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THE METHOD OF POWER SERIES
EQUATIONS OF THE FIRST ORDER
CLASSIFICATION OF PARTIAL
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analytic function approximations arbitrary boundary condition boundary dD boundary value problem bounded canonical form Cauchy data Cauchy problem circle coefficients complex domain const constant convergence corresponding defined difference equation Dirichlet integral Dirichlet problem domain of dependence dx dy eigenfunctions eigenvalues elliptic equation establish Exercise existence extremal problem finite difference flow Fredholm free boundary free streamlines fundamental solution Green's function harmonic function hyperbolic equation identity independent variables inequality initial conditions initial curve initial data initial value problem integral equation kernel Laplace's equation linear maximum principle method Neumann problem nonlinear normal derivative obtain ordinary differential equations parameter parametrix partial derivatives partial differential equation prescribed proof quasi-linear representation result Riemann function satisfies second order Section sequence Show singularity solution of Cauchy's solution of Dirichlet's solve space surface theorem transformation uniqueness vanishes vector wave equation zero