Elementary Partial Differential Equations |
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applied arbitrary constants assume atē behaviour boundary conditions c₁ c₂ cable Chapter characteristics coefficients consider const convergent coordinates corresponding cosh D'Alembert's solution defined determined diffusion equation Dirichlet problem discussed in Section displacement ditions drawn in Fig du/dx energy equation 3.1 example Exercise finite fluid Fourier series Fourier sine series function given grad harmonic heat flow Hence incident wave independent variables infinite initial conditions initial value integral irrotational Laplace's equation linear mass mathematical mesh points motion obtain one-dimensional ordinary differential equations oscillations parabolic partial differential equations physical plane poker potential pressure region result satisfies Section 2.3 separation of variables sinh slab solution of Laplace's string Superposition surface temperature distribution theorem u₁ unique unit area vanishes vector velocity velocity potential viscosity wall wave equation x-axis zero ηπα дв дг ди др дх ду