# Solutions for homework assignment #4 - Texas A&M …

**Solutions** for **homework** assignment #4 Problem 1. Solve Laplace’s equation inside a rectangle 0 ≤ x ≤ L, 0 ≤ y ≤ H, with the following boundary conditions: ∂u ∂x ... of **solutions** u(r,θ) = h(r)φ(θ) with separated variables of Laplace’s equation that satisfy the three

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NoweachofthevariablesS1 canbeusedtoderiveastringwi ∈A,i.e.,fromthe ithS1,wegetS1 ⇒∗ w i.Thus, S2 ⇒∗ S 1S1 ···S1 ntimes ⇒∗ w 1w2···wn ∈A ∗ since each wi ∈ A.Therefore, we end up with a string in A∗.Toconvince ourselves that the productions applied to the various separate S1 terms do not interfereinundesiredways,weneedonlythinkoftheparsetree.