Partial differential equations: theory and technique
This is the second edition of the well-established text in partial differential equations, emphasizing modern, practical solution techniques. This updated edition includes a new chapter on transform methods and a new section on integral equations in the numerical methods chapter. The authors have also included additional exercises.
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THE DIFFUSION EQUATION
LAPLACE TRANSFORM METHODS
THE WAVE EQUATION
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approach appropriate approximation arbitrary boundary conditions boundary layer boundary values Cauchy data Chapter choice choose coefficient complete integral compute consider const convergence corresponding defined denote depend derivatives determine diffusion equation direction discontinuity discussion divergence theorem du/dn dx/dt eigenfunctions eigenvalue envelope example finite first-order equations flow Fourier transform given function Green's function harmonic function initial conditions integral equation involving Laplace transform Laplace's equation Laplacian Let u(x membrane method of characteristics multiply nodes normal obtain ordinary differential equation orthogonal parameter partial differential equation perturbation plane polar coordinates positive constant prescribed function problem of Eq region replace require respect result satisfy Eq satisfy the equation Section series expansion Show solution of Eq solve space specified spherical stationary technique temperature theorem tion triangle two-dimensional vanish vector velocity wave equation zero