Math 2250 Linear Algebra and Differential Equations
Chapter 10: Laplace Transforms Review
Be absolutely certain in your ability to perform the following tasks. As you should
already know, integration by parts and partial fractions are fundamental to the use of
Laplace transforms and may be required on the exam.
Find the Laplace transform of a function f(t) by definition. Be sure to give
careful treatment of the limit in the improper integral.
Write a piecewise continuous function in terms of unit step functions.
Find the Laplace transform of a piecewise continuous function, possibly given
only its graph (this may be done by definition or by using the Second Sift
Theorem)
Show that a given function F(s) approaches 0 as s approaches infinity (this is
required of all Laplace transforms)
Solve an initial value problem by using Laplace transforms
Find the Laplace transform of any transformable function as discussed in class.
Use completing the square to find the inverse transform whose denominator is a
non-factorable quadratic with a linear term.
Use convolution to find
)}()({
1
sGsFL
.
Use the Integral Theorem and Derivative Theorem to find the Laplace
transform of either
)(ttf
or
t
tf )(
where f has a known Laplace transform.
Use the Integral Theorem and Derivative Theorem to find the inverse Laplace
transform of an unknown transform F(s).
Use the Second Shift Theorem to find the Laplace transform of a piecewise
continuous function.
Use the Second Shift Theorem to find the inverse Laplace transform of
)(sFe
at
for a known transform F.
Find the transform of a periodic function.