Lectures on Cauchy's Problem in Linear Partial Differential EquationsCourier Corporation, 1 de jan. de 2003 - 316 páginas Would well repay study by most theoretical physicists."--Physics Today "An overwhelming influence on subsequent work on the wave equation."--Science Progress "One of the classical treatises on hyperbolic equations."--Royal Naval Scientific Service Delivered at Columbia University and the Universities of Rome and Zürich, these lectures represent a pioneering investigation. Jacques Hadamard based his research on prior studies by Riemann, Kirchhoff, and Volterra. He extended and improved Volterra's work, applying its theories relating to spherical and cylindrical waves to all normal hyperbolic equations instead of only to one. Topics include the general properties of Cauchy's problem, the fundamental formula and the elementary solution, equations with an odd number of independent variables, and equations with an even number of independent variables and the method of descent. 1923 ed. |
Conteúdo
CAUCHYS FUNDAMENTAL THEOREM CHARACTER | 3 |
DISCUSSION OF CAUCHYS RESULT | 23 |
CLASSIC CASES AND RESULTS | 47 |
THE FUNDAMENTAL FORMULA | 58 |
THE ELEMENTARY SOLUTION | 70 |
INTRODUCTION OF A NEW KIND OF IMPROPER | 117 |
THE INTEGRATION FOR AN ODD NUMBER OF INDE | 159 |
SYNTHESIS OF THE SOLUTION OBTAINED | 181 |
APPLICATIONS TO FAMILIAR EQUATIONS | 207 |
THE EQUATIONS WITH AN EVEN NUMBER | 213 |
OTHER APPLICATIONS OF THE PRINCIPLE OF DESCENT | 262 |
| 313 | |
Outras edições - Ver todos
Lectures on Cauchy's Problem in Linear Partial Differential Equations Jacques Hadamard Visualização completa - 1923 |
Lectures on Cauchy's Problem in Linear Partial Differential Equations Jacques Hadamard Visualização parcial - 2014 |
Termos e frases comuns
adjoint admit analytic function arbitrary assumed Book boundary calculation Calculus of Variations Cauchy Cauchy's problem characteristic cone characteristic conoid coefficients considered constant convergence coordinates corresponding curvilinear coordinates cylinder Darboux deduced defined denoting derivatives determinate domain double integral duly inclined edition element elementary solution equal exist expansion expression factor finite formula geodesic given gives half conoid holomorphic function improper integral independent variables infinitesimal inside instance integration with respect Jacobian latter Leçons linear m₁ method neighbourhood obtained ordinary ordinary differential equations parameters partial derivatives partial differential equation plane polynomial positive quantity regular replaced result right-hand side satisfy simple integral singular space surface tangent term theorem transversal u₁ U₂ Unabridged republication vertex Volterra's θα ди дх მყ