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answer
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watching
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13 Nov 2019
Q1. Wave equation on an in infinite domain
Q1. Wave equation on an infinite domain Let c> 0 and consider the wave equation on, oo): 0t2 Or2 (a) By making the change of variable ξ := x-ct and η := x + ct, show that u(z,t) is a solution of if and only if u(ξ, η) is a solution of LI Hint: Using the chain rule, show that (b) By integrating (2) show that u(z,t) = F(z-ct) + G(z + ct) for arbitrary functions of F(E) and G(η) (c) Given initial conditions u(r, 0)u( andv(), show that the solution to is co(s)ds Hint: Using the initial conditions and part (b), show that for some constants a, A v(s)ds -A
Q1. Wave equation on an in infinite domain
Q1. Wave equation on an infinite domain Let c> 0 and consider the wave equation on, oo): 0t2 Or2 (a) By making the change of variable ξ := x-ct and η := x + ct, show that u(z,t) is a solution of if and only if u(ξ, η) is a solution of LI Hint: Using the chain rule, show that (b) By integrating (2) show that u(z,t) = F(z-ct) + G(z + ct) for arbitrary functions of F(E) and G(η) (c) Given initial conditions u(r, 0)u( andv(), show that the solution to is co(s)ds Hint: Using the initial conditions and part (b), show that for some constants a, A v(s)ds -A
Irving HeathcoteLv2
23 Jul 2019