The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative
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.
LOC Call Number
QA174.7 .S96 W35 2015
Department of Mathematics
Society for Industrial and Applied Mathematics
Walker, Shawn W., "The Shapes of Things: A Practical Guide to Differential Geometry and the Shape Derivative" (2015).