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Geometric optics for surface waves in nonlinear elasticity / / Jean-François Coulombel, Mark Williams
| Geometric optics for surface waves in nonlinear elasticity / / Jean-François Coulombel, Mark Williams |
| Autore | Coulombel Jean-François |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2020] |
| Descrizione fisica | 1 online resource (164 pages) |
| Disciplina | 530.4/16 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Partial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Nonlinear second-order hyperbolic equations
Optics, electromagnetic theory {For quantum optics, see 81V80} -- General -- Geometric optics Mechanics of deformable solids -- Elastic materials -- Nonlinear elasticity Geometrical optics - Mathematics Nonlinear difference equations Elasticity |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-5650-8 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Derivation of the weakly nonlinear amplitude equation -- Existence of exact solutions -- Approximate solutions -- Error analysis and proof of Theorem 3.8 -- Some extensions. |
| Record Nr. | UNINA-9910480835003321 |
Coulombel Jean-François
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| Providence, Rhode Island : , : American Mathematical Society, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric optics for surface waves in nonlinear elasticity / / Jean-François Coulombel, Mark Williams
| Geometric optics for surface waves in nonlinear elasticity / / Jean-François Coulombel, Mark Williams |
| Autore | Coulombel Jean-François |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2020] |
| Descrizione fisica | 1 online resource (164 pages) |
| Disciplina | 530.4/16 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Partial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Nonlinear second-order hyperbolic equations
Optics, electromagnetic theory {For quantum optics, see 81V80} -- General -- Geometric optics Mechanics of deformable solids -- Elastic materials -- Nonlinear elasticity Geometrical optics - Mathematics Nonlinear difference equations Elasticity |
| ISBN | 1-4704-5650-8 |
| Classificazione | 35L7074B2078A05 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Derivation of the weakly nonlinear amplitude equation -- Existence of exact solutions -- Approximate solutions -- Error analysis and proof of Theorem 3.8 -- Some extensions. |
| Record Nr. | UNINA-9910794067803321 |
|
Coulombel Jean-François
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Geometric optics for surface waves in nonlinear elasticity / / Jean-François Coulombel, Mark Williams
| Geometric optics for surface waves in nonlinear elasticity / / Jean-François Coulombel, Mark Williams |
| Autore | Coulombel Jean-François |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2020] |
| Descrizione fisica | 1 online resource (164 pages) |
| Disciplina | 530.4/16 |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Partial differential equations -- Hyperbolic equations and systems [See also 58J45] -- Nonlinear second-order hyperbolic equations
Optics, electromagnetic theory {For quantum optics, see 81V80} -- General -- Geometric optics Mechanics of deformable solids -- Elastic materials -- Nonlinear elasticity Geometrical optics - Mathematics Nonlinear difference equations Elasticity |
| ISBN | 1-4704-5650-8 |
| Classificazione | 35L7074B2078A05 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Derivation of the weakly nonlinear amplitude equation -- Existence of exact solutions -- Approximate solutions -- Error analysis and proof of Theorem 3.8 -- Some extensions. |
| Record Nr. | UNINA-9910818674303321 |
|
Coulombel Jean-François
|
||
| Providence, Rhode Island : , : American Mathematical Society, , [2020] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch
| Hyperbolic partial differential equations and geometric optics / Jeffrey Rauch |
| Autore | Rauch, Jeffrey |
| Pubbl/distr/stampa | Providence, R. I. : American Mathematical Society, c2012 |
| Descrizione fisica | xix, 363 p. : ill. ; 27 cm |
| Disciplina | 535.32 |
| Collana | Graduate studies in mathematics, 1065-7339 ; 133 |
| Soggetto topico |
Singularities (Mathematics)
Microlocal analysis Geometrical optics - Mathematics Differential equations, Hyperbolic |
| ISBN | 9780821872918 |
| Classificazione |
AMS 35A18
AMS 35A21 AMS 35A27 AMS 35A30 AMS 35Q31 AMS 35Q60 AMS 78A05 AMS 78A60 AMS 78M35 AMS 93B07 LC QC20.7.S54R38 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001827889707536 |
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Rauch, Jeffrey
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| Providence, R. I. : American Mathematical Society, c2012 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis
| The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis |
| Autore | Stavroudis O. N (Orestes Nicholas), <1923-> |
| Pubbl/distr/stampa | Weinheim, : Wiley-VCH, c2006 |
| Descrizione fisica | 1 online resource (242 p.) |
| Disciplina | 535.32 |
| Soggetto topico |
Geometrical optics - Mathematics
Physical optics - Mathematics |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-280-72360-2
9786610723607 3-527-60817-6 3-527-60829-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Mathematics of Geometrical and Physical Optics; Acknowledgements; Introduction; Contents; Part I Preliminaries; 1 Fermat's Principle and the Variational Calculus; 1.1 Rays in Inhomogeneous Media; 1.2 The Calculus of Variations; 1.3 The Parametric Representation; 1.4 The Vector Notation; 1.5 The Inhomogeneous Optical Medium; 1.6 The Maxwell Fish Eye; 1.7 The Homogeneous Medium; 1.8 Anisotropic Media; 2 Space Curves and Ray Paths; 2.1 Space Curves; 2.2 The Vector Trihedron; 2.3 The Frenet-Serret Equations; 2.4 When the Parameter is Arbitrary; 2.5 The Directional Derivative
2.6 The Cylindrical Helix2.7 The Conic Section; 2.8 The Ray Equation; 2.9 More on the Fish Eye; 3 The Hilbert Integral and the Hamilton-Jacobi Theory; 3.1 A Digression on the Gradient; 3.2 The Hilbert Integral. Parametric Case; 3.3 Application to Geometrical Optics; 3.4 The Condition for Transversality; 3.5 The Total Differential Equation; 3.6 More on the Helix; 3.7 Snell's Law; 3.8 The Hamilton-Jacobi Partial Differential Equations; 3.9 The Eikonal Equation; 4 The Differential Geometry of Surfaces.; 4.1 Parametric Curves; 4.2 Surface Normals; 4.3 The Theorem of Meusnier 5.7 The Eikonal Equation. The Complete Integral5.8 The Eikonal Equation. The General Solution; 5.9 The Eikonal Equation. Proof of the Pudding; Part II The k-function; 6 The Geometry of Wave Fronts; 6.1 Preliminary Calculations; 6.2 The Caustic Surface; 6.3 Special Surfaces I: Plane and Spherical Wavefronts; 6.4 Parameter Transformations; 6.5 Asymptotic Curves and Isotropic Directions; 7 Ray Tracing: Generalized and Otherwise; 7.1 The Transfer Equations; 7.2 The Ancillary Quantities; 7.3 The Refraction Equations; 7.4 Rotational Symmetry; 7.5 The Paraxial Approximation 7.6 Generalized Ray Tracing - Transfer7.7 Generalized Ray Tracing - Preliminary Calculations; 7.8 Generalized Ray Tracing - Refraction; 7.9 The Caustic; 7.10 The Prolate Spheroid; 7.11 Rays in the Spheroid; 8 Aberrations in Finite Terms; 8.1 Herzberger's Diapoints; 8.2 Herzberger's Fundamental Optical Invariant; 8.3 The Lens Equation; 8.4 Aberrations in Finite Terms; 8.5 Half-Symmetric, Symmetric and Sharp Images; 9 Refracting the k-Function; 9.1 Refraction; 9.2 The Refracting Surface; 9.3 The Partial Derivatives; 9.4 The Finite Object Point; 9.5 The Quest for C; 9.6 Developing the Solution 9.7 Conclusions |
| Record Nr. | UNINA-9910144706103321 |
|
Stavroudis O. N (Orestes Nicholas), <1923->
|
||
| Weinheim, : Wiley-VCH, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis
| The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis |
| Autore | Stavroudis O. N (Orestes Nicholas), <1923-> |
| Pubbl/distr/stampa | Weinheim, : Wiley-VCH, c2006 |
| Descrizione fisica | 1 online resource (242 p.) |
| Disciplina | 535.32 |
| Soggetto topico |
Geometrical optics - Mathematics
Physical optics - Mathematics |
| ISBN |
1-280-72360-2
9786610723607 3-527-60817-6 3-527-60829-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Mathematics of Geometrical and Physical Optics; Acknowledgements; Introduction; Contents; Part I Preliminaries; 1 Fermat's Principle and the Variational Calculus; 1.1 Rays in Inhomogeneous Media; 1.2 The Calculus of Variations; 1.3 The Parametric Representation; 1.4 The Vector Notation; 1.5 The Inhomogeneous Optical Medium; 1.6 The Maxwell Fish Eye; 1.7 The Homogeneous Medium; 1.8 Anisotropic Media; 2 Space Curves and Ray Paths; 2.1 Space Curves; 2.2 The Vector Trihedron; 2.3 The Frenet-Serret Equations; 2.4 When the Parameter is Arbitrary; 2.5 The Directional Derivative
2.6 The Cylindrical Helix2.7 The Conic Section; 2.8 The Ray Equation; 2.9 More on the Fish Eye; 3 The Hilbert Integral and the Hamilton-Jacobi Theory; 3.1 A Digression on the Gradient; 3.2 The Hilbert Integral. Parametric Case; 3.3 Application to Geometrical Optics; 3.4 The Condition for Transversality; 3.5 The Total Differential Equation; 3.6 More on the Helix; 3.7 Snell's Law; 3.8 The Hamilton-Jacobi Partial Differential Equations; 3.9 The Eikonal Equation; 4 The Differential Geometry of Surfaces.; 4.1 Parametric Curves; 4.2 Surface Normals; 4.3 The Theorem of Meusnier 5.7 The Eikonal Equation. The Complete Integral5.8 The Eikonal Equation. The General Solution; 5.9 The Eikonal Equation. Proof of the Pudding; Part II The k-function; 6 The Geometry of Wave Fronts; 6.1 Preliminary Calculations; 6.2 The Caustic Surface; 6.3 Special Surfaces I: Plane and Spherical Wavefronts; 6.4 Parameter Transformations; 6.5 Asymptotic Curves and Isotropic Directions; 7 Ray Tracing: Generalized and Otherwise; 7.1 The Transfer Equations; 7.2 The Ancillary Quantities; 7.3 The Refraction Equations; 7.4 Rotational Symmetry; 7.5 The Paraxial Approximation 7.6 Generalized Ray Tracing - Transfer7.7 Generalized Ray Tracing - Preliminary Calculations; 7.8 Generalized Ray Tracing - Refraction; 7.9 The Caustic; 7.10 The Prolate Spheroid; 7.11 Rays in the Spheroid; 8 Aberrations in Finite Terms; 8.1 Herzberger's Diapoints; 8.2 Herzberger's Fundamental Optical Invariant; 8.3 The Lens Equation; 8.4 Aberrations in Finite Terms; 8.5 Half-Symmetric, Symmetric and Sharp Images; 9 Refracting the k-Function; 9.1 Refraction; 9.2 The Refracting Surface; 9.3 The Partial Derivatives; 9.4 The Finite Object Point; 9.5 The Quest for C; 9.6 Developing the Solution 9.7 Conclusions |
| Record Nr. | UNINA-9910830948603321 |
|
Stavroudis O. N (Orestes Nicholas), <1923->
|
||
| Weinheim, : Wiley-VCH, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis
| The mathematics of geometrical and physical optics [[electronic resource] ] : the k-function and its ramifications / / Orestes N. Stavroudis |
| Autore | Stavroudis O. N (Orestes Nicholas), <1923-> |
| Pubbl/distr/stampa | Weinheim, : Wiley-VCH, c2006 |
| Descrizione fisica | 1 online resource (242 p.) |
| Disciplina | 535.32 |
| Soggetto topico |
Geometrical optics - Mathematics
Physical optics - Mathematics |
| ISBN |
1-280-72360-2
9786610723607 3-527-60817-6 3-527-60829-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
The Mathematics of Geometrical and Physical Optics; Acknowledgements; Introduction; Contents; Part I Preliminaries; 1 Fermat's Principle and the Variational Calculus; 1.1 Rays in Inhomogeneous Media; 1.2 The Calculus of Variations; 1.3 The Parametric Representation; 1.4 The Vector Notation; 1.5 The Inhomogeneous Optical Medium; 1.6 The Maxwell Fish Eye; 1.7 The Homogeneous Medium; 1.8 Anisotropic Media; 2 Space Curves and Ray Paths; 2.1 Space Curves; 2.2 The Vector Trihedron; 2.3 The Frenet-Serret Equations; 2.4 When the Parameter is Arbitrary; 2.5 The Directional Derivative
2.6 The Cylindrical Helix2.7 The Conic Section; 2.8 The Ray Equation; 2.9 More on the Fish Eye; 3 The Hilbert Integral and the Hamilton-Jacobi Theory; 3.1 A Digression on the Gradient; 3.2 The Hilbert Integral. Parametric Case; 3.3 Application to Geometrical Optics; 3.4 The Condition for Transversality; 3.5 The Total Differential Equation; 3.6 More on the Helix; 3.7 Snell's Law; 3.8 The Hamilton-Jacobi Partial Differential Equations; 3.9 The Eikonal Equation; 4 The Differential Geometry of Surfaces.; 4.1 Parametric Curves; 4.2 Surface Normals; 4.3 The Theorem of Meusnier 5.7 The Eikonal Equation. The Complete Integral5.8 The Eikonal Equation. The General Solution; 5.9 The Eikonal Equation. Proof of the Pudding; Part II The k-function; 6 The Geometry of Wave Fronts; 6.1 Preliminary Calculations; 6.2 The Caustic Surface; 6.3 Special Surfaces I: Plane and Spherical Wavefronts; 6.4 Parameter Transformations; 6.5 Asymptotic Curves and Isotropic Directions; 7 Ray Tracing: Generalized and Otherwise; 7.1 The Transfer Equations; 7.2 The Ancillary Quantities; 7.3 The Refraction Equations; 7.4 Rotational Symmetry; 7.5 The Paraxial Approximation 7.6 Generalized Ray Tracing - Transfer7.7 Generalized Ray Tracing - Preliminary Calculations; 7.8 Generalized Ray Tracing - Refraction; 7.9 The Caustic; 7.10 The Prolate Spheroid; 7.11 Rays in the Spheroid; 8 Aberrations in Finite Terms; 8.1 Herzberger's Diapoints; 8.2 Herzberger's Fundamental Optical Invariant; 8.3 The Lens Equation; 8.4 Aberrations in Finite Terms; 8.5 Half-Symmetric, Symmetric and Sharp Images; 9 Refracting the k-Function; 9.1 Refraction; 9.2 The Refracting Surface; 9.3 The Partial Derivatives; 9.4 The Finite Object Point; 9.5 The Quest for C; 9.6 Developing the Solution 9.7 Conclusions |
| Record Nr. | UNINA-9910841113403321 |
|
Stavroudis O. N (Orestes Nicholas), <1923->
|
||
| Weinheim, : Wiley-VCH, c2006 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
