Math 442: Intro to Partial Differential Equations Homework 2
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Homework 2
MATH 442: INTRO TO PARTIAL DIFFERENTIAL EQUATIONS
(Exercises are taken from paTtial DifeTential Equations An IntToduction, second Edition by walter A. strauss.)
1. Exercise &3.2 #5. solve utt = 4uxx for 0 < x < ∞, u(0, t) = 0, u(x, 0) 三 1, ut(x, 0) 三 0 using the relection method. This solution has a singularity; ind its location.
2. Exercise &3.2 #7.
(a) show that φodd(x) = (signx)φ(|x|).
(b) show that φext (x) = φodd(x — 2l[x/2l]), where [.] denotes the greatest integer function.
(c) show that
3. Exercise &3.2 #9.
4. Exercise &3.4 #12. Derive the solution of the fully inhomogeneous wave equation on the half-line
by means of the method using Green,s Theorem. (Hint: Integrate over the domain of dependence.)
2023-07-22