Math 230 - Chapter 7 Study Guide

  1. You are given the result of an indefinite integral for the Laplace transform. Identify any restrictions on s so the integral converges, find the Laplace transform, identify the original function, and find the Laplace transform if the function is periodic. For example, if the original function was \( f(t) = \cos 3t \), then you would be given \( \frac{e^{-st}}{s^2+9}\left(3 \sin 3t - s \cos 3t \right ) \)
  2. Rewrite the piece-wise function using the unit step function. Then find the Laplace transform for the function.
  3. Solve the initial value problems using Laplace transforms. 3 parts.
  4. Use Laplace transforms to solve the system of differential equations.
  5. Solve the initial value problems as far as Y(s) =. Do not use partial fractions or attempt to find the inverse Laplace transform. 3 parts.
  6. The Y(s) from solving a differential equation is given. Use it to find the solution y(t). 4 parts.


Points per problem

# 1 2 3 4 5 6 Total
Pts 16 8 24 10 18 24 100