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INTRODUCTION AND ELEMENTARY CONCEPTS
SOME UNIFYING PRINCIPLES
ORIGIN OF SOME PARTIAL DIFFERENTIAL SYSTEMS
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analysis applied arbitrary backward difference becomes boundary and initial boundary conditions boundary-value problem canonical form central differences coefficients compute Consider convergence coordinate system Crandall defined deflection derivatives determine diffusion equation discretization error displacements dx dy edges elliptic engineering differential systems error example finite number finite-difference approximation fluid form of Eq forward difference Fourier Gauss-Seidel Gauss-Seidel method given homogeneous hyperbolic independent variables initial and boundary initial conditions integration iteration Laplace equation Laplace's Let h linear mathematical membrane mode shape motion nondimensional nonhomogeneous obtain operators ordinary differential equation orthogonal partial differential equation plate Poisson's equation rectangular reduces region residual separation of variables shown in Fig simply-supported sinh slab solution of Eq Solve Prob steady-state stress function surface Table technique theorem Timoshenko tion torsional transformation uniform usually values velocity potential Verify vibrating vorticity wave equation write yields zero temperature