Elementary Topics in Differential Geometry 1st Edition by J A Thorpe ISBN 1461261538 9781461261537 by Gorniewicz L. 9781402046650, 1402046650 instant download after payment.

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ISBN 10: 1461261538

ISBN 13: 9781461261537

Author: J. A. Thorpe

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.

Table of contents:

1. Graphs and Level Sets

2. 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

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Tags: J A Thorpe, Elementary, Topics, Differential, Geometry