Many things around us have properties that depend on their shape - for example, the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function (in the calculus sense) with respect to a "shape variable". This approach, which is useful for understanding mathematical models containing geometric partial differential equations (PDEs), allows readers to obtain formulas for geometric quantities (such as curvature) that are clearer than those usually offered in differential geometry texts. Readers will learn how to compute sensitivities with respect to geometry by developing basic calculus tools on surfaces and combining them with the calculus of variations. Several applications that utilize shape derivatives and many illustrations that help build intuition are included.

Book Information
ISBN 9781611973952
Author Shawn W. Walker
Format Paperback
Page Count 163
Imprint Society for Industrial & Applied Mathematics,U.S.
Publisher Society for Industrial & Applied Mathematics,U.S.
Weight(grams) 360g