OpenLab #3: Flipping the class – Inverse Laplace Transforms and Partial Fraction Decomposition

One of the strongest results from our OpenLab #2 Survey was a request for more examples & problems in class.  As you know, our class time is quite limited – so to take maximum advantage of the time we have, we are going to try an experiment.  This OpenLab assignment, to be completed over the Spring Break, will ask you to get a head start on upcoming material by watching a few videos on the material.  This will hopefully free up some class time for more examples & problems.

Assignment (Due Thursday, April 24, at start of class).  Watch the videos below.  You MUST watch the videos marked “required”.  You CAN also watch the videos marked “optional,” – if you have any questions about today’s lecture, or if you need a reminder of how to do Partial Fractions, you should watch the appropriate videos here.  Test your understanding by completing this problem:

Example. Find the Inverse Laplace Transform of :  

SOLUTION:
Partial fraction decomposition:
Inverse Laplace Transform:  

Then respond to the following prompts.

1. What is one thing you learned from (any) one of the videos? What is one thing that you didn’t understand, or found confusing?
2. Any questions about the example above?
3. Any comment on this assignment? (helpful, confusing, useful, irritating, etc – what did you think of it?)

Extra Credit.  You can earn extra credit by making up a problem and posting it here (do NOT post the solution yourself – let other people solve it!), or by giving a solution to someone else’s posted problem.  Simple problems are fine – it can be much simpler than my example above.  It should be one of the following types of problems:

1. Finding the Laplace Transform (like we did today)
2. Finding the Inverse Laplace Transform, or
3. Partial Fractions

How do I type math formulas on the OpenLab? You can always type mathematical formulas just as you would type them into a TI-83 calculator, for example “sin(2t)+e^x”.  But if you want them to look pretty (like this:  ) you can do that too – here’s a guide (see the section “Typing math on the OpenLab” about halfway down the page).

VIDEOS – REQUIRED

1. Overview: How do we use the Laplace Transform to solve differential equations?  2 min.  https://www.youtube.com/watch?v=Z_wQvCyKjwE
2. The Inverse Laplace Transform.  6 min.  https://www.youtube.com/watch?v=Y8GXpS31CGI
   NOTE: The first minute and a half is a more abstract discussion – follow it as best you can.  BUT hold on for the example, which starts at 1:25.
3. (This is not required, but if you like these videos, he has a whole playlist of videos on the Laplace Transform here:  https://www.youtube.com/playlist?list=PL5750E3CE53DB625A )

VIDEOS – OPTIONAL

1. Finding the Laplace Transform of a Function:  3 min.  This is a useful example of what we did in class today – it will also help you with WeBWorK 14.
   http://youtu.be/ES2Lwzrw_UE
2. Partial Fraction Decomposition – a basic example.  This is a good basic example.
   https://www.youtube.com/watch?v=HZTv4zCgEnA 
3. Partial Fraction Decomposition – another example. This is a slightly longer example, and it includes a good explanation of how to set up your partial fractions for different kinds of factors in the denominator.
   https://www.youtube.com/watch?v=pZ9FfGy3Cfw