Hyperbolic Systems of Conservation Laws in Several Space Variables (Classic Reprint)

Excerpt from Hyperbolic Systems of Conservation Laws in Several Space Variables In Section 1 we show how to associate to each analytic function f of one variable a complex conservation law. When written in terms of real variables, this equation turns into a symmetric hyperbolic system of two first order conservation laws in time and two space variables for two unknowns. The hope is that the theory of analytic functions can be exploited to study the properties of the solutions of these model equations. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Science & Math

PETER D. LAX

Mathematics

Forgotten Books

Excerpt from Difference Schemes With High Order of Accuracy for Solving Hyperbolic EquationsIt is well Known that a difference scheme, in order to furnish accurate answers over a reasonably long range of time has to be stable. The bulk of this paper is devoted to determining the conditions under which the proposed dif ference schemes are stable.In Section 1 we give a brief review of the general theory of accuracy and stability of difference schemes. In Section 2 we show that the set of matrices whose field of value belongs to the unit circle forms a stable family.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

Difference Schemes With High Order of Accuracy for Solving Hyperbolic Equations (Classic Reprint)

History

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 student of 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.

Selected Papers II

Andrew J. Majda

Springer

The theory of hyperbolic equations is a large subject, and its applications are many: fluid dynamics and aerodynamics, the theory of elasticity, optics, electromagnetic waves, direct and inverse scattering, and the general theory of relativity. This book is an introduction to most facets of the theory and is an ideal text for a second-year graduate course on the subject. The first part deals with the basic theory: the relation of hyperbolicity to the finite propagation of signals, the concept and role of characteristic surfaces and rays, energy, and energy inequalities. The structure of solutions of equations with constant coefficients is explored with the help of the Fourier and Radon transforms. The existence of solutions of equations with variable coefficients with prescribed initial values is proved using energy inequalities. The propagation of singularities is studied with the help of progressing waves. The second part describes finite difference approximations of hyperbolic equations, presents a streamlined version of the Lax-Phillips scattering theory, and covers basic concepts and results for hyperbolic systems of conservation laws, an active research area today. Four brief appendices sketch topics that are important or amusing, such as Huygens' principle and a theory of mixed initial and boundary value problems. A fifth appendix by Cathleen Morawetz describes a nonstandard energy identity and its uses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Hyperbolic Partial Differential Equations (Courant Lecture Notes in Mathematics)

American Mathematical Society/Courant Institute of Mathematical Sciences

Complex Proofs of Real Theorems is an extended meditation on Hadamard's famous dictum, "The shortest and best way between two truths of the real domain often passes through the imaginary one." Directed at an audience acquainted with analysis at the first year graduate level, it aims at illustrating how complex variables can be used to provide quick and efficient proofs of a wide variety of important results in such areas of analysis as approximation theory, operator theory, harmonic analysis, and complex dynamics. Topics discussed include weighted approximation on the line, MÃ¼ntz's theorem, Toeplitz operators, Beurling's theorem on the invariant spaces of the shift operator, prediction theory, the Riesz convexity theorem, the Paley-Wiener theorem, the Titchmarsh convolution theorem, the Gleason-Kahane- elazko theorem, and the Fatou-Julia-Baker theorem. The discussion begins with the world's shortest proof of the fundamental theorem of algebra and concludes with Newman's almost effortless proof of the prime number theorem. Four brief appendices provide all necessary background in complex analysis beyond the standard first year graduate course. Lovers of analysis and beautiful proofs will read and reread this slim volume with pleasure and profit.

Complex Proofs of Real Theorems (University Lecture Series) (University Lecture Series, 58)

Lawrence Zalcman

American Mathematical Society

Functional Analysis

Wiley-Interscience

Linear Algebra and Its Applications

Excerpt from The Small Dispersion Limit of the Korteweg-Devries Equations We also show that leads, in an appropriate weak sense, to a limit. In Section 3 we show that Q is continuous in a weak sequential topology, and that the space of admissible functions is compact in that topology. We further show that Q is a strictly convex function; since the admissible functions form a convex set, this implies not only that the minimum of Q is taken on at a unique function, but that this function is the only one which satisfies variational conditions. The variational conditions are then converted to a riemann-hilbert problem, i.a. To the problem of determining an analytic function of class Hp in the upper half plane whose real and imaginary parts are prescribed on alternate intervals of the real axis. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

The Small Dispersion Limit of the Korteweg-Devries Equations (Classic Reprint)

Excerpt from Hyperbolic Systems of Conservation Laws in Several Space VariablesIn Section 1 we show how to associate to each analytic function f of one variable a complex conservation law. When written in terms of real variables, this equation turns into a symmetric hyperbolic system of two first order conservation laws in time and two space variables for two unknowns. The hope is that the theory of analytic functions can be exploited to study the properties of the solutions of these model equations.About the PublisherForgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.comThis book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.

LINEAR ALGEBRA AND ITS APPLICATIONS, 2ND EDITION

Wiley-India

See the best price to sell, buy, or rent books by PETER D. LAX. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by PETER D. LAX

See the best price to sell, buy, or rent books by PETER D. LAX. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Hyperbolic Systems of Conservation Laws in Several Space Variables (Classic Reprint)

Difference Schemes With High Order of Accuracy for Solving Hyperbolic Equations (Classic Reprint)

Selected Papers II

Hyperbolic Partial Differential Equations (Courant Lecture Notes in Mathematics)

Complex Proofs of Real Theorems (University Lecture Series) (University Lecture Series, 58)

Functional Analysis

Linear Algebra and Its Applications

The Small Dispersion Limit of the Korteweg-Devries Equations (Classic Reprint)

Hyperbolic Systems of Conservation Laws in Several Space Variables (Classic Reprint)

LINEAR ALGEBRA AND ITS APPLICATIONS, 2ND EDITION