微分幾何学の実用ガイド The Shapes of Things : A Practical Guide to Differential Geometry and the Shape Derivative (Advances in Design and Control)

Walker, Shawn W.

Society for Industrial & Applied Mathematics,U.S.（2015/06発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 163 p.
• 言語 ENG
• 商品コード 9781611973952
• DDC分類 516.36

Full Description

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.

Contents

Chapter 1: Introduction
Chapter 2: Surfaces and Differential Geometry
Chapter 3: The Fundamental Forms of Differential Geometry
Chapter 4: Calculus on Surfaces
Chapter 5: Shape Differential Calculus
Chapter 6: Applications
Chapter 7: Willmore Flow
Appendix A: Vectors and Matrices
Appendix B: Derivatives and Integrals