Elementary Topics in Differential Geometry
(Sprache: Englisch)
In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore...
Leider schon ausverkauft
versandkostenfrei
Buch
85.59 €
Produktdetails
Produktinformationen zu „Elementary Topics in Differential Geometry “
Klappentext zu „Elementary Topics in Differential Geometry “
In the past decade there has been a significant change in the freshman/ sophomore mathematics curriculum as taught at many, if not most, of our colleges. This has been brought about by the introduction of linear algebra into the curriculum at the sophomore level. The advantages of using linear algebra both in the teaching of differential equations and in the teaching of multivariate calculus are by now widely recognized. Several textbooks adopting this point of view are now available and have been widely adopted. Students completing the sophomore year now have a fair preliminary under standing of spaces of many dimensions. It should be apparent that courses on the junior level should draw upon and reinforce the concepts and skills learned during the previous year. Unfortunately, in differential geometry at least, this is usually not the case. Textbooks directed to students at this level generally restrict attention to 2-dimensional surfaces in 3-space rather than to surfaces of arbitrary dimension. Although most of the recent books do use linear algebra, it is only the algebra of ~3. The student's preliminary understanding of higher dimensions is not cultivated.
Inhaltsverzeichnis zu „Elementary Topics in Differential Geometry “
1 Graphs and Level Sets2 Vector Fields
3 The Tangent Space
4 Surfaces
5 Vector Fields on Surfaces; Orientation
6 The Gauss Map
7 Geodesics
8 Parallel Transport
9 The Weingarten Map
10 Curvature of Plane Curves
11 Arc Length and Line Integrals
12 Curvature of Surfaces
13 Convex Surfaces
14 Parametrized Surfaces
15 Local Equivalence of Surfaces and Parametrized Surfaces
16 Focal Points
17 Surface Area and Volume
18 Minimal Surfaces
19 The Exponential Map
20 Surfaces with Boundary
21 The Gauss-Bonnet Theorem
22 Rigid Motions and Congruence
23 Isometries
24 Riemannian Metrics
- Notational Index
Bibliographische Angaben
- Autor: J. A. Thorpe
- 1994, 256 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, New York
- ISBN-10: 0387903577
- ISBN-13: 9780387903576
- Erscheinungsdatum: 27.10.1994
Sprache:
Englisch
Kommentar zu "Elementary Topics in Differential Geometry"
0 Gebrauchte Artikel zu „Elementary Topics in Differential Geometry“
Zustand | Preis | Porto | Zahlung | Verkäufer | Rating |
---|
Schreiben Sie einen Kommentar zu "Elementary Topics in Differential Geometry".
Kommentar verfassen