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

A differential geometry-based guide to understanding mathematical models which feature an underlying geometry which evolves in time.

Shawn W. Walker (Author)

9781611973952

Paperback / softback, published 30 June 2015

163 pages
25.5 x 18 x 1.1 cm, 0.368 kg

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.

Preface
1. Introduction
2. Surfaces and differential geometry
3. The fundamental forms of differential geometry
4. Calculus on surfaces
5. Shape differential calculus
6. Applications
7. Willmore flow
Appendix A. Vectors and matrices
Appendix B. Derivatives and integrals
Bibliography
Index.

Subject Areas: Miscellaneous items [WZ]