Problem Sets
Problem Set 1 (due 02/14 /2024, W)
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Prob 1. Find the general solution of the differential equation
$y^{\prime\prime}-y=x^{2}+\sin3x+e^{x}+e^{\sin x}.$
- Prob 2. Prob 1a in Chapter 1.
Problem Set 2 (due 03/11 /2024, M)
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Prob 1. Consider the function
$f(z)=\dfrac{1}{z(4-z)}.$
- Express this function as a Taylor seies expanded about $z=2$. In which region of the complex plane is this series convergent?
- Express this function as a Laurent series expanded about $z=2$ convergent in other region or regions.
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Prob 2. Find $u(x,y)$ which satisfies the Laplace equation
$u_{xx}+u_{yy}=0,$ $x^{2}+y^{2}$ < $4,$
and the boundary condition
$u=2\cos2\theta$, $x^{2}+y^{2}=4.$
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Prob 3. Find the values of the integrals
$\int_{-\infty}^{\infty}\dfrac{\sin x} {x+2i}dx$
and
$\int_{-\infty}^{\infty}\dfrac{1}{(x^{2}+16)^{2}}dx$
- Prob 4. Problem 4a and 4d in Chapter 2 of the text book.