Download or read book Differential Calculas in Normed Linear Spaces written by Kalyan Mukherjea and published by Springer. This book was released on 2007-08-15 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab initio exposition of the basic results concerning the topology of metric spaces, particularly of normed linear spaces.The last chapter deals with miscellaneous applications of the Differential Calculus including an introduction to the Calculus of Variations. As a corollary to this, there is a brief discussion of geodesics in Euclidean and hyperbolic planes and non-Euclidean geometry.
Download or read book Differential Calculus in Normed Linear Spaces written by Kalyan Mukherjea and published by . This book was released on 2003-01 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces." "The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a red variable and a little Linear Algebra should provide adequate background for understanding the book."--BOOK JACKET.
Download or read book Calculus on Normed Vector Spaces written by Rodney Coleman and published by Springer Science & Business Media. This book was released on 2012-07-25 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Calculus in Normed Linear Spaces written by Daniel W. Lozier and published by . This book was released on 1969 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculus in Vector Spaces Revised Expanded written by Lawrence Corwin and published by Routledge. This book was released on 2017-11-22 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Calculus in Vector Spaces Second Edition Revised Expanded written by Lawrence Corwin and published by CRC Press. This book was released on 1994-12-08 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Calculus in Vector Spaces without Norm written by A. Frölicher and published by Springer. This book was released on 2006-11-15 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Classical Analysis on Normed Spaces written by Tsoy-Wo Ma and published by World Scientific. This book was released on 1995 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Differential Calculus on Normed Spaces written by Henri Cartan and published by Createspace Independent Publishing Platform. This book was released on 2017-08-02 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic and long out of print text by the famous French mathematician Henri Cartan, has finally been retitled and reissued as an unabridged reprint of the Kershaw Publishing Company 1971 edition at remarkably low price for a new generation of university students and teachers. It provides a concise and beautifully written course on rigorous analysis. Unlike most similar texts, which usually develop the theory in either metric or Euclidean spaces, Cartan's text is set entirely in normed vector spaces, particularly Banach spaces. This not only allows the author to develop carefully the concepts of calculus in a setting of maximal generality, it allows him to unify both single and multivariable calculus over either the real or complex scalar fields by considering derivatives of nth orders as linear transformations. This prepares the student for the subsequent study of differentiable manifolds modeled on Banach spaces as well as graduate analysis courses, where normed spaces and their isomorphisms play a central role. More importantly, it's republication in an inexpensive edition finally makes available again the English translations of both long separated halves of Cartan's famous 1965-6 analysis course at the University of Paris: The second half has been in print for over a decade as Differential Forms , published by Dover Books. Without the first half, it has been very difficult for readers of that second half text to be prepared with the proper prerequisites as Cartan originally intended. With both texts now available at very affordable prices, the entire course can now be easily obtained and studied as it was originally intended. The book is divided into two chapters. The first develops the abstract differential calculus. After an introductory section providing the necessary background on the elements of Banach spaces, the Frechet derivative is defined, and proofs are given of the two basic theorems of differential calculus: The mean value theorem and the inverse function theorem. The chapter proceeds with the introduction and study of higher order derivatives and a proof of Taylor's formula. It closes with a study of local maxima and minima including both necessary and sufficient conditions for the existence of such minima. The second chapter is devoted to differential equations. Then the general existence and uniqueness theorems for ordinary differential equations on Banach spaces are proved. Applications of this material to linear equations and to obtaining various properties of solutions of differential equations are then given. Finally the relation between partial differential equations of the first order and ordinary differential equations is discussed. The prerequisites are rigorous first courses in calculus on the real line (elementary analysis), linear algebra on abstract vectors spaces with linear transformations and the basic definitions of topology (metric spaces, topology,etc.) A basic course in differential equations is advised as well. Together with its' sequel, Differential Calculus On Normed Spaces forms the basis for an outstanding advanced undergraduate/first year graduate analysis course in the Bourbakian French tradition of Jean Dieudonn�'s Foundations of Modern Analysis, but a more accessible level and much more affordable then that classic.
Download or read book Differential Calculus and Its Applications written by Michael J. Field and published by Courier Corporation. This book was released on 2013-04-10 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.
Download or read book Differential Calculus in Topological Linear Spaces written by Sadayuki Yamamuro and published by . This book was released on 1974 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Calculus Revised Edition written by Lynn Harold Loomis and published by World Scientific Publishing Company. This book was released on 2014-02-26 with total page 595 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Holomorphy and Calculus in Normed SPates written by Soo Bong Chae and published by CRC Press. This book was released on 2020-11-26 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a systematic introduction to the theory of holomorphic mappings in normed spaces which has been scattered throughout the literature. It gives the necessary, elementary background for all branches of modern mathematics involving differential calculus in higher dimensional spaces.
Download or read book Differential Calculus in Topological Linear Spaces written by S. Yamamuro and published by . This book was released on 2014-01-15 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Methods Linear algebra normed spaces distributions integration written by Jacob Korevaar and published by . This book was released on 1968 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Calculus in Vector Spaces written by Lawrence J. Corwin and published by . This book was released on 1979 with total page 806 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Linear and Nonlinear Functional Analysis with Applications written by Philippe G. Ciarlet and published by SIAM. This book was released on 2013-10-10 with total page 847 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
