Lectures on Cauchy's Problem in Linear Partial Differential Equations

adjoint admit analytic function arbitrary assumed Book boundary calculation Calculus of Variations Cauchy Cauchy's problem characteristic cone characteristic conoid coefficients considered const constant convergence coordinates corresponding curvilinear coordinates cylinder Darboux deduced defined denoting derivatives determinate domain double integral duly inclined element elementary solution equal exist expansion expression factor finite formula geodesic given gives half conoid holomorphic function hyperbolic improper integral independent variables infinitesimal inside instance integrand integration with respect Jacobian latter Leçons m₁ method neighbourhood notation obtained ordinary ordinary differential equations P₁ 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 vertex Volterra's ди ду дх