This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.

J. Eggers is Professor of Applied Mathematics at the University of Bristol. His career has been devoted to the understanding of self-similar phenomena, and he has more than fifteen years of experience in teaching non-linear and scaling phenomena to undergraduate and postgraduate students. Eggers has made fundamental contributions to our mathematical understanding of free-surface flows, in particular the break-up and coalescence of drops. His work was instrumental in establishing the study of singularities as a research field in applied mathematics and in fluid mechanics. He is a member of the Academy of Arts and Sciences in Erfurt, Germany, a fellow of the American Physical Society, and has recently been made a Euromech Fellow.

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.