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Differential geometry [[electronic resource] /] / [by] J. J. Stoker
| Differential geometry [[electronic resource] /] / [by] J. J. Stoker |
| Autore | Stoker J. J (James Johnston), <1905-> |
| Pubbl/distr/stampa | New York, : Wiley-Interscience, 1989, c1969 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
516
516.7 |
| Collana | Pure and applied mathematics, v. 20 |
| Soggetto topico |
Geometry, Differential
Manifolds (Mathematics) |
| ISBN |
1-283-27398-5
9786613273987 1-118-16546-2 1-118-16547-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Differential Geometry; CONTENTS; Chapter I Operations with Vectors; 1. The vector notation; 2. Addition of vectors; 3. Multiplication by scalars; 4. Representation of a vector by means of linearly independent vectors; 5. Scalar product; 6. Vector product; 7. Scalar triple product; 8. Invariance under orthogonal transformations; 9. Vector calculus; Chapter II Plane Curves; 1. Introduction; 2. Regular curves; 3. Change of parameters; 4. Invariance under changes of parameter; 5. Tangent lines and tangent vectors of a curve; 6. Orientation of a curve; 7. Length of a curve
1. Regular curves2. Length of a curve; 3. Curvature of space curves; 4. Principal normal and osculating plane; 5. Binormal vector; 6. Torsion τ of a space curve; 7. The Frenet equations for space curves; 8. Rigid body motions and the rotation vector; 9. The Darboux vector; 10. Formulas for κ and τ; 11. The sign of τ; 12. Canonical representation of a curve; 13. Existence and uniqueness of a space curve for given κ (S), τ (S); 14. What about κ = 0?; 15. Another way to define space curves; 16. Some special curves; Chapter IV The Basic Elements of Surface Theory 1. Regular surfaces in Euclidean space2. Change of parameters; 3. Curvilinear coordinate curves on a surface; 4. Tangent plane and normal vector; 5. Length of curves and first fundamental form; 6. Invariance of the first fundamental form; 7. Angle measurement on surfaces; 8. Area of a surface; 9. A few examples; 10. Second fundamental form of a surface; 11. Osculating paraboloid; 12. Curvature of curves on a surface; 13. Principal directions and principal curvatures; 14. Mean curvature H and Gaussian curvature K; 15. Another definition of the Gaussian curvature K; 16. Lines of curvature 17. Third fundamental form18. Characterization of the sphere as a locus of umbilical points; 19. Asymptotic lines; 20. Torsion of asymptotic lines; 21. Introduction of special parameter curves; 22. Asymptotic lines and lines of curvature as parameter curves; 23. Embedding a given arc in a system of parameter curves; 24. Analogues of polar coordinates on a surface; Chapter V Some Special Surfaces; 1. Surfaces of revolution; 2. Developable surfaces in the small made up of parabolic points; 3. Edge of regression of a developable; 4. Why the name developable? 5. Developable surfaces in the large1 |
| Record Nr. | UNINA-9910139601203321 |
Stoker J. J (James Johnston), <1905->
|
||
| New York, : Wiley-Interscience, 1989, c1969 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometry [[electronic resource] /] / [by] J. J. Stoker
| Differential geometry [[electronic resource] /] / [by] J. J. Stoker |
| Autore | Stoker J. J (James Johnston), <1905-> |
| Pubbl/distr/stampa | New York, : Wiley-Interscience, 1989, c1969 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
516
516.7 |
| Collana | Pure and applied mathematics, v. 20 |
| Soggetto topico |
Geometry, Differential
Manifolds (Mathematics) |
| ISBN |
1-283-27398-5
9786613273987 1-118-16546-2 1-118-16547-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Differential Geometry; CONTENTS; Chapter I Operations with Vectors; 1. The vector notation; 2. Addition of vectors; 3. Multiplication by scalars; 4. Representation of a vector by means of linearly independent vectors; 5. Scalar product; 6. Vector product; 7. Scalar triple product; 8. Invariance under orthogonal transformations; 9. Vector calculus; Chapter II Plane Curves; 1. Introduction; 2. Regular curves; 3. Change of parameters; 4. Invariance under changes of parameter; 5. Tangent lines and tangent vectors of a curve; 6. Orientation of a curve; 7. Length of a curve
1. Regular curves2. Length of a curve; 3. Curvature of space curves; 4. Principal normal and osculating plane; 5. Binormal vector; 6. Torsion τ of a space curve; 7. The Frenet equations for space curves; 8. Rigid body motions and the rotation vector; 9. The Darboux vector; 10. Formulas for κ and τ; 11. The sign of τ; 12. Canonical representation of a curve; 13. Existence and uniqueness of a space curve for given κ (S), τ (S); 14. What about κ = 0?; 15. Another way to define space curves; 16. Some special curves; Chapter IV The Basic Elements of Surface Theory 1. Regular surfaces in Euclidean space2. Change of parameters; 3. Curvilinear coordinate curves on a surface; 4. Tangent plane and normal vector; 5. Length of curves and first fundamental form; 6. Invariance of the first fundamental form; 7. Angle measurement on surfaces; 8. Area of a surface; 9. A few examples; 10. Second fundamental form of a surface; 11. Osculating paraboloid; 12. Curvature of curves on a surface; 13. Principal directions and principal curvatures; 14. Mean curvature H and Gaussian curvature K; 15. Another definition of the Gaussian curvature K; 16. Lines of curvature 17. Third fundamental form18. Characterization of the sphere as a locus of umbilical points; 19. Asymptotic lines; 20. Torsion of asymptotic lines; 21. Introduction of special parameter curves; 22. Asymptotic lines and lines of curvature as parameter curves; 23. Embedding a given arc in a system of parameter curves; 24. Analogues of polar coordinates on a surface; Chapter V Some Special Surfaces; 1. Surfaces of revolution; 2. Developable surfaces in the small made up of parabolic points; 3. Edge of regression of a developable; 4. Why the name developable? 5. Developable surfaces in the large1 |
| Record Nr. | UNINA-9910830341303321 |
|
Stoker J. J (James Johnston), <1905->
|
||
| New York, : Wiley-Interscience, 1989, c1969 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Differential geometry [[electronic resource] /] / [by] J. J. Stoker
| Differential geometry [[electronic resource] /] / [by] J. J. Stoker |
| Autore | Stoker J. J (James Johnston), <1905-> |
| Pubbl/distr/stampa | New York, : Wiley-Interscience, 1989, c1969 |
| Descrizione fisica | 1 online resource (428 p.) |
| Disciplina |
516
516.7 |
| Collana | Pure and applied mathematics, v. 20 |
| Soggetto topico |
Geometry, Differential
Manifolds (Mathematics) |
| ISBN |
1-283-27398-5
9786613273987 1-118-16546-2 1-118-16547-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Differential Geometry; CONTENTS; Chapter I Operations with Vectors; 1. The vector notation; 2. Addition of vectors; 3. Multiplication by scalars; 4. Representation of a vector by means of linearly independent vectors; 5. Scalar product; 6. Vector product; 7. Scalar triple product; 8. Invariance under orthogonal transformations; 9. Vector calculus; Chapter II Plane Curves; 1. Introduction; 2. Regular curves; 3. Change of parameters; 4. Invariance under changes of parameter; 5. Tangent lines and tangent vectors of a curve; 6. Orientation of a curve; 7. Length of a curve
1. Regular curves2. Length of a curve; 3. Curvature of space curves; 4. Principal normal and osculating plane; 5. Binormal vector; 6. Torsion τ of a space curve; 7. The Frenet equations for space curves; 8. Rigid body motions and the rotation vector; 9. The Darboux vector; 10. Formulas for κ and τ; 11. The sign of τ; 12. Canonical representation of a curve; 13. Existence and uniqueness of a space curve for given κ (S), τ (S); 14. What about κ = 0?; 15. Another way to define space curves; 16. Some special curves; Chapter IV The Basic Elements of Surface Theory 1. Regular surfaces in Euclidean space2. Change of parameters; 3. Curvilinear coordinate curves on a surface; 4. Tangent plane and normal vector; 5. Length of curves and first fundamental form; 6. Invariance of the first fundamental form; 7. Angle measurement on surfaces; 8. Area of a surface; 9. A few examples; 10. Second fundamental form of a surface; 11. Osculating paraboloid; 12. Curvature of curves on a surface; 13. Principal directions and principal curvatures; 14. Mean curvature H and Gaussian curvature K; 15. Another definition of the Gaussian curvature K; 16. Lines of curvature 17. Third fundamental form18. Characterization of the sphere as a locus of umbilical points; 19. Asymptotic lines; 20. Torsion of asymptotic lines; 21. Introduction of special parameter curves; 22. Asymptotic lines and lines of curvature as parameter curves; 23. Embedding a given arc in a system of parameter curves; 24. Analogues of polar coordinates on a surface; Chapter V Some Special Surfaces; 1. Surfaces of revolution; 2. Developable surfaces in the small made up of parabolic points; 3. Edge of regression of a developable; 4. Why the name developable? 5. Developable surfaces in the large1 |
| Record Nr. | UNINA-9910840749203321 |
|
Stoker J. J (James Johnston), <1905->
|
||
| New York, : Wiley-Interscience, 1989, c1969 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Water waves [[electronic resource] ] : the mathematical theory with applications / / J.J. Stoker
| Water waves [[electronic resource] ] : the mathematical theory with applications / / J.J. Stoker |
| Autore | Stoker J. J (James Johnston), <1905-> |
| Pubbl/distr/stampa | New York, : Wiley, 1992 |
| Descrizione fisica | 1 online resource (598 p.) |
| Disciplina | 532.593 |
| Collana | Wiley classics library |
| Soggetto topico |
Water waves
Hydrodynamics Hydraulics |
| ISBN |
1-283-24650-3
9786613246509 1-118-03315-9 1-118-03135-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Water Waves: The Mathematical Theory with Applications; Introduction; Acknowledgments; Contents; PART I; 1. Basic Hydrodynamics; 1.1 The laws of conservation of momentum and mass; 1.2 Helmholtz's theorem; 1.3 Potential flow and Bernoulli's law; 1.4 Boundary conditions; 1.5 Singularities of the velocity potential; 1.6 Notions concerning energy and energy flux; 1.7 Formulation of a surface wave problem; 2. The Two Basic Approximate Theories; 2.1 Theory of waves of small amplitude; 2.2 Shallow water theory to lowest order. Tidal theory; 2.3 Gas dynamics analogy
2.4 Systematic derivation of the shallow water theoryPART II; Subdivision A Waves Simple Harmonic in the Time; 3. Simple Harmonic Oscillations in Water of Constant Depth; 3.1 Standing waves; 3.2 Simple harmonic progressing waves; 3.3 Energy transmission for simple harmonic waves of small amplitude; 3.4 Group velocity. Dispersion; 4. Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth. Forced Oscillations; 4.1 Introduction; 4.2 The surface pressure is periodic for all values of x; 4.3 The variable surface pressure is confined to a segment of the surface 4.4 Periodic progressing waves against a vertical cliff5. Waves on Sloping Beaches and Past Obstacles; 5.1 Introduction and summary; 5.2 Two-dimensional waves over beaches sloping at angles ω=π/2n; 5.3 Three-dimensional waves against a vertical cliff; 5.4 Waves on sloping beaches. General case; 5.5 Diffraction of waves around a vertical wedge. Sommerfeld's diffraction problem; 5.6 Brief discussions of additional applications and of other methods of solution; Subdivision B Motions Starting from Rest. Transients; 6. Unsteady Motions; 6.1 General formulation of the problem of unsteady motions 6.2 Uniqueness of the unsteady motions in bounded domains6.3 Outline of the Fourier transform technique; 6.4 Motions due to disturbances originating at the surface; 6.5 Application of Kelvin's method of stationary phase; 6.6 Discussion of the motion of the free surface due to disturbances initiated when the water is at rest; 6.7 Waves due to a periodic impulse applied to the water when initially at rest. Derivation of the radiation condition for purely periodic waves; 6.8 Justification of the method of stationary phase 6.9 A time-dependent Green's function. Uniqueness of unsteady motions in unbounded domains when obstacles are presentSubdivision C Waves on a Running Stream. Ship Waves; 7. Two-dimensional Waves on a Running Stream in Water of Uniform Depth; 7.1 Steady motions in water of infinite depth with p = 0 on the free surface; 7.2 Steady motions in water of infinite depth with a disturbing pressure on the free surface; 7.3 Steady waves in water of constant finite depth; 7.4 Unsteady waves created by a disturbance on the surface of a running stream 8. Waves Caused by a Moving Pressure Point. Kelvin's Theory of the Wave Pattern created by a Moving Ship |
| Record Nr. | UNINA-9910139599903321 |
|
Stoker J. J (James Johnston), <1905->
|
||
| New York, : Wiley, 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Water waves [[electronic resource] ] : the mathematical theory with applications / / J.J. Stoker
| Water waves [[electronic resource] ] : the mathematical theory with applications / / J.J. Stoker |
| Autore | Stoker J. J (James Johnston), <1905-> |
| Pubbl/distr/stampa | New York, : Wiley, 1992 |
| Descrizione fisica | 1 online resource (598 p.) |
| Disciplina | 532.593 |
| Collana | Wiley classics library |
| Soggetto topico |
Water waves
Hydrodynamics Hydraulics |
| ISBN |
1-283-24650-3
9786613246509 1-118-03315-9 1-118-03135-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Water Waves: The Mathematical Theory with Applications; Introduction; Acknowledgments; Contents; PART I; 1. Basic Hydrodynamics; 1.1 The laws of conservation of momentum and mass; 1.2 Helmholtz's theorem; 1.3 Potential flow and Bernoulli's law; 1.4 Boundary conditions; 1.5 Singularities of the velocity potential; 1.6 Notions concerning energy and energy flux; 1.7 Formulation of a surface wave problem; 2. The Two Basic Approximate Theories; 2.1 Theory of waves of small amplitude; 2.2 Shallow water theory to lowest order. Tidal theory; 2.3 Gas dynamics analogy
2.4 Systematic derivation of the shallow water theoryPART II; Subdivision A Waves Simple Harmonic in the Time; 3. Simple Harmonic Oscillations in Water of Constant Depth; 3.1 Standing waves; 3.2 Simple harmonic progressing waves; 3.3 Energy transmission for simple harmonic waves of small amplitude; 3.4 Group velocity. Dispersion; 4. Waves Maintained by Simple Harmonic Surface Pressure in Water of Uniform Depth. Forced Oscillations; 4.1 Introduction; 4.2 The surface pressure is periodic for all values of x; 4.3 The variable surface pressure is confined to a segment of the surface 4.4 Periodic progressing waves against a vertical cliff5. Waves on Sloping Beaches and Past Obstacles; 5.1 Introduction and summary; 5.2 Two-dimensional waves over beaches sloping at angles ω=π/2n; 5.3 Three-dimensional waves against a vertical cliff; 5.4 Waves on sloping beaches. General case; 5.5 Diffraction of waves around a vertical wedge. Sommerfeld's diffraction problem; 5.6 Brief discussions of additional applications and of other methods of solution; Subdivision B Motions Starting from Rest. Transients; 6. Unsteady Motions; 6.1 General formulation of the problem of unsteady motions 6.2 Uniqueness of the unsteady motions in bounded domains6.3 Outline of the Fourier transform technique; 6.4 Motions due to disturbances originating at the surface; 6.5 Application of Kelvin's method of stationary phase; 6.6 Discussion of the motion of the free surface due to disturbances initiated when the water is at rest; 6.7 Waves due to a periodic impulse applied to the water when initially at rest. Derivation of the radiation condition for purely periodic waves; 6.8 Justification of the method of stationary phase 6.9 A time-dependent Green's function. Uniqueness of unsteady motions in unbounded domains when obstacles are presentSubdivision C Waves on a Running Stream. Ship Waves; 7. Two-dimensional Waves on a Running Stream in Water of Uniform Depth; 7.1 Steady motions in water of infinite depth with p = 0 on the free surface; 7.2 Steady motions in water of infinite depth with a disturbing pressure on the free surface; 7.3 Steady waves in water of constant finite depth; 7.4 Unsteady waves created by a disturbance on the surface of a running stream 8. Waves Caused by a Moving Pressure Point. Kelvin's Theory of the Wave Pattern created by a Moving Ship |
| Record Nr. | UNISA-996204084603316 |
|
Stoker J. J (James Johnston), <1905->
|
||
| New York, : Wiley, 1992 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||