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Shapes and Geometries

Shapes and Geometries
Metrics, Analysis, Differential Calculus, and Optimization

2nd Edition

£94.00

Part of Advances in Design and Control

  • Date Published: January 2011
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • format: Hardback
  • isbn: 9780898719369

£ 94.00
Hardback

This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
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About the Authors
  • A self-contained presentation of the mathematical foundations, constructions and tools necessary for studying problems where the modeling, optimization or control variable is no longer a set of parameters or functions but the shape or the structure of a geometric object. This second edition presents the latest ground breaking theoretical foundation to shape optimization in a form that can used by the engineering and scientific communities. It also clearly explains the state-of-the-art developments in a mathematical language that will attract mathematicians to open questions in this important field. The area of research is very broad, rich and fascinating from both theoretical and numerical standpoints and this book reflects this exciting expanding field. This book will be of great importance to applied mathematicians, as well as advanced engineers and scientists working in this area.

    • Completely reworked and considerably enriched second edition
    • The material at the beginning of each chapter is accessible to a broad audience, while the subsequent sections may sometimes require more mathematical maturity
    • Some chapters are self-contained and can be used as lecture notes for short courses
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    Product details

    • Edition: 2nd Edition
    • Date Published: January 2011
    • format: Hardback
    • isbn: 9780898719369
    • length: 646 pages
    • dimensions: 260 x 183 x 32 mm
    • weight: 1.27kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial & Applied Mathematics for availability.
  • Table of Contents

    List of figures
    Preface
    1. Introduction: examples, background, and perspectives
    2. Classical descriptions of geometries and their properties
    3. Courant metrics on images of a set
    4. Transformations generated by velocities
    5. Metrics via characteristic functions
    6. Metrics via distance functions
    7. Metrics via oriented distance functions
    8. Shape continuity and optimization
    9. Shape and tangential differential calculuses
    10. Shape gradients under a state equation constraint
    Elements of bibliography
    Index of notation
    Index.

  • Authors

    Michael C. Delfour, Université de Montréal
    M. C. Delfour is a Professor of Mathematics and Statistics at the University of Montreal in Canada, a member of the Canadian Academy of Sciences (FRSC), a former Guggenheim and Killam Fellow and a SIAM Fellow.

    Jean-Paul Zolésio, Centre National de la Recherche Scientifique (CNRS), Paris
    J.-P. Zolésio is Research Director in Mathematics at the CNRS. He is member of the Institut Non Linéaire de Nice (INLN) associated with the Institut National de Recherche en Informatique et Automatique (INRIA) In Sophia Antipolis (France).

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