Singularities: Formation, Structure, and Propagation (Cambridge Texts in Applied Mathematics, nr. 53)

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en Limba Engleză Paperback – 17 Sep 2015
Many key phenomena in physics and engineering are described as singularities in the solutions to the differential equations describing them. Examples covered thoroughly in this book include the formation of drops and bubbles, the propagation of a crack and the formation of a shock in a gas. Aimed at a broad audience, this book provides the mathematical tools for understanding singularities and explains the many common features in their mathematical structure. Part I introduces the main concepts and techniques, using the most elementary mathematics possible so that it can be followed by readers with only a general background in differential equations. Parts II and III require more specialised methods of partial differential equations, complex analysis and asymptotic techniques. The book may be used for advanced fluid mechanics courses and as a complement to a general course on applied partial differential equations.
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ISBN-13: 9781107485495
ISBN-10: 1107485495
Pagini: 470
Ilustrații: 125 b/w illus. 8 colour illus. 180 exercises
Dimensiuni: 152 x 227 x 20 mm
Greutate: 0.74 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria Cambridge Texts in Applied Mathematics

Locul publicării: New York, United States


Preface; Part I. Setting the Scene: 1. What are singularities all about?; 2. Blow-up; 3. Similarity profile; 4. Continuum equations; 5. Local singular expansions; 6. Asymptotic expansions of PDEs; Part II. Formation of Singularities: 7. Drop break-up; 8. A numerical example: drop pinch-off; 9. Slow convergence; 10. Continuation; Part III. Persistent Singularities – Propagation: 11. Shock waves; 12. The dynamical system; 13. Vortices; 14. Cusps and caustics; 15. Contact lines and cracks; Appendix A. Vector calculus; Appendix B. Index notation and the summation convention; Appendix C. Dimensional analysis; References; Index.


'The book will serve as an excellent introduction to the field of singularities in continuum mechanics, and a valuable resource for researchers … In short, a wonderful achievement!' H. K. Moffatt, Journal of Fluid Mechanics