LEADER 04708nam 2200625Ia 450 001 9910139597703321 005 20170815152945.0 010 $a1-283-27395-0 010 $a9786613273956 010 $a1-118-16458-X 010 $a1-118-16459-8 035 $a(CKB)2550000000054316 035 $a(EBL)818913 035 $a(OCoLC)751969645 035 $a(SSID)ssj0000566792 035 $a(PQKBManifestationID)11389890 035 $a(PQKBTitleCode)TC0000566792 035 $a(PQKBWorkID)10550228 035 $a(PQKB)11072974 035 $a(MiAaPQ)EBC818913 035 $a(EXLCZ)992550000000054316 100 $a20080725d2009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAnalysis in vector spaces$b[electronic resource] $ea course in advanced calculus /$fMustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha 210 $aHoboken, N.J. $cWiley-Interscience$dc2009 215 $a1 online resource (480 p.) 300 $aIncludes index. 311 $a0-470-14824-1 327 $aAnalysis in Vector Spaces: A Course in Advanced Calculus; CONTENTS; Preface; PART I BACKGROUND MATERIAL; 1 Sets and Functions; 1.1 Sets in General; 1.2 Sets of Numbers; 1.3 Functions; 2 Real Numbers; 2.1 Review of the Order Relations; 2.2 Completeness of Real Numbers; 2.3 Sequences of Real Numbers; 2.4 Subsequences; 2.5 Series of Real Numbers; 2.6 Intervals and Connected Sets; 3 Vector Functions; 3.1 Vector Spaces: The Basics; 3.2 Bilinear Functions; 3.3 Multilinear Functions; 3.4 Inner Products; 3.5 Orthogonal Projections; 3.6 Spectral Theorem; PART II DIFFERENTIATION; 4 Normed Vector Spaces 327 $a4.1 Preliminaries4.2 Convergence in Normed Spaces; 4.3 Norms of Linear and Multilinear Transformations; 4.4 Continuity in Normed Spaces; 4.5 Topology of Normed Spaces; 5 Derivatives; 5.1 Functions of a Real Variable; 5.2 Differentiable Functions; 5.3 Existence of Derivatives; 5.4 Partial Derivatives; 5.5 Rules of Differentiation; 5.6 Differentiation of Products; 6 Diffeomorphisms and Manifolds; 6.1 The Inverse Function Theorem; 6.2 Graphs; 6.3 Manifolds in Parametric Representations; 6.4 Manifolds in Implicit Representations; 6.5 Differentiation on Manifolds; 7 Higher-Order Derivatives 327 $a7.1 Definitions7.2 Change of Order in Differentiation; 7.3 Sequences of Polynomials; 7.4 Local Extremal Values; PART III INTEGRATION; 8 Multiple Integrals; 8.1 Jordan Sets and Volume; 8.2 Integrals; 8.3 Images of Jordan Sets; 8.4 Change of Variables; 9 Integration on Manifolds; 9.1 Euclidean Volumes; 9.2 Integration on Manifolds; 9.3 Oriented Manifolds; 9.4 Integrals of Vector Fields; 9.5 Integrals of Tensor Fields; 9.6 Integration on Graphs; 10 Stokes' Theorem; 10.1 Basic Stokes' Theorem; 10.2 Flows; 10.3 Flux and Change of Volume in a Flow; 10.4 Exterior Derivatives 327 $a10.5 Regular and Almost Regular Sets10.6 Stokes' theorem on Manifolds; PART IV APPENDICES; Appendix A: Construction of the real numbers; A.1 Field and Order Axioms in Q; A.2 Equivalence Classes of Cauchy Sequences in Q; A.3 Completeness of R; Appendix B: Dimension of a vector space; B.1 Bases and linearly independent subsets; Appendix C: Determinants; C.1 Permutations; C.2 Determinants of Square Matrices; C.3 Determinant Functions; C.4 Determinant of a Linear Transformation; C.5 Determinants on Cartesian Products; C.6 Determinants in Euclidean Spaces; C.7 Trace of an Operator 327 $aAppendix D: Partitions of unityD.1 Partitions of Unity; Index 330 $aA 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 606 $aVector spaces 606 $aFunctional analysis 608 $aElectronic books. 615 0$aVector spaces. 615 0$aFunctional analysis. 676 $a512.52 676 $a512/.52 700 $aAkcoglu$b Mustafa A$g(Mustafa Agah),$f1934-$0896408 701 $aBartha$b Paul F. A.$f1964-$0896409 701 $aHa$b Dzung Minh$0896410 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910139597703321 996 $aAnalysis in vector spaces$92002598 997 $aUNINA