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Analysis in vector spaces [[electronic resource] ] : a course in advanced calculus / / Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha
| Analysis in vector spaces [[electronic resource] ] : a course in advanced calculus / / Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha |
| Autore | Akcoglu Mustafa A (Mustafa Agah), <1934-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2009 |
| Descrizione fisica | 1 online resource (480 p.) |
| Disciplina |
512.52
512/.52 |
| Altri autori (Persone) |
BarthaPaul F. A. <1964->
HaDzung Minh |
| Soggetto topico |
Vector spaces
Functional analysis |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-283-27395-0
9786613273956 1-118-16458-X 1-118-16459-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Analysis 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
4.1 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 7.1 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 10.5 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 Appendix D: Partitions of unityD.1 Partitions of Unity; Index |
| Record Nr. | UNINA-9910139597703321 |
Akcoglu Mustafa A (Mustafa Agah), <1934->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Analysis in vector spaces [[electronic resource] ] : a course in advanced calculus / / Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha
| Analysis in vector spaces [[electronic resource] ] : a course in advanced calculus / / Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha |
| Autore | Akcoglu Mustafa A (Mustafa Agah), <1934-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2009 |
| Descrizione fisica | 1 online resource (480 p.) |
| Disciplina |
512.52
512/.52 |
| Altri autori (Persone) |
BarthaPaul F. A. <1964->
HaDzung Minh |
| Soggetto topico |
Vector spaces
Functional analysis |
| ISBN |
1-283-27395-0
9786613273956 1-118-16458-X 1-118-16459-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Analysis 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
4.1 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 7.1 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 10.5 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 Appendix D: Partitions of unityD.1 Partitions of Unity; Index |
| Record Nr. | UNINA-9910830147503321 |
|
Akcoglu Mustafa A (Mustafa Agah), <1934->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Analysis in vector spaces [[electronic resource] ] : a course in advanced calculus / / Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha
| Analysis in vector spaces [[electronic resource] ] : a course in advanced calculus / / Mustafa A. Akcoglu, Paul F.A. Bartha, Dzung M. Ha |
| Autore | Akcoglu Mustafa A (Mustafa Agah), <1934-> |
| Pubbl/distr/stampa | Hoboken, N.J., : Wiley-Interscience, c2009 |
| Descrizione fisica | 1 online resource (480 p.) |
| Disciplina |
512.52
512/.52 |
| Altri autori (Persone) |
BarthaPaul F. A. <1964->
HaDzung Minh |
| Soggetto topico |
Vector spaces
Functional analysis |
| ISBN |
1-283-27395-0
9786613273956 1-118-16458-X 1-118-16459-8 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Analysis 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
4.1 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 7.1 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 10.5 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 Appendix D: Partitions of unityD.1 Partitions of Unity; Index |
| Record Nr. | UNINA-9910841899403321 |
|
Akcoglu Mustafa A (Mustafa Agah), <1934->
|
||
| Hoboken, N.J., : Wiley-Interscience, c2009 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||