Partial Fraction Expansion/Decomposition

[@ChristopherLum]

In case it is helpful, here are all my ODE videos in a single playlist kzbin.info/aero/PLxdnSsBqCrrHHvoFPxWq4l9D93jkCNIFN. Please let me know what you think in the comments. Thanks for watching!

[@hshams28]

AE501: This was a really good review of PFEs and how it works for the certain cases and I really liked that you showed how it doesn't work the same for each case!

[@maxschreiber843]

AE501: this topic used to mess with my head so much in undergrad, yet now it seems very simple. Great video!

[@sunnysarkar7643]

AE 501: Showing multiple methods is super helpful. I wish you had an example of cleaning up the polynomial in MATLAB because I think that would also be extremely helpful.

[@ryoonoue1076]

AE501. I'm glad we're going over these again. I've done them once, but been a while..

[@elijahleonen198]

AE501: Very helpful video! I now have a great understanding on poles and partial fraction decomposition.

[@AlejandroMartinez-nv9ri]

AE501: Helpful examples, thank you for the video. Its all coming back from undergrad

[@joshrubi1618]

Number one. Thanks for the techinques.

[@carlydunford2546]

AE 501: Super helpful review of partial fraction decomposition, I used this a lot in undergrad and didn't realize how much I had forgot

[@PathwaytoEngineeringDegree]

AE501: excellent lecture, enjoyed it very much!

[@keyshawnb4845]

AE 501: I enjoyed learning about PFEs and learning about the different cases and the methods involved.

[@KennethWright-k2h]

AE501 : Great review of partial fraction expansion. Thank you for showing multiple methods where they exist and explaining all three possible cases.

[@jasonfranklin4614]

AE501 - I had to bookmark this one. I like the clear explanations and after so many years, much of this material seems new. The CAS solutions for symbolic manipulation are really nice!

[@jesusespinoza2349]

Thanks for the refresher

[@daniellerogers5959]

Some powerful methods to expanding those polynomials to be more digestible, very cool!

[@mitchellnakaki7900]

Learned quite a bit from this video, some material completely new to me!

[@masontelander3847]

Great video

[@thomasireson1427]

Great refresher!

[@JulieWarchol]

AE 501 - Great refresher! I tried to work one of the homework problems out by hand when the roots were complex conjugates. This video was very helpful. I typically like to do the HW by hand and then sanity check in Mathematica. Thanks for the great content!

[@ChristopherLum]

Glad to hear it, sometimes a little bit of hand calculation makes the computer output a lot more satisfying.

[@JonathanRiosRoman90]

AE501: Excellent refresher and examples for Mathematica.

[@BennettBoyd-h1f]

AE501: Good review of partial fraction expansion and decomposition

[@ericwang161]

I appreciate the refresher!

[@matthewbajamundi8774]

I enjoyed the review especially the repeated root section

[@sajeew]

Thank you for the video Sam

[@astall135]

AE501: It helps to see the generic forms for PFE explained in a way that facilitates computer programming. Its clear that the algebra is not the focus here and we are just building out the numerical toolbox.

[@BenLandes]

AE501 - For cases 1 and 2 it seems fairly intuitive to use the methods presented higher order transfer functions. For case 3 your example seems very targeted to a certain format of the transfer function. Anytime you have complex poles do you have to memorize the form of the equation to put the denominator in for each different order of polynomial?

[@RajChhabraUW]

AE501: Good review of Partial Fraction Expansion. For homework assignments, are we free to do steps in Mathematica/MATLAB like you did in the video, or does everything have to be written out by hand?

[@ChristopherLum]

Unless the problem explicitly asks for a hand calculation you are free to use a tool

[@jakegalleryn6200]

Seems like very useful tools.

[@brentpaul7650]

good video

[@jonathonlaird6279]

Thanks for the video!

[@Tamanaaaa1]

AE 501- Very helpful thank you.

[@Richard_Le]

AE501 How would a combination of cases work, say for example, a real distinct with complex conjugates?

[@ryanjorgensen8192]

AE501: How do you derive the expressions for alpha and omega (around 53:20 of the video)?

[@ChristopherLum]

Hi Ryan, expand the second equation and then solve the coefficient of s and the constant to make the two equations equal.

[@jacobgivens2000]

AE 501: Jacob Givens, This video really helped with the homework!

[@sethwhittington28]

AE501: It seems like this technique is only used to get the equation set up in a way thats easier to take the upcoming inverse laplace transform of? If the equations is already in a format that can be found in a laplace table, can we skip this whole step..?

[@ChristopherLum]

Seth, correct, if you already have it in a form you recognize, you can skip this step. In fact, doing this by hand is a bit of a pain so once we understand how the poles contribute to the eventual time response, we should just skip the entire manual process and just use Mathematica's InverseLaplaceTransform function.

[@keelythompson8657]

AE501 - How does the form of F(s) of Case 3 change for higher order polynomials?

[@ChristopherLum]

The process should be the same, you should be able to break it apart into one of the 3 aforementioned cases. Let me know if you'd like to chat about this at office hours.

[@LilanieAlfredaAbdur-Rahman]

AE501... Great refresher. Though I will need to review that synthetic division

[@ChristopherLum]

Don't worry too much about the synthetic division, we won't use this anywhere else in the class and Mathematica or other tools can get your roots of higher order polynomials.

[@paulpietrowicz3683]

AE501 Student: The multiple cases and situations shown are helpful for future use. More tools in the toolbox!

[@ChristopherLum]

Yep, I hope you've gone to Home Depot and bought a bigger toolbox because we are going to fill it up this quarter😊!

[@tranpham7120]

AE501. I apreciate for your video.

[@Chuan-YuTsai]

AE501: Nice review of PFE

[@MagdaleneRachelleShelton]

AE501 : Do you have a video where synthetic division is covered? I vaguely recall the method and struggled through to use it for a problem on HW01 but additional practice would be useful to me. -Maggie Shelton

[@ChristopherLum]

Unfortunately I don't have a video of this yet. It is on my list of videos to make.

[@edwardmau5877]

AE501 Didn't know there were two methods, I only remember being taught the coefficient method.

[@trevorubrown]

Great vid

[@atruon17uw]

[AE501] These videos are simple and easy to understand

[@ahmedashmaig]

AE501: "there's more than one way to ride this donkey" @ 35:20 😂. What happened to multiple ways of skinning cats?

[@MarcoIacoviello-r3w]

AE 501: "There is more than one way to ride this donkey"

[@joewalker5753]

Some of this i remembered but some i didnt!

[@CodySmith]

AE501, Cody Smith.

[@B_Foland767]

AE 501 Bryce Foland

[@tranpham7120]

AE511: I watched this video in AE501:

[@malachimorris1649]

AE501 - Malachi Morris

[@GiovanniRiggi-j2q]

AE501: Johnny Riggi - It has ben a while since I have done this. Great refresher on PVE