Partial Differential EquationsThis book is intended to fill the gap between the standard introductory material on partial differential equations: separation of variables, the basics of the second-order equations from mathematical physics and the advanced methods such as Sobolev spaces and fixed point theorems. |
Contents
THE METHOD OF POWER SERIES | 1 |
EQUATIONS OF THE FIRST ORDER | 18 |
CLASSIFICATION OF PARTIAL | 57 |
Copyright | |
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analytic function arbitrary boundary condition boundary value problem bounded canonical form Cauchy data Cauchy problem circle coefficients complex domain constant continuous convergence corresponding defined difference equation Dirichlet integral Dirichlet problem domain of dependence dx dy eigenfunctions eigenvalues elliptic equation establish Exercise existence flow Fredholm free boundary free streamline fundamental solution Green's function harmonic function hyperbolic equation identity independent variables inequality initial curve initial data initial value problem integral equation kernel Laplace's equation linear maximum principle method Neumann problem obtain ordinary differential equations parameter partial derivatives partial differential equation plane prescribed proof quasi-linear region region D representation result Riemann function satisfies second order Section Show solution of Cauchy's solution of Dirichlet's solve space surface theorem transformation u₁ um,n uniqueness vanishes vector wave equation x-axis x₁ y₁ zero θν ди ду дх