Current and Future Directions in Applied Mathematics

With tight funding in pure mathematics, it has become increasingly necessary for mathematicians to address the question of what applications their work has in the real world of engineering and science. This text discusses the types of problems that are of current interest. Mark Alber, Bei Hu and Joachim Rosenthal ...vii Part I Some Remarks on Applied Mathematics Roger Brockett ...1 Mathematics is a Profession Christopher 1. Byrnes ...4 Comments on Applied Mathematics Avner Friedman ...9 Towards an Applied Mathematics for Computer Science Jeremy Gunawardena ...11 Infomercial for Applied Mathematics Darryl Holm ...15 On Research in Mathematical Economics M. Ali Khan ...21 Applied Mathematics in the Computer and Communications Industry Brian Marcus ...25 'frends in Applied Mathematics Jerrold E. Marsden ...28 Applied Mathematics as an Interdisciplinary Subject Clyde F. Martin ...31 vi Contents Panel Discussion on Future Directions in Applied Mathe- matics Laurence R. Taylor ...38 Part II Feedback Stabilization of Relative Equilibria for Mechanical Systems with Symmetry A. M. Bloch, J. E. Marsden and G. Sanchez ...43 Oscillatory Descent for Function Minimization R. Brockett ...65 On the Well-Posedness of the Rational Covariance Extension Problem C. l. Byrnes, H. J. Landau and A. Lindquist ...83 Singular Limits in Fluid Mechanics P. Constantin ...109 Singularities and Defects in Patterns Far from Threshold N. M. Ercolani ...1 37 Mathematical Modeling and Simulation for Applications of Fluid Flow in Porous Media R. E. Ewing ...161 On Loeb Measure Spaces and their Significance for N on- Cooperative Game Theory M. A. Khan and Y. Sun ...183 Mechanical Systems with Symmetry, Variational Principles, and Integration Algorithms J. E. Marsden and J. M. Wendlandt ...219 Preface The applied sciences are faced with increasingly complex problems which call for sophisticated mathematical models.