Differential Geometry and its Applications (Mathematical Association of America Textbooks) - Hardcover

Oprea, John

Hardcover

ISBN 10: 0883857480 ISBN 13: 9780883857489

Publisher: The Mathematical Association of America, 2007

Synopsis

This book studies the differential geometry of surfaces and its relevance to engineering and the sciences.

About this title

About the Author

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

From the Inside Flap

Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of four-manifolds to the creation of theories of natures fundamental forces to the study of DNA. This book 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. Differential geometry is not just for mathematics majors, it is 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. Students will not only see geodesics on surfaces, but they will also see the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. Students will also see how particles move under constraints. 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.

Edition details

• Publisher: The Mathematical Association of America
• Publication date: 2007
• Language: English
• ISBN 10: 0883857480
• ISBN 13: 9780883857489
• Binding: Hardcover
• Edition number: 2
• Number of pages: 487