Shapes and Geometries
Analysis, Differential Calculus, and Optimization
Seiten
1987
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-489-0 (ISBN)
Society for Industrial & Applied Mathematics,U.S. (Verlag)
978-0-89871-489-0 (ISBN)
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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 book provides 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. Shapes and Geometries: Analysis, Differential Calculus, and Optimization presents the extensive, recently developed theoretical foundation to shape optimization in a form that can be used by the engineering community. 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.
This book provides 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. Shapes and Geometries: Analysis, Differential Calculus, and Optimization presents the extensive, recently developed theoretical foundation to shape optimization in a form that can be used by the engineering community. 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.
List of Figures; Preface; 1. Introduction; 2. Classical Descriptions and Properties of Domains; 3. Relaxation to Measurable Domains; 4. Topologies Generated by Distance Functions; 5. Oriented Distance Function and Smoothness of Sets; 6. Optimization of Shape Functions; 7. Transformations versus Flows of Velocities; 8. Shape Derivatives and Calculus, and Tangential Differential Calculus; 9. Shape Gradients under a State Equation Constraint; Elements of Bibliography; Index of Notation; Index.
| Reihe/Serie | Advances in Design and Control |
|---|---|
| Verlagsort | New York |
| Sprache | englisch |
| Maße | 182 x 260 mm |
| Gewicht | 1085 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
| ISBN-10 | 0-89871-489-3 / 0898714893 |
| ISBN-13 | 978-0-89871-489-0 / 9780898714890 |
| Zustand | Neuware |
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Buch | Hardcover (2022)
Hanser, Carl (Verlag)
CHF 41,95
