DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
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 DGA
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 $77.00
Product Details
Differential Geometry and Its Applications
by John Oprea
Differential geometry has a long, wonderful history it has found relevance in areas ranging from machinery design of the classification of fourmanifolds to the creation of theories of nature's 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 handinhand 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.
 Brand name: MAA
 Author: John Oprea
 ISBN:9780883857489
 510pp.
 Hardcover
 2007
 Series: Textbooks
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