1. Calculate the Laplace transform of exp(-10t) x u(t)
2. Calculate the convolution of exp(-t) and sin(t) using (a) the Laplace transform (b) direct integration
3. Compute the inverse transform of (3s^2 + 4s + 1) / (s^4 + 3s^3 +3s^2+2s)
4. Use Laplace transform to calculate the solution to the ODE y"+6y'+8y=u(t) y(0)=0 y'(0)=1
5. Determine the final value of (3s^2 + 4s + 1) / (s^4 + 3s^3 +3s^2+2s)
The 11 pages file contain full derivations and explanations of the solutions to these questions.