6760, Math 21a, Fall 2009
Week 5 Problems B, Math 21a, Multivariable Calculus
A PDE Problem
Course head: Oliver Knill
Office: SciCtr 434
Email: knill@math.harvard.edu
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Problem B:
a) Verify that the function u(t,x) = sin(sin(t+x)) is a solution of the transport equation
ut(t,x) = ux(t,x). b) Verify that the function f(x,y) = 3 y2+x3 satisfies the Euler-Tricomi partial differential equation uxx = x uyy. This partial differential equation is useful in describing transonic flow. Find an other solution which is not a multiple of the solution given in this problem. |