© Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. Contributors David Acheson, Emeritus Fellow, Jesus College, Thomas J. Brennan, Professor of Law, Harvard Law School University of Oxford portfolio theory [V.10] inverted pendulums [VI.4], teaching applied mathematics [VIII.7] David S. Broomhead, Professor of Applied Mathematics, The University of Manchester (deceased) Miguel A. Alonso, Associate Professor, applications of max-plus algebra [VII.4] The Institute of Optics at the University of Rochester modern optics [V.14] Kurt Bryan, Professor of Mathematics, Rose–Hulam Institute of Technology Douglas N. Arnold, McKnight Presidential Professor of cloaking [VI.1] Mathematics, University of Minnesota the flight of a golf ball [VI.6] Dorothy Buck, Reader in BioMathematics, Imperial College London Karl Johan Åström, Emeritus Professor, knotting and linking of macromolecules [VI.8] Department of Automatic Control, Lund Institute of Technology/University of Lund Chris Budd, Professor of Applied Mathematics, control theory [IV.34] University of Bath; Professor of Mathematics, Royal Institution of Great Britain David H. Bailey, Lawrence Berkeley National Laboratory slipping, sliding, rattling, and impact: (retired); Research Fellow, University of California, Davis nonsmooth dynamics and its applications [VI.15] experimental applied mathematics [VIII.6] John A. Burns, Hatcher Professor of Mathematics and June Barrow-Green, Senior Lecturer in the History of Technical Director for the Interdisciplinary Center for Mathematics, The Open University Applied Mathematics, Virginia Tech the history of applied mathematics [I.6] optimal sensor location in the control of energy-efficient buildings [VI.13] Peter Benner, Director, Max Planck Institute for Dynamics of Complex Technical Systems model reduction Daniela Calvetti, The James Wood Williamson Professor, [II.26] Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University Andrew J. Bernoff, Kenneth and Diana Jonsson Professor of dimensional analysis and scaling Mathematics, Harvey Mudd College [II.9] the thin-film equation [III.29] Eric Cancès, Professor of Analysis, Ecole des Ponts and INRIA electronic structure calculations (solid state physics) Michael V. Berry, Melville Wills Professor of Physics (Emeritus), University of Bristol [VII.14] divergent series: taming the tails [V.8] René Carmona, Paul M. Wythes ’55 Professor of Michael W. Berry, Professor, Department of Electrical Engineering and Finance, Bendheim Center for Finance, Engineering and Computer Science, University of Tennessee ORFE, Princeton University financial mathematics text mining [VII.24] [V.9] Brett Borden, Professor of Physics, C. J. Chapman, Professor of Applied Mathematics, The Naval Postgraduate School, Monterey, California University of Keele radar imaging [VII.17] shock waves [V.20], aircraft noise [VII.1] Jeffrey T. Borggaard, Professor of Mathematics, Virginia Tech S. Jonathan Chapman, Professor of Mathematics and Its optimal sensor location in the control of Applications, University of Oxford energy-efficient buildings [VI.13] the ginzburg–landau equation [III.14] Jonathan M. Borwein, Laureate Professor, Gui-Qiang G. Chen, Statutory Professor in the Analysis of Partial School of Mathematical and Physical Sciences, Differential Equations and Professorial Fellow of Keble College, University of Newcastle, Australia University of Oxford experimental applied mathematics [VIII.6] the tricomi equation [III.30] Fred Brauer, Professor Emeritus of Mathematics, Margaret Cheney, Professor of Mathematics and Albert C. Yates University of Wisconsin–Madison Endowment Chair, Colorado State University the spread of infectious diseases [V.16] radar imaging [VII.17] For general queries, contact [email protected] © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. xiv Contributors Peter A. Clarkson, Professor of Mathematics, University of Kent Charles L. Epstein, Thomas A. Scott Professor of Mathematics, the painlevé equations [III.24] University of Pennsylvania medical imaging [VII.9] Eugene M. Cliff, Professor Emeritus, Interdisciplinary Center for Applied Mathematics, Virginia Tech Bard Ermentrout, Distinguished University Professor of optimal sensor location in the control of Computational Biology and Professor of Mathematics, energy-efficient buildings [VI.13] University of Pittsburgh mathematical neuroscience [VII.21] Paul G. Constantine, Ben L. Fryrear Assistant Professor of Applied Mathematics and Statistics, Colorado School of Mines Maria Esteban, Director of Research, CNRS ranking web pages [VI.9] mathematics and policy [VIII.9] William Cook, Professor of Combinatorics and Optimization, Lawrence C. Evans, Professor, Department of Mathematics, University of Waterloo University of California, Berkeley the traveling salesman problem [VI.18] partial differential equations [IV.3] Robert M. Corless, Distinguished University Professor, Hans G. Feichtinger, Faculty of Mathematics, Department of Applied Mathematics, University of Vienna The University of Western Ontario function spaces [II.15] the lambert W function [III.17] Martin Feinberg, Morrow Professor of Chemical & Biomolecular Darren Crowdy, Professor of Applied Mathematics, Engineering and Professor of Mathematics, Imperial College London The Ohio State University conformal mapping [II.5] chemical reactions [V.7] James M. Crowley, Executive Director, Alistair D. Fitt, Vice-Chancellor, Oxford Brookes University Society for Industrial and Applied Mathematics mathematics and policy [VIII.9] mathematics and policy [VIII.9] Irene Fonseca, Mellon College of Science University Professor of Annie Cuyt, Professor, Department of Mathematics & Mathematics and Director of Center for Nonlinear Analysis, Computer Science, University of Antwerp Carnegie Mellon University approximation theory [IV.9] calculus of variations [IV.6] E. Brian Davies, Emeritus Professor of Mathematics, L. B. Freund, Adjunct Professor, Department of Materials Science King’s College London and Engineering, University of Illinois at Urbana-Champaign spectral theory [IV.8] mechanics of solids [IV.32] Timothy A. Davis, Professor, Department of Computer Science and Engineering, Texas A&M University David F. Gleich, Assistant Professor of Computer Science, Purdue University graph theory [II.16], searching a graph [VI.10] ranking web pages [VI.9] Florent de Dinechin, Professor of Applied Sciences, INSA—Lyon Paul Glendinning, Professor of Applied Mathematics, evaluating elementary functions [VI.11] The University of Manchester chaos and ergodicity [II.3], complex systems [II.4], Mark R. Dennis, Professor of Theoretical Physics, hybrid systems [II.18], the euler–lagrange equations University of Bristol [III.12], the logistic equation [III.19], the lorenz equations bifurcation theory invariants and conservation laws [II.21], [III.20], [IV.21] tensors and manifolds [II.33], the dirac equation [III.9], maxwell’s equations [III.22], Joe D. Goddard, Professor of Applied Mechanics and schrödinger’s equation [III.26] Engineering Science, University of California, San Diego granular flows [V.13] Jack Dongarra, Professor, University of Tennessee; Professor, Oak Ridge National Laboratory; Kenneth M. Golden, Professor of Mathematics/Adjunct Professor Professor, The University of Manchester of Bioengineering, University of Utah high-performance computing [VII.12] the mathematics of sea ice [V.17] David L. Donoho, Anne T. and Robert M. Bass Professor in the Timothy Gowers, Royal Society Research Professor, Humanities and Sciences, Stanford University Department of Pure Mathematics and Mathematical Statistics, reproducible research in the mathematical sciences University of Cambridge [VIII.5] mathematical writing [VIII.1] Ivar Ekeland, Professor Emeritus, CEREMADE and Thomas A. Grandine, Senior Technical Fellow, Institut de Finance, Université Paris-Dauphine The Boeing Company mathematical economics [VII.20] a hybrid symbolic–numeric approach to geometry processing and modeling [VII.2] Yonina C. Eldar, Professor of Electrical Engineering, Technion—Israel Institute of Technology, Haifa Andreas Griewank, Professor of Mathematics, compressed sensing [VII.10] Humboldt University of Berlin automatic differentiation [VI.7] George F. R. Ellis, Professor Emeritus, Mathematics Department, University of Cape Town David Griffiths, Emeritus Professor of Physics, Reed College general relativity and cosmology [IV.40] quantum mechanics [IV.23] For general queries, contact [email protected] © Copyright, Princeton University Press. No part of this book may be distributed, posted, or reproduced in any form by digital or mechanical means without prior written permission of the publisher. Contributors xv Peter Grindrod, Professor of Mathematics, University of Oxford Julian C. R. Hunt, Emeritus Professor of Climate Modelling and evolving social networks, attitudes, and Honorary Professor of Mathematics, University College London beliefs—and counterterrorism [VII.5] turbulence [V.21] Julio C. Gutiérrez-Vega, Director of the Optics Center, Stefan Hutzler, Associate Professor, School of Physics, Technológico de Monterrey Trinity College Dublin mathieu functions [III.21] foams [VI.3] Ernst Hairer, Honorary Professor