Differential Geometry and Its Applications

John Oprea (Autor)

Buch | Softcover

469 Seiten

2007
American Mathematical Society (Verlag)
978-1-4704-7791-2 (ISBN)

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Differential Geometry and Its Applications studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. That mix of ideas offers students the opportunity to visualize concepts through the use of computer algebra systems such as Maple.

Differential Geometry and Its Applications emphasizes that this visualization goes hand in hand with understanding the mathematics behind the computer construction. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.

Chapters
1. The Geometry of Curves
2. Surfaces
3. Curvatures
4. Constant Mean Curvature Surfaces
5. Geodesics, Metrics and Isometries
6. Holonomy and the Gauss-Bonnet Theorem
7. The Calculus of Variations and Geometry
8. A Glimpse at Higher Dimensions

Erscheinungsdatum	08.07.2025
Reihe/Serie	Classroom Resource Materials
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-7791-2 / 1470477912
ISBN-13	978-1-4704-7791-2 / 9781470477912
Zustand	Neuware