**Unformatted text preview: **u versus x ) for t = 1 2 a/c , t = a/c , t = 3 2 a/c , t = 2 a/c and t = 5 2 a/c . 4. In the preceding problem, for each value of t , determine the maximum value of u ( x,t ) (your pictures should help!). 5. Solve u xx + u xt-20 u tt = 0, with initial conditions u ( x, 0) = φ ( x ), u t ( x, 0) = ψ ( x ). (“Factor” the operator the way we did for the wave equation.) 6. Show that, for any function u ( x,t ) that satisﬁes the wave equation u tt = u xx (with c = 1), we have u ( x + h,t + k ) + u ( x-h,t-k ) = u ( x + k,t + h ) + u ( x-k,t-h ) for all x , t , h , k . 7. Solve u tt = 9 u xx on 0 < x < π/ 2, with u ( x, 0) = cos x , u t ( x, 0) = 0, u x (0 ,t ) = 0, u ( π/ 2 ,t ) = 0. 8. Textbook page 17, problems 3, 10; page 27, problems 2, 5....

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