Shapes and Geometries
Metrics, Analysis, Differential Calculus, and Optimization
2nd Edition
£94.00
Part of Advances in Design and Control
- Authors:
- Michael C. Delfour, Université de Montréal
- Jean-Paul Zolésio, Centre National de la Recherche Scientifique (CNRS), Paris
- 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
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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.
Read more- 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.
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