F tovena (11 Ergebnisse)
- Softcover
Anbieter: Grand Eagle Retail, Bensenville, IL, USAGrand Eagle Retail
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Paperback. Zustand: new. Paperback. The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of p…arametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenets formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves.The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss Teorema Egregium.Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fullyproved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincare-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.
- Softcover
Anbieter: Ria Christie Collections, Uxbridge, Vereinigtes KönigreichRia Christie Collections
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Zustand: New. In English.
- Softcover
Anbieter: Revaluation Books, Exeter, Vereinigtes KönigreichRevaluation Books
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EUR 114,46
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Paperback. Zustand: Brand New. 2012 edition. 409 pages. 9.00x6.00x0.75 inches. In Stock.
- Softcover
Anbieter: AussieBookSeller, Truganina, VIC, AustralienAussieBookSeller
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EUR 114,35
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Paperback. Zustand: new. Paperback. The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in particular the classification of 1-dimensional manifolds. We then present the classical local theory of p…arametrized plane and space curves (curves in n-dimensional space are discussed in the complementary material): curvature, torsion, Frenets formulas and the fundamental theorem of the local theory of curves. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves.The local theory of surfaces begins with a comparison of the concept of parametrized (i.e., immersed) surface with the concept of regular (i.e., embedded) surface. We then develop the basic differential geometry of surfaces in R3: definitions, examples, differentiable maps and functions, tangent vectors (presented both as vectors tangent to curves in the surface and as derivations on germs of differentiable functions; we shall consistently use both approaches in the whole book) and orientation. Next we study the several notions of curvature on a surface, stressing both the geometrical meaning of the objects introduced and the algebraic/analytical methods needed to study them via the Gauss map, up to the proof of Gauss Teorema Egregium.Then we introduce vector fields on a surface (flow, first integrals, integral curves) and geodesics (definition, basic properties, geodesic curvature, and, in the complementary material, a full proof of minimizing properties of geodesics and of the Hopf-Rinow theorem for surfaces). Then we shall present a proof of the celebrated Gauss-Bonnet theorem, both in its local and in its global form, using basic properties (fullyproved in the complementary material) of triangulations of surfaces. As an application, we shall prove the Poincare-Hopf theorem on zeroes of vector fields. Finally, the last chapter will be devoted to several important results on the global theory of surfaces, like for instance the characterization of surfaces with constant Gaussian curvature, and the orientability of compact surfaces in R3. Then, after a self-contained presentation of degree theory for continuous self-maps of the circumference, we study the global theory of plane curves, introducing winding and rotation numbers, and proving the Jordan curve theorem for curves of class C2, and Hopf theorem on the rotation number of closed simple curves. Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
- Softcover
Anbieter: Books Puddle, New York, NY, USABooks Puddle
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Zustand: New. pp. xiii + 396 1st Edition.
- Softcover
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Zustand: New.
- Softcover
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Paperback. Zustand: New. New .Ships From Multiple Locations. book.
- Softcover
- Print-on-Demand
Anbieter: Revaluation Books, Exeter, Vereinigtes KönigreichRevaluation Books
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Paperback. Zustand: Brand New. 2012 edition. 409 pages. 9.00x6.00x0.75 inches. In Stock. This item is printed on demand.
- Softcover
- Print-on-Demand
Anbieter: moluna, Greven, Deutschlandmoluna
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Kartoniert / Broschiert. Zustand: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The book provides an introduction to Differential Geometry of Curves and Surfaces. The theory of curves starts with a discussion of possible definitions of the concept of curve, proving in parti…cular the classification of 1-dimensional manifolds. We then p.
- Softcover
- Print-on-Demand
Anbieter: Majestic Books, Hounslow, Vereinigtes KönigreichMajestic Books
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Zustand: New. Print on Demand pp. xiii + 396.
- Softcover
- Print-on-Demand
Anbieter: Biblios, frankfurt am main, HESSE, DeutschlandBiblios
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EUR 59,34
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Zustand: New. PRINT ON DEMAND pp. xiii + 396.
