We thus have a first example of what I shall call a 'method of descent'. Creating a phrase for an idea which is merely childish and has been used since the first steps of the theory is, I must confess, rather ambitious; but we shall come across it rather frequently, so that it will be convenient to have a word to denote it. It consists in noticing that he who can do more can do less: if we can integrate equations with m variables, we can do the same for equations with (m – 1) variables.
hadamard, method, descent, method, descent, redirects, here, confused, with, proof, infinite, descent, mathematics, method, descent, term, coined, french, mathematician, jacques, hadamard, method, solving, partial, differential, equation, several, real, comple. Method of descent redirects here Not to be confused with Proof by infinite descent In mathematics the method of descent is the term coined by the French mathematician Jacques Hadamard as a method for solving a partial differential equation in several real or complex variables by regarding it as the specialisation of an equation in more variables constant in the extra parameters This method has been used to solve the wave equation the heat equation and other versions of the Cauchy initial value problem As Hadamard 1923 wrote We thus have a first example of what I shall call a method of descent Creating a phrase for an idea which is merely childish and has been used since the first steps of the theory is I must confess rather ambitious but we shall come across it rather frequently so that it will be convenient to have a word to denote it It consists in noticing that he who can do more can do less if we can integrate equations with m variables we can do the same for equations with m 1 variables References editHadamard Jacques 1923 Lectures on Cauchy s Problem in Linear Partial Differential Equations Dover Publications p 49 ISBN 0486495493 Bers Lipman John Fritz Schechter Martin 1964 Partial differential equations American Mathematical Society p 16 ISBN 0821800493 Courant Richard Hilbert David 1953 Methods of mathematical physics Vol II Interscience p 205 Folland Gerald B 1995 Introduction to partial differential equations Princeton University Press p 171 ISBN 0691043612 Maz ya V G Shaposhnikova T O 1998 Jacques Hadamard a universal mathematician American Mathematical Society p 472 ISBN 0821819232 nbsp This mathematical analysis related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Hadamard 27s method of descent amp oldid 1055783744, wikipedia, wiki, book, books, library,
