This marks the 100th volume to appear in the Applied Mathematical Sci ences series. Partial Differential Equations, by Fritz John, the first volume of the series, appeared in 1971. One year prior to its appearance, the then mathematics editor of Springer-Verlag, Klaus Peters, organized a meeting to look into the possibility of starting a series slanted toward applications. The meeting took place in New Rochelle, at the home of Fritz and Char lotte John. K.O. Friedrichs, Peter Lax, Monroe Donsker, Joe Keller, and others from the Courant Institute (previously, the Institute for Mathemat ical Sciences) were present as were Joe LaSalle and myself, the two of us having traveled down from Providence for the meeting. The John home, a large, comfortable house, especially lent itself to the informal, relaxed, and wide-ranging discussion that ensued. What emerged was a consensus that mathematical applications appeared to be poised for a period of growth and that there was a clear need for a series committed to applied mathematics. The first paragraph ofthe editorial statement written at that time reads as follows: The mathematization of all sciences, the fading of traditional scientific boundaries, the impact of computer technology, the growing importance of mathematical-computer modeling and the necessity of scientific planning all create the need both in education and research for books that are introductory to and abreast of these developments. This will be the 100th volume of the Applied Mathematical Sciences series. In order to mark the occasion, this special volume has been created which will impact in an important way on the community that practices and is served by applied mathematics. Ten leading figures in the field present their own perspective of applied mathematics. The articles that are collected in this volume bear testimony to both the vitality and diversity of the subject. The contributors included here are: V.I. Arnol'd, Peter Constantin, Mitchell J. Feigenbaum, Martin Golubitsky, Daniel D. Joseph, Leo P. Kadanoff, Heinz-Otto Kreiss, H.P. McKean, Jerrold Marsden, and Roger Temam. The articles cover such topics as: mathematical problems in classical physics; geometric and analytic studies in turbulence; viscous and viscoelastic potential flow; difference methods for time dependent partial differential equations; geometric mechanics, stability and control. This special volume will be dedicated to Fritz John. John is one of the earliest advisors for the Springer- Verlag mathematics program, which includes his capacity as a series editor for the Applied Mathematical Sciences series. This volume appears in his honor. Front Matter....Pages i-xii Mathematical Problems in Classical Physics....Pages 1-20 Geometric and Analytic Studies in Turbulence....Pages 21-54 Riemann Maps and World Maps....Pages 55-71 Symmetry of Attractors and the Karhunen-Loève Decomposition....Pages 73-108 Viscous and Viscoelastic Potential Flow....Pages 109-154 Singularities and Similarities in Interface Flows....Pages 155-208 Difference Methods for Time-Dependent Partial Differential Equations....Pages 209-238 Statistical Mechanics of Nonlinear Wave Equations....Pages 239-264 Geometric Mechanics, Stability, and Control....Pages 265-291 Applications of Inertial Manifolds to Scientific Computing: A New Insight in Multilevel Methods....Pages 293-336 Back Matter....Pages 337-337
