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Elementary differential geometry /
Written primarily for students who have completed first courses in calculus and linear algebra, this textbook provides an introduction to the geometry of curves and surfaces. This revised second edition gives an update of commands for the symbolic computation programs Mathematica or Maple.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; Boston :
Elsevier Academic Press,
�2006.
|
| Edición: | Rev. 2nd ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a O'Neill, Barrett. | |
| 245 | 1 | 0 | |a Elementary differential geometry / |c Barrett O'Neill. |
| 250 | |a Rev. 2nd ed. | ||
| 260 | |a Amsterdam ; |a Boston : |b Elsevier Academic Press, |c �2006. | ||
| 300 | |a 1 online resource (xi, 503 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 504 | |a Includes bibliographical references (page 467) and index. | ||
| 520 | |a Written primarily for students who have completed first courses in calculus and linear algebra, this textbook provides an introduction to the geometry of curves and surfaces. This revised second edition gives an update of commands for the symbolic computation programs Mathematica or Maple. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a Preface -- Introduction -- Chapter 1: Calculus on Euclidean Space: -- 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. -- Appendix -- Bibliography -- Answers to Odd-Numbered Exercises -- Subject Index. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 6 | |a G�eom�etrie diff�erentielle. |0 (CaQQLa)201-0001184 | |
| 650 | 7 | |a MATHEMATICS |x Geometry |x Differential. |2 bisacsh | |
| 650 | 7 | |a Geometry, Differential |2 fast |0 (OCoLC)fst00940919 | |
| 650 | 7 | |a Differentialgeometrie |2 gnd |0 (DE-588)4012248-7 | |
| 650 | 7 | |a Geometria diferencial (textos elementares) |2 larpcal | |
| 650 | 7 | |a Geometr�ia diferencial. |2 lemb | |
| 650 | 1 | 7 | |a G�eom�etrie diff�erentielle. |2 rasuqam |
| 650 | 7 | |a Surface (Math�ematiques) |2 rasuqam | |
| 650 | 7 | |a Courbe. |2 rasuqam | |
| 776 | 0 | 8 | |i Print version: |a O'Neill, Barrett. |t Elementary differential geometry. |b Rev. 2nd ed. |d Amsterdam ; Boston : Elsevier Academic Press, �2006 |z 9780120887354 |w (DLC) 2005057176 |w (OCoLC)62493605 |
| 856 | 4 | 0 | |u https://sciencedirect.uam.elogim.com/science/book/9780120887354 |z Texto completo |