Quiz 2 Review

$\hangindent\parindent \item{1.} State the definition of the convolution product $f*g$.$

$\item{2.} Let $f(t)=\sin(t)$ and $g(t)=t$. Compute $(f*g)(t)$.$

$\item{3.} Use Theorem 5.3.1 to find a lower bound on the radius of convergence of a series solution of the form $$ y=\sum_{n=0}^\infty a_n x^n $$ to the ordinary differential equation $$ (1-x)y''+xy'+(\sin x)y=0. $$$

$\item{4.} Find the first four terms of the power series solution to the initial value problem $$ y''+xy'+(1-x)y=0;\quad y(0)=1,\quad y'(0)=1. $$$

Last Updated: Tue Apr 15 15:45:58 PDT 2003