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Differential Geometry and its Applications

£54.99

textbook

Part of Mathematical Association of America Textbooks

Author: John Oprea, Cleveland State University

Date Published: September 2007
availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
format: Hardback
isbn: 9780883857489

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This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.

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Description

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About the Authors

Differential geometry has a long, wonderful history and has found relevance in many areas. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the standard university curriculum to a type of mathematics that is a unified whole, by mixing geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors, but also for students in engineering and the sciences. Into the mix of these ideas comes the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of 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.
- Helps students make the transition from the compartmentalized courses to mathematics that is a unified whole
- Includes a rich selection of exercises
- Gradually transforms graduates from calculators to thinkers
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Product details
- Date Published: September 2007
- format: Hardback
- isbn: 9780883857489
- length: 487 pages
- dimensions: 261 x 182 x 34 mm
- weight: 1.17kg
- availability: This item is not supplied by Cambridge University Press in your region. Please contact Mathematical Association of America for availability.
Table of Contents
Preface
The Point of this Book
Projects
Prerequisites
Book Features
Elliptic Functions and Maple Note
Thanks
For Users of Previous Editions
Maple 8 to 9
Note to students
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
Appendix A. List of examples
Appendix B. Hints and solutions to selected problems.

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Author
John Oprea, Cleveland State University
John Oprea is a Professor of mathematics at Cleveland State University in Ohio and a Lester R. Ford award recipient