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Differential and Riemannian Manifolds [[electronic resource] /] / by Serge Lang
| Differential and Riemannian Manifolds [[electronic resource] /] / by Serge Lang |
| Autore | Lang Serge |
| Edizione | [3rd ed. 1995.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1995 |
| Descrizione fisica | 1 online resource (XIV, 364 p.) |
| Disciplina | 516.36 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Differential geometry
Mathematical analysis Analysis (Mathematics) Algebraic topology Differential Geometry Analysis Algebraic Topology |
| ISBN | 1-4612-4182-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Differential Calculus -- §1. Categories -- §2. Topological Vector Spaces -- §3. Derivatives and Composition of Maps -- §4. Integration and Taylor’s Formula -- §5. The Inverse Mapping Theorem -- II Manifolds -- §1. Atlases, Charts, Morphisms -- §2. Submanifolds, Immersions, Submersions -- §3. Partitions of Unity -- §4. Manifolds with Boundary -- III Vector Bundles -- §1. Definition, Pull Backs -- §2. The Tangent Bundle -- §3. Exact Sequences of Bundles -- §4. Operations on Vector Bundles -- §5. Splitting of Vector Bundles -- IV Vector Fields and Differential Equations -- §1. Existence Theorem for Differential Equations -- §2. Vector Fields, Curves, and Flows -- §3. Sprays -- §4. The Flow of a Spray and the Exponential Map -- §5. Existence of Tubular Neighborhoods -- §6. Uniqueness of Tubular Neighborhoods -- V Operations on Vector Fields and Differential Forms -- §1. Vector Fields, Differential Operators, Brackets -- §2. Lie Derivative -- $3. Exterior Derivative -- §4. The Poincaré Lemma -- §5. Contractions and Lie Derivative -- §6. Vector Fields and 1-Forms Under Self Duality -- §7. The Canonical 2-Form -- §8. Darboux’s Theorem -- VI The Theorem of Frobenius -- §1. Statement of the Theorem -- §2. Differential Equations Depending on a Parameter -- §3. Proof of the Theorem -- §4. The Global Formulation -- §5. Lie Groups and Subgroups -- VII Metrics -- §1. Definition and Functoriality -- §2. The Hilbert Group -- §3. Reduction to the Hilbert Group -- §4. Hilbertian Tubular Neighborhoods -- §5. The Morse—Palais Lemma -- §6. The Riemannian Distance -- §7. The Canonical Spray -- VIII Covariant Derivatives and Geodesics -- §1. Basic Properties -- §2. Sprays and Covariant Derivatives -- §3. Derivative Along a Curve and Parallelism -- §4. The Metric Derivative -- §5. More Local Results on the Exponential Map -- §6. Riemannian Geodesic Length and Completeness -- IX Curvature -- §1. The Riemann Tensor -- §2. Jacobi Lifts -- §3. Application of Jacobi Lifts to dexpx -- §4. The Index Form, Variations, and the Second Variation Formula -- §5. Taylor Expansions -- X Volume Forms -- §1. The Riemannian Volume Form -- §2. Covariant Derivatives -- §3. The Jacobian Determinant of the Exponential Map -- §4. The Hodge Star on Forms -- §5. Hodge Decomposition of Differential Forms -- XI Integration of Differential Forms -- §1. Sets of Measure 0 -- §2. Change of Variables Formula -- §3. Orientation -- §4. The Measure Associated with a Differential Form -- XII Stokes’ Theorem -- §1. Stokes’ Theorem for a Rectangular Simplex -- §2. Stokes’ Theorem on a Manifold -- §3. Stokes’ Theorem with Singularities -- XIII Applications of Stokes’ Theorem -- §1. The Maximal de Rham Cohomology -- §2. Moser’s Theorem -- §3. The Divergence Theorem -- §4. The Adjoint of d for Higher Degree Forms -- §5. Cauchy’s Theorem -- §6. The Residue Theorem -- Appendix The Spectral Theorem -- §1. Hilbert Space -- §2. Functionals and Operators -- §3. Hermitian Operators. |
| Record Nr. | UNINA-9910789224303321 |
Lang Serge
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential and Riemannian Manifolds / / by Serge Lang
| Differential and Riemannian Manifolds / / by Serge Lang |
| Autore | Lang Serge |
| Edizione | [3rd ed. 1995.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1995 |
| Descrizione fisica | 1 online resource (XIV, 364 p.) |
| Disciplina | 516.36 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Geometry, Differential
Mathematical analysis Algebraic topology Differential Geometry Analysis Algebraic Topology |
| ISBN | 1-4612-4182-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Differential Calculus -- §1. Categories -- §2. Topological Vector Spaces -- §3. Derivatives and Composition of Maps -- §4. Integration and Taylor’s Formula -- §5. The Inverse Mapping Theorem -- II Manifolds -- §1. Atlases, Charts, Morphisms -- §2. Submanifolds, Immersions, Submersions -- §3. Partitions of Unity -- §4. Manifolds with Boundary -- III Vector Bundles -- §1. Definition, Pull Backs -- §2. The Tangent Bundle -- §3. Exact Sequences of Bundles -- §4. Operations on Vector Bundles -- §5. Splitting of Vector Bundles -- IV Vector Fields and Differential Equations -- §1. Existence Theorem for Differential Equations -- §2. Vector Fields, Curves, and Flows -- §3. Sprays -- §4. The Flow of a Spray and the Exponential Map -- §5. Existence of Tubular Neighborhoods -- §6. Uniqueness of Tubular Neighborhoods -- V Operations on Vector Fields and Differential Forms -- §1. Vector Fields, Differential Operators, Brackets -- §2. Lie Derivative -- $3. Exterior Derivative -- §4. The Poincaré Lemma -- §5. Contractions and Lie Derivative -- §6. Vector Fields and 1-Forms Under Self Duality -- §7. The Canonical 2-Form -- §8. Darboux’s Theorem -- VI The Theorem of Frobenius -- §1. Statement of the Theorem -- §2. Differential Equations Depending on a Parameter -- §3. Proof of the Theorem -- §4. The Global Formulation -- §5. Lie Groups and Subgroups -- VII Metrics -- §1. Definition and Functoriality -- §2. The Hilbert Group -- §3. Reduction to the Hilbert Group -- §4. Hilbertian Tubular Neighborhoods -- §5. The Morse—Palais Lemma -- §6. The Riemannian Distance -- §7. The Canonical Spray -- VIII Covariant Derivatives and Geodesics -- §1. Basic Properties -- §2. Sprays and Covariant Derivatives -- §3. Derivative Along a Curve and Parallelism -- §4. The Metric Derivative -- §5. More LocalResults on the Exponential Map -- §6. Riemannian Geodesic Length and Completeness -- IX Curvature -- §1. The Riemann Tensor -- §2. Jacobi Lifts -- §3. Application of Jacobi Lifts to dexpx -- §4. The Index Form, Variations, and the Second Variation Formula -- §5. Taylor Expansions -- X Volume Forms -- §1. The Riemannian Volume Form -- §2. Covariant Derivatives -- §3. The Jacobian Determinant of the Exponential Map -- §4. The Hodge Star on Forms -- §5. Hodge Decomposition of Differential Forms -- XI Integration of Differential Forms -- §1. Sets of Measure 0 -- §2. Change of Variables Formula -- §3. Orientation -- §4. The Measure Associated with a Differential Form -- XII Stokes’ Theorem -- §1. Stokes’ Theorem for a Rectangular Simplex -- §2. Stokes’ Theorem on a Manifold -- §3. Stokes’ Theorem with Singularities -- XIII Applications of Stokes’ Theorem -- §1. The Maximal de Rham Cohomology -- §2. Moser’s Theorem -- §3. The Divergence Theorem -- §4. The Adjoint of d for Higher Degree Forms -- §5. Cauchy’s Theorem -- §6. The Residue Theorem -- Appendix The Spectral Theorem -- §1. Hilbert Space -- §2. Functionals and Operators -- §3. Hermitian Operators. |
| Record Nr. | UNINA-9910961077703321 |
|
Lang Serge
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1995 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi
| Problems and Solutions for Complex Analysis [[electronic resource] /] / by Rami Shakarchi |
| Autore | Shakarchi Rami |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 246 p. 17 illus.) |
| Disciplina | 515/.9 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Analysis |
| ISBN | 1-4612-1534-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy’s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy’s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy’s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy’s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen’s Formula -- XII.1 Jensen’s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and Meromorphic Functions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. |
| Record Nr. | UNINA-9910789219403321 |
|
Shakarchi Rami
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Problems and Solutions for Complex Analysis / / by Rami Shakarchi
| Problems and Solutions for Complex Analysis / / by Rami Shakarchi |
| Autore | Shakarchi Rami |
| Edizione | [1st ed. 1999.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 |
| Descrizione fisica | 1 online resource (XI, 246 p. 17 illus.) |
| Disciplina | 515/.9 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Soggetto topico |
Mathematical analysis
Analysis |
| ISBN | 1-4612-1534-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Complex Numbers and Functions -- I.1 Definition -- I.2 Polar Form -- I.3 Complex Valued Functions -- I.4 Limits and Compact Sets -- I.6 The Cauchy-Riemann Equations -- II Power Series -- II.1 Formal Power Series -- II.2 Convergent Power Series -- II.3 Relations Between Formal and Convergent Series -- II.4 Analytic Functions -- II.5 Differentiation of Power Series -- II.6 The Inverse and Open Mapping Theorems -- III Cauchy’s Theorem, First Part -- III.1 Holomorphic Functions on Connected Sets -- III.2 Integrals over Paths -- III.5 The Homotopy Form of Cauchy’s Theorem -- III.6 Existence of Global Primitives Definition of the Logarithm -- III.7 The Local Cauchy Formula -- IV Winding Numbers and Cauchy’s Theorem -- IV.2 The Global Cauchy Theorem -- V Applications of Cauchy’s Integral Formula -- V.1 Uniform Limits of Analytic Functions -- V.2 Laurent Series -- V.3 Isolated Singularities -- VI Calculus of Residues -- VI.1 The Residue Formula -- VI.2 Evaluation of Definite Integrals -- VII Conformal Mappings -- VII.2 Analytic Automorphisms of the Disc -- VII.3 The Upper Half Plane -- VII.4 Other Examples -- VII.5 Fractional Linear Transformations -- VIII Harmonic Functions -- VIII.1 Definition -- VIII.2 Examples -- VIII.3 Basic Properties of Harmonic Functions -- VIII.4 The Poisson Formula -- VIII.5 Construction of Harmonic Functions -- IX Schwarz Reflection -- IX.2 Reflection Across Analytic Arcs -- X The Riemann Mapping Theorema -- X.1 Statement of the Theorem -- X.2 Compact Sets in Function Spaces -- XI Analytic Continuation along Curves -- XI.1 Continuation Along a Curve -- XI.2 The Dilogarithm -- XII Applications of the Maximum Modulus Principle and Jensen’s Formula -- XII.1 Jensen’s Formula -- XII.2 The Picard-Borel Theorem -- XII.6 The Phragmen-Lindelof and Hadamard Theorems -- XIII Entire and MeromorphicFunctions -- XIII.1 Infinite Products -- XIII.2 Weierstrass Products -- XIII.3 Functions of Finite Order -- XIII.4 Meromorphic Functions, Mittag-Leffler Theorem -- XV The Gamma and Zeta Functions -- XV.1 The Differentiation Lemma -- XV.2 The Gamma Function -- XV.3 The Lerch Formula -- XV.4 Zeta Functions -- XVI The Prime Number Theorem -- XVI.1 Basic Analytic Properties of the Zeta Function -- XVI.2 The Main Lemma and its Application. |
| Record Nr. | UNINA-9910971116803321 |
|
Shakarchi Rami
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1999 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Real and Functional Analysis [[electronic resource] /] / by Serge Lang
| Real and Functional Analysis [[electronic resource] /] / by Serge Lang |
| Autore | Lang Serge |
| Edizione | [3rd ed. 1993.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XIV, 580 p.) |
| Disciplina | 515 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Mathematical analysis
Analysis (Mathematics) Functions of real variables Analysis Real Functions |
| ISBN | 1-4612-0897-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Sets -- II Topological Spaces -- III Continuous Functions on Compact Sets -- IV Banach Spaces -- V Hilbert Space -- VI The General Integral -- VII Duality and Representation Theorems -- VIII Some Applications of Integration -- IX Integration and Measures on Locally Compact Spaces -- X Riemann-Stieltjes Integral and Measure -- XI Distributions -- XII Integration on Locally Compact Groups -- XIII Differential Calculus -- XIV Inverse Mappings and Differential Equations -- XV The Open Mapping Theorem, Factor Spaces, and Duality -- XVI The Spectrum -- XVII Compact and Fredholm Operators -- XVIII Spectral Theorem for Bounded Hermltian Operators -- XIX Further Spectral Theorems -- XX Spectral Measures -- XXI Local Integration off Differential Forms -- XXII Manifolds -- XXIII Integration and Measures on Manifolds -- Table of Notation. |
| Record Nr. | UNINA-9910789341203321 |
|
Lang Serge
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Real and Functional Analysis / / by Serge Lang
| Real and Functional Analysis / / by Serge Lang |
| Autore | Lang Serge |
| Edizione | [3rd ed. 1993.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 |
| Descrizione fisica | 1 online resource (XIV, 580 p.) |
| Disciplina | 515 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Collana | Graduate Texts in Mathematics |
| Soggetto topico |
Mathematical analysis
Functions of real variables Analysis Real Functions |
| ISBN | 1-4612-0897-1 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | I Sets -- II Topological Spaces -- III Continuous Functions on Compact Sets -- IV Banach Spaces -- V Hilbert Space -- VI The General Integral -- VII Duality and Representation Theorems -- VIII Some Applications of Integration -- IX Integration and Measures on Locally Compact Spaces -- X Riemann-Stieltjes Integral and Measure -- XI Distributions -- XII Integration on Locally Compact Groups -- XIII Differential Calculus -- XIV Inverse Mappings and Differential Equations -- XV The Open Mapping Theorem, Factor Spaces, and Duality -- XVI The Spectrum -- XVII Compact and Fredholm Operators -- XVIII Spectral Theorem for Bounded Hermltian Operators -- XIX Further Spectral Theorems -- XX Spectral Measures -- XXI Local Integration off Differential Forms -- XXII Manifolds -- XXIII Integration and Measures on Manifolds -- Table of Notation. |
| Record Nr. | UNINA-9910961070603321 |
|
Lang Serge
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1993 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions Manual for Geometry [[electronic resource] ] : A High School Course / / by Philip Carlson
| Solutions Manual for Geometry [[electronic resource] ] : A High School Course / / by Philip Carlson |
| Autore | Carlson Philip |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (VI, 140 p.) |
| Disciplina | 516.2 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Soggetto topico |
Education
Geometry Popular Science in Education |
| ISBN | 1-4612-0861-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Distance and Angles -- 2 Coordinates -- 3 Area and the Pythagoras Theorem -- 4 The Distance Formula -- 5 Some Applications of Right Triangles -- 6 Polygons -- 7 Congruent Triangles -- 8 Dilations and Similarities -- 9 Volumes -- 10 Vectors and Dot Products -- 11 Transformations -- 12 Isometrics. |
| Record Nr. | UNINA-9910789341703321 |
|
Carlson Philip
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Solutions Manual for Geometry : A High School Course / / by Philip Carlson
| Solutions Manual for Geometry : A High School Course / / by Philip Carlson |
| Autore | Carlson Philip |
| Edizione | [1st ed. 1994.] |
| Pubbl/distr/stampa | New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 |
| Descrizione fisica | 1 online resource (VI, 140 p.) |
| Disciplina | 516.2 |
| Altri autori (Persone) | LangSerge <1927-2005.> |
| Soggetto topico |
Education
Geometry |
| ISBN | 1-4612-0861-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | 1 Distance and Angles -- 2 Coordinates -- 3 Area and the Pythagoras Theorem -- 4 The Distance Formula -- 5 Some Applications of Right Triangles -- 6 Polygons -- 7 Congruent Triangles -- 8 Dilations and Similarities -- 9 Volumes -- 10 Vectors and Dot Products -- 11 Transformations -- 12 Isometrics. |
| Record Nr. | UNINA-9910962002203321 |
|
Carlson Philip
|
||
| New York, NY : , : Springer New York : , : Imprint : Springer, , 1994 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||