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 :
Partial fraction decomposition:
Inverse Laplace Transform:
Then respond to the following prompts.
- What is one thing you learned from (any) one of the videos? What is one thing that you didn’t understand, or found confusing?
- Any questions about the example above?
- 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:
- Finding the Laplace Transform (like we did today)
- Finding the Inverse Laplace Transform, or
- 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
- Overview: How do we use the Laplace Transform to solve differential equations? 2 min. https://www.youtube.com/watch?v=Z_wQvCyKjwE
- 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.
- (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
- 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.
- Partial Fraction Decomposition – a basic example. This is a good basic example.
- 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.