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Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings.
Chapter 2: Frame Fields:
Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations.
Chapter 3: Euclidean Geometry:
Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds.
Chapter 5: Shape Operators:
The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution.
Chapter 6: Geometry of Surfaces in R3:
The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces.
Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet.
Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard.
| Erscheinungsjahr: | 2006 |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | Gebunden |
| ISBN-13: | 9780120887354 |
| ISBN-10: | 0120887355 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | O'Neill, Barrett |
| Hersteller: | Elsevier Science Publishing Co Inc |
| Maße: | 235 x 162 x 34 mm |
| Von/Mit: | Barrett O'Neill |
| Erscheinungsdatum: | 16.05.2006 |
| Gewicht: | 0,954 kg |
Euclidean Space. Tangent Vectors. Directional Derivatives. Curves in R3. 1-forms. Differential Forms. Mappings.
Chapter 2: Frame Fields:
Dot Product. Curves. The Frenet Formulas. ArbitrarySpeed Curves. Covariant Derivatives. Frame Fields. Connection Forms. The Structural Equations.
Chapter 3: Euclidean Geometry:
Isometries of R3. The Tangent Map of an Isometry. Orientation. Euclidean Geometry. Congruence of Curves.
Chapter 4: Calculus on a Surface:
Surfaces in R3. Patch Computations. Differentiable Functions and Tangent Vectors. Differential Forms on a Surface. Mappings of Surfaces. Integration of Forms. Topological Properties. Manifolds.
Chapter 5: Shape Operators:
The Shape Operator of M R3. Normal Curvature. Gaussian Curvature. Computational Techniques. The Implicit Case. Special Curves in a Surface. Surfaces of Revolution.
Chapter 6: Geometry of Surfaces in R3:
The Fundamental Equations. Form Computations. Some Global Theorems. Isometries and Local Isometries. Intrinsic Geometry of Surfaces in R3. Orthogonal Coordinates. Integration and Orientation. Total Curvature. Congruence of Surfaces.
Chapter 7: Riemannian Geometry: Geometric Surfaces. Gaussian Curvature. Covariant Derivative. Geodesics. Clairaut Parametrizations. The Gauss-Bonnet Theorem. Applications of Gauss-Bonnet.
Chapter 8: Global Structures of Surfaces: Length-Minimizing Properties of Geodesics. Complete Surfaces. Curvature and Conjugate Points. Covering Surfaces. Mappings that Preserve Inner Products. Surfaces of Constant Curvature. Theorems of Bonnet and Hadamard.
| Erscheinungsjahr: | 2006 |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: | Gebunden |
| ISBN-13: | 9780120887354 |
| ISBN-10: | 0120887355 |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | O'Neill, Barrett |
| Hersteller: | Elsevier Science Publishing Co Inc |
| Maße: | 235 x 162 x 34 mm |
| Von/Mit: | Barrett O'Neill |
| Erscheinungsdatum: | 16.05.2006 |
| Gewicht: | 0,954 kg |
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