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The Shape of Things

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

£52.00

Part of Advances in Design and Control

  • Date Published: December 2015
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9781611973952

£ 52.00
Paperback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
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About the Authors
  • 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.

    • 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
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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.
  • 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.

  • Author

    Shawn W. Walker, Louisiana State University
    Shawn Walker is an assistant professor of mathematics at Louisiana State University (LSU), with a joint appointment in the Center for Computation and Technology (CCT). He held a postdoctoral position at the Courant Institute (New York University) and joined the LSU faculty in 2010 in the computational mathematics group. He is a member of SIAM, AMS, MRS, and APS. His research interests include PDEs for fluids and moving/free boundaries, geometric evolution problems, numerical analysis and finite element methods, mesh generation, and optimal PDE control of shape.

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