PS607 Exam 0



September 12, 2003, 50 minutes, closed book.


Please start each solution on a fresh sheet of paper, use only one side of the paper. Try to show how well you understand the problems. Always justify your reasoning.


  1. Evaluate

    \begin{displaymath}
\int_0^3 \int_0^4 \int_{x=y/2}^{x=(y/2)+1} \left(\frac{2x-y}{2} + \frac{z}{3}
\right) dx dy dz
\end{displaymath}

  2. Find a general solution of the equation

    \begin{displaymath}y'' + y = \frac{3}{\sin x} \end{displaymath}

  3. Find eigenvalues and eigenvectors of the matrix

    \begin{displaymath}
\left[ \begin{array}{rrr}
0 & 1 & 0 \\
1 & 0 & 0 \\
0 & 0 & 0 \\
\end{array} \right]
\end{displaymath}



2003-09-18