Trends and Perspectives in Applied Mathematics

1. Front Matter

   Pages i-xii

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2. Mathematical Problems in Classical Physics

   • V. I. Arnold

   Pages 1-20

3. Geometric and Analytic Studies in Turbulence

   • Peter Constantin

   Pages 21-54

4. Riemann Maps and World Maps

   • Mitchell J. Feigenbaum

   Pages 55-71

5. Symmetry of Attractors and the Karhunen-Loève Decomposition

   • Michael Dellnitz, Martin Golubitsky, Matthew Nicol

   Pages 73-108

6. Viscous and Viscoelastic Potential Flow

   • Daniel D. Joseph, Terrence Y. Liao

   Pages 109-154

7. Singularities and Similarities in Interface Flows

   • Andrea L. Bertozzi, Michael P. Brenner, Todd F. Dupont, Leo P. Kadanoff

   Pages 155-208

8. Difference Methods for Time-Dependent Partial Differential Equations

   • Heinz-Otto Kreiss

   Pages 209-238

9. Statistical Mechanics of Nonlinear Wave Equations

   • H. P. Mc Kean, K. L. Vaninsky

   Pages 239-264

10. Geometric Mechanics, Stability, and Control

    • Jerrold E. Marsden

    Pages 265-291

11. Applications of Inertial Manifolds to Scientific Computing: A New Insight in Multilevel Methods

    • Roger Temam

    Pages 293-336

12. Back Matter

    Pages 337-337

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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.

• Mathematica
• STATISTICA
• applied mathematics
• scientific computing

• Division of Applied Mathematics, Brown University, Providence, USA

  Lawrence Sirovich

• Rockefeller University, New York, USA

  Lawrence Sirovich

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