Elements of Partial Differential Equations
This text features numerous worked examples in its presentation of elements from the theory of partial differential equations. It emphasizes forms suitable for students and researchers whose interest lies in solving equations rather than in general theory. Solutions to odd-numbered problems appear at the end. 1957 edition.
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arbitrary constants arbitrary function axis boundary conditions boundary value problem Chap characteristic curve charge complete integral complex potential consider corresponding cylinder Deduce deﬁned denotes determine diffusion equation diﬂerential Dirichlet problem displacement dx dy envelope equation 17 equivalent Example expression ﬁeld ﬁnd ﬁnding ﬁnite ﬁrst ﬁrst-order ﬁxed ﬂow ﬂuid follows Fourier transform function f given grad Green’s function harmonic Hence independent variables inﬁnite initial condition integral curves integral equation integral surface intersection Laplace transform Laplace’s equation linear partial differential method Neumann problem normal obtain one-dimensional ordinary differential equation parameter partial differential equation position vector potential function prescribed Prove readily shown reduces region relation satisﬁes the equation satisfying the conditions separation of variables Show solution of equation sphere of radius spherical string subsystem theorem theory two-dimensional uniform velocity potential wave equation xy plane