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Unformatted text preview: Dorthy experiences at time t = . 5. Let f : R 2 R and dene g ( x, y ) = f (sin y, cos x ). Find g xx and g yy . State any assumptions you needed to make. 6. Let f, g : R R where f and g are twice dierentiable. Show that u ( x, t ) = f ( x-at ) + g ( x + at ) is a solution of the wave equation: u tt = a 2 u xx . 7. Let g : R R and let f ( x, y ) = g ( u 2 v ), where u = e x and v = x 2 + y 3 . Use the chain rule to nd 2 f xy . State any assumptions you needed to make....
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This note was uploaded on 10/12/2010 for the course MATH 237 taught by Professor Wolczuk during the Fall '08 term at Waterloo.
- Fall '08