The Shape of Things
A Practical Guide to Differential Geometry and the Shape Derivative

Many things have properties that depend on their shape, such as the drag characteristics of a rigid body in a flow. This self-contained overview of differential geometry explains how to differentiate a function with respect to a 'shape variable'. This approach, useful for understanding mathematical models containing geometric 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 geometric sensitivities by developing basic calculus on surfaces alongside calculus of variations, aided by plenty of applications and illustrations. This book, a convenient reference for various shape derivative formulas, will be valuable to anyone interested in surface geometry and shape optimization. Graduate students can use it to quickly get acquainted with shape differentiation while scientists will find the book helpful for problems where surface geometry is critical or geometry evolves in time.

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Product details

• Date Published: December 2015
• format: Paperback
• isbn: 9781611973952
• length: 162 pages

• dimensions: 255 x 180 x 12 mm
• weight: 0.36kg
• availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.