# Электронная книга: Paul F.A. Bartha «Analysis in Vector Spaces»

A rigorous introduction to calculus in vector spaces The concepts and theorems of advanced calculus combined with related computational methods are essential to understanding nearly all areas of quantitative science. Analysis in Vector Spaces presents the central results of this classic subject through rigorous arguments, discussions, and examples. The book aims to cultivate not only knowledge of the major theoretical results, but also the geometric intuition needed for both mathematical problem-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. An elegant approach to eigenvector problems and the spectral theorem sets the stage for later results on volume and integration. Subsequent chapters present the major results of differential and integral calculus of several variables as well as the theory of manifolds. 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 to reinforce new concepts and to illustrate how results can be applied to additional problems. Furthermore, proofs and examples are presented in a clear style that emphasizes the underlying intuitive ideas. Counterexamples are provided throughout the book to warn against possible mistakes, and extensive appendices outline the construction of real numbers, include a fundamental result about dimension, and present general results about determinants. Assuming only a fundamental understanding of linear algebra and single variable calculus, Analysis in Vector Spaces is an excellent book for a second course in analysis for mathematics, physics, computer science, and engineering majors at the undergraduate and graduate levels. It also serves as a valuable reference for further study in any discipline that requires a firm understanding of mathematical techniques and concepts. Издательство: "John Wiley&Sons Limited"
ISBN: 9781118164594 электронная книга Купить за 12895.31 руб и скачать на Litres |

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**Examples of vector spaces**— This page lists some examples of vector spaces. See vector space for the definitions of terms used on this page. See also: dimension, basis. Notation . We will let F denote an arbitrary field such as the real numbers R or the complex numbers C.… … Wikipedia**Vector space**— This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… … Wikipedia**analysis**— /euh nal euh sis/, n., pl. analyses / seez /. 1. the separating of any material or abstract entity into its constituent elements (opposed to synthesis). 2. this process as a method of studying the nature of something or of determining its… … Universalium**Vector calculus**— Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus Derivative Change of variables Implicit differentiation Taylor s theorem Related rates … Wikipedia**Vector bundle**— The Möbius strip is a line bundle over the 1 sphere S1. Locally around every point in S1, it looks like U × R, but the total bundle is different from S1 × R (which is a cylinder instead). In mathematics, a vector bundle is a… … Wikipedia**vector analysis**— the branch of calculus that deals with vectors and processes involving vectors. * * * ▪ mathematics Introduction a branch of mathematics that deals with quantities that have both magnitude and direction. Some physical and geometric… … Universalium**List of real analysis topics**— This is a list of articles that are considered real analysis topics. Contents 1 General topics 1.1 Limits 1.2 Sequences and Series 1.2.1 Summation Methods … Wikipedia**Functional analysis**— For functional analysis as used in psychology, see the functional analysis (psychology) article. Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon… … Wikipedia**Locally convex topological vector space**— In functional analysis and related areas of mathematics, locally convex topological vector spaces or locally convex spaces are examples of topological vector spaces (TVS) which generalize normed spaces. They can be defined as topological vector… … Wikipedia**Normed vector space**— In mathematics, with 2 or 3 dimensional vectors with real valued entries, the idea of the length of a vector is intuitive and can easily be extended to any real vector space Rn. The following properties of vector length are crucial. 1. The zero… … Wikipedia**Topological vector space**— In mathematics, a topological vector space is one of the basic structures investigated in functional analysis. As the name suggests the space blends a topological structure (a uniform structure to be precise) with the algebraic concept of a… … Wikipedia