Elements of Partial Differential EquationsThis 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 axis boundary conditions boundary value problem c₁ characteristic curve complete integral coordinates curl cylinder Deduce defined denotes density derivatives determine diffusion equation Dirichlet problem dx dy envelope equation 11 Example first-order function F given grad Green's function Green's theorem harmonic Hence integral curves integral surface intersection Laplace's equation linear partial differential method obtain one-parameter ordinary differential equation orthogonal parameter partial differential equation Pfaffian differential equation position vector Prove readily shown region relation S₁ satisfies the equation Show sinh solution of equation solve string Substituting temperature theorem theory two-dimensional U₁ velocity potential wave equation zero аф ди ди дл дп др дуг дх ду дха