The Shape of Things
The Shape of Things
$80.00
USDMany 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.
- A self-contained overview of differential geometry that provides clearer derivations of geometric quantities than are usually found in geometry texts
- A convenient reference for various shape differential formulas as well as a handbook on shape differentiation for graduate students
- Of interest to all scientists who study phenomena where surface geometry is important
Product details
No date availablePaperback
9781611973952
162 pages
255 × 180 × 12 mm
0.36kg
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Table of Contents
- 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.
