Media
ISBN: 9780387257907
Size: 40.81 MB
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Having evolved from Runde’s notes for an introductory topology course at the University of Alberta, this essential text provides a concise introduction to set-theoretic topology. In places, Runde’s text treats its material differently to other books on the subject, providing a fresh perspective.

Notes On Geometry

Author: Elmer Rees
Publisher: Springer Science & Business Media
ISBN: 3642617778
Size: 60.53 MB
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In recent years, geometry has played a lesser role in undergraduate courses than it has ever done. Nevertheless, it still plays a leading role in mathematics at a higher level. Its central role in the history of mathematics has never been disputed. It is important, therefore, to introduce some geometry into university syllabuses. There are several ways of doing this, it can be incorporated into existing courses that are primarily devoted to other topics, it can be taught at a first year level or it can be taught in higher level courses devoted to differential geometry or to more classical topics. These notes are intended to fill a rather obvious gap in the literature. It treats the classical topics of Euclidean, projective and hyperbolic geometry but uses the material commonly taught to undergraduates: linear algebra, group theory, metric spaces and complex analysis. The notes are based on a course whose aim was two fold, firstly, to introduce the students to some geometry and secondly to deepen their understanding of topics that they have already met. What is required from the earlier material is a familiarity with the main ideas, specific topics that are used are usually redone.

Non Associative Normed Algebras

Author: Miguel Cabrera García
Publisher: Cambridge University Press
ISBN: 1107043115
Size: 22.79 MB
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The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.

Vector Analysis Versus Vector Calculus

Author: Antonio Galbis
Publisher: Springer Science & Business Media
ISBN: 1461422000
Size: 17.79 MB
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The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Key topics include vectors and vector fields, line integrals, regular k-surfaces, flux of a vector field, orientation of a surface, differential forms, Stokes' theorem, and divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.

Postmodern Analysis

Author: Jürgen Jost
Publisher: Springer Science & Business Media
ISBN: 9783540258308
Size: 79.85 MB
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What is the title of this book intended to signify, what connotations is the adjective “Postmodern” meant to carry? A potential reader will surely pose this question. To answer it, I should describe what distinguishes the - proach to analysis presented here from what has by its protagonists been called “Modern Analysis”. “Modern Analysis” as represented in the works of the Bourbaki group or in the textbooks by Jean Dieudonn ́ e is characterized by its systematic and axiomatic treatment and by its drive towards a high level of abstraction. Given the tendency of many prior treatises on analysis to degenerate into a collection of rather unconnected tricks to solve special problems, this de?nitely represented a healthy achievement. In any case, for the development of a consistent and powerful mathematical theory, it seems to be necessary to concentrate solely on the internal problems and structures and to neglect the relations to other ?elds of scienti?c, even of mathematical study for a certain while. Almost complete isolation may be required to reach the level of intellectual elegance and perfection that only a good mathem- ical theory can acquire. However, once this level has been reached, it can be useful to open one’s eyes again to the inspiration coming from concrete external problems.

Linear And Nonlinear Functional Analysis With Applications

Author: Philippe G. Ciarlet
Publisher: SIAM
ISBN: 1611972582
Size: 49.26 MB
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This single-volume textbook covers the fundamentals of linear and nonlinear functional analysis, illustrating most of the basic theorems with numerous applications to linear and nonlinear partial differential equations and to selected topics from numerical analysis and optimization theory. This book has pedagogical appeal because it features self-contained and complete proofs of most of the theorems, some of which are not always easy to locate in the literature or are difficult to reconstitute. It also offers 401 problems and 52 figures, plus historical notes and many original references that provide an idea of the genesis of the important results, and it covers most of the core topics from functional analysis.

Analysis For Applied Mathematics

Author: Ward Cheney
Publisher: Springer Science & Business Media
ISBN: 1475735596
Size: 57.76 MB
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This well-written book contains the analytical tools, concepts, and viewpoints needed for modern applied mathematics. It treats various practical methods for solving problems such as differential equations, boundary value problems, and integral equations. Pragmatic approaches to difficult equations are presented, including the Galerkin method, the method of iteration, Newton’s method, projection techniques, and homotopy methods.