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A renowned mathematician who considers himself both applied and theoretical in his approach, Peter Lax has spent most of his professional career at NYU, making significant contributions to both mathematics and computing. He has written several important published works and has received numerous honors including the National Medal of Science, the Lester R. Ford Award, the Chauvenet Prize, the Semmelweis Medal, the Wiener Prize, and the Wolf Prize. Several students he has mentored have become leaders in their fields.
Two volumes span the years from 1952 up until 1999, and cover many varying topics, from functional analysis, partial differential equations, and numerical methods to conservation laws, integrable systems and scattering theory. After each paper, or collection of papers, is a commentary placing the paper in context and where relevant discussing more recent developments. Many of the papers in these volumes have become classics and should be read by any serious studentof these topics. In terms of insight, depth, and breadth, Lax has few equals. The reader of this selecta will quickly appreciate his brilliance as well as his masterful touch. Having this collection of papers in one place allows one to follow the evolution of his ideas and mathematical interests and to appreciate how many of these papers initiated topics that developed lives of their own.
List of contents
Partial Differential Equations.- On the existence of Green's Function.- Parabolic Equations.- On Cauchy's Problem for Hyperbolic Equations and the Differentiability of Solutions of Elliptic Equations.- The Propagation of Discontinuities in Wave Motion.- Asymptotic Solutions of Oscillatory Initial Value Problems.- Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations.- On Stability for Difference Schemes; a Sharp Form of Gårding's Inequality.- An Example of Huygens' Principle.- A Simple One-dimensional Model for the Three-dimensional Vorticity Equation.- Commentary on Part I.- Difference Approximations to PDE.- Survey of the Stability of Linear Finite Difference Equations.- On the Stability of Difference Approximations to Solutions of Hyperbolic Equations With Variable Coefficients.- The Computation of Discontinuous Solutions of Linear Hyperbolic Equations.- Accuracy and Resolution in the Computation of Solutions of Linear and Nonlinear Equations.- Commentary on Part II.- Hyperbolic Systems of Conservation Laws.- Weak Solutions of Nonlinear Hyperbolic Equations and Their Numerical Computation.- Hyperbolic Systems of Conservation Laws II.- Systems of Conservation Laws.- Difference Schemes for Hyperbolic Equations with High Order of Accuracy.- Shock Waves and Entropy.- Systems of Conservation Equations with a Convex Extension.- Positive Schemes for Solving Multi-Dimensional Hyperbolic Systems of Conservation Laws.- Commentary on Part III.- Integrable Systems.- Integrals of Nonlinear Equations of Evolution and Solitary Waves.- Periodic Solutions of the KdV Equation.- Almost Periodic Solutions of the KdV Equation.- The Small Dispersion Limit of the Korteweg-de Vries Equation. I.- The Small Dispersion Limit of the Korteweg-de Vries Equation. II.- The Small Dispersion Limit of the Korteweg-deVries Equation. III.- On Dispersive Difference Schemes. I.- Dispersive Approximations in Fluid Dynamics.- Commentary on Part IV.
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From the reviews:
"This is a collection of papers by one of the great mathematicians of our time. ... The depth and wide range covered by Lax's research contributions illustrate his broad view of mathematical analysis as a whole. The editors ... have done an excellent job: they didn't just collect some papers 'at random', but also explain, in detailed commentaries, the contents and importance of the included publications at the end of each section." (Jürgen Appell, Zentralblatt MATH, Vol. 1087, 2006)
"Since Peter Lax was chosen as the recipient of the 2005 Abel Prize, it's hardly necessary to say that his work is important. Libraries should consider his Selected Papers an essential acquisition. This first volume collects papers on partial differential equations, difference equations approximating PDEs, hyperbolic systems of conservation laws, and integrable systems." (Fernando Q. Gouvêa, MathDL, October, 2005)
