The Taylor Series

[@ChristopherLum]

In case it is helpful, all my Optimization videos in a single playlist are located at kzbin.info/aero/PLxdnSsBqCrrHo2EYb_sMctU959D-iPybT. Please let me know what you think in the comments. Thanks for watching!

[@lukewideman1]

AE501: You never cease to explain these topics that I was previously unsure about in undergrad so clearly. thanks so much again. Bummer this class is almost over!

[@JonathanRiosRoman90]

AE501: Always had issues with Taylor Series, but this is probably the best explanation of it I’ve had this far. Excellent!

[@ethanngo3203]

AE501: I think Mathematica shines the most when it comes to problems like these! Such a great way to add the visual component to these analytical problems.

[@EfremNickel]

AE501: Ahhh good ol' Taylor Series. Brings back memories haha Great video!

[@GiovanniRiggi-j2q]

AE 501 - Johnny Riggi. I half remembered Maclaurin series being used for beam equations during my undergrad coursework, so this was a good recap of how it relates to the Taylor series and how they are applied.

[@ryanmeinhardt81]

AE501 : Good refresher on the 1D taylor/ Maclaurin series, and very interesting to see the multi-variable version of it and how it generates a planar approximation of the 3d surface

[@_Aeroguy]

I'm always glad to see one of your videos, it is nice to see this kind of content well explained, I wish I had teachers like you in university. Looking forward to seeing more GNC videos in the near future too!. Keep up the good work!

[@ChristopherLum]

Thanks, I'm glad the GNC related videos are helpful. In case you are interested, I have a Flight Mechanics playlist at kzbin.info/aero/PLxdnSsBqCrrEx3A6W94sQGClk6Q4YCg-h . I hope to update this with several more videos over the next several months. Hopefully I'll catch you at one of these in the future, thanks for watching!

[@Chuan-YuTsai]

AE501: thank you for explaining the series clearly and concisely.

[@wiloberlies9598]

I know I keep repeating myself here Dr Lum, but thank you making these available!! I owe you a huge debt of gratitude; I've learned a lot from you, and have enjoyed the process. Hope you and yours are well.

[@ChristopherLum]

Wil, thanks for dropping in again. It is my pleasure and I plan to keep making the videos as long as people keep watching them!

[@RayaneBelbachir-u4j]

@@ChristopherLum Respect

[@KevinKdep]

AE501: This is a great refresher. I haven't heard these terms for a very long time. Now they are starting to back. Great explanation. Thank you, Professor.

[@kurtkara3580]

[A E 501] The graphing example that starts at 28 minutes helped me to see how my plot should change as the number of terms in the series increases, thanks!

[@rowellcastro2683]

AA516: Great referesher. I have never been taught the Taylor Series this way. Your visualizing techiniques using Mathematica are underrated. Thank you Professor.

[@rowellcastro2683]

Before, It was hard for me to understand how the Taylor Series was related to the linearization of a nonlinear system but with your explanation, I can easily see the connection now.

[@TuanTran-fs8ll]

AE501-Tuan Tran: This is very detail explanation of Tayler Series and Maclaurin series. I was taught how to use Taylor series for approximation in undergrad but not the detail like this video. Thanks Professor!

[@calebwatson6331]

AE501: This is super helpful. I didn't learn the Taylor series theory well in undergrad so much needed refresher

[@RajChhabraUW]

AE501: Great review of Taylor Series! You really nailed down the point of linearization vs first order approximation.

[@milesbridges3547]

AA 516: Great refresher of taylor series and cool to see how it works in higher dimensions!

[@jacobgivens2000]

AE501: I appreciated the visuals in this lecture! They really helped.

[@jasonfranklin4614]

AE501 - A very clear and detailed explanation of the 2 series. It's really helpful to have all the little details explained like this in a practical way.

[@nghihoang2952]

I had known the Taylor and Maclaurin series before, but this is the best explaination by far, also those example using Mathematica really helpful. AE501

[@AndysWorldAW]

Thank you so much for this video. From the first 1min introduction, I already knew that I am going to learn the Taylor series today. Yesss! You did deliver it with a very clear explanation with great examples. Once again, thank you so much

[@ChristopherLum]

Thanks for the kind words, I'm glad you enjoyed the video. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching!

[@enigma5627]

AE 501: Jesse Perez - Great explanation on Taylor and Maclaurin series with analytical and Mathematica calculation. Maclaurin summation is easy to implement in Mathematica but Taylor Series was a bit more complicated as it appears one can write the sum in different forms.

[@Evan.M.Phillips]

AE501: This was a great review of Maclaurin and Taylor series!

[@brianas1711]

AE501: great lecture as usual. Really appreciate the examples in Mathematica. Incredibly useful tool.

[@KennethWright-k2h]

AE501: I learned these series in high school calculus, but never saw them applied to multiple variables. It was interesting watching the series approximate the 3D surface.

[@joshshort8815]

AE501: great explanation, the plots really helped me understand the concept.

[@ChristopherLum]

I am glad to hear that the plots helped!

[@ryoonoue1076]

AE501. Great review of Maclaurin and Taylor Series!

[@mateusvianacarius855]

I am from Brazil, I like your videos, I learn about math, tecnology and mainly english. Hugs from Brazil

[@ChristopherLum]

That's great, I'm glad they are helpful. Thanks for watching!

[@mateusvianacarius855]

Hi I'm from Brazil. I like your videos I learn about math, tecnology and english too. Hugs from Brazil

[@michealdean3750]

Yada-yada-yada... OK. That explains a lot. In fact it explains most things. like the insanity of the last year. Dude seems a bit rushed and anxious. Slow down, take a breath. If my tired old brain can get its' self around SOME of this , your presentation will and has succeeded. Look forward to more of your videos.

[@iremerkan725]

AE501: There should be an "(x-2)^p" included in Taylor Series in Mathematica, right? Oops, now seeing that you already addressed that.

[@arupkanka]

This was really helpful and interesting!! Please continue posting more such videos!

[@ChristopherLum]

Hi Ayushi, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@KylePetittEdu]

AE501 Can you elaborate on what you mean by a perturbation away from the expansion point? are we just talking about any offset to move the origin? [45:25]

[@paulpietrowicz3683]

AE501- Good explanation of the Taylor and MacLaurin Series with examples

[@CharlotteGill-v2w]

AE501: the video was easy to follow and the examples were really helpful!

[@ChristopherLum]

I’m glad you found the examples helpful!

[@mutiur7396]

Good lecture on these two topics.

[@edwardmau5877]

AE 501 I don't think there was any information here that was different than what I learned in high school/undergrad, but I understood the concepts much more for some reason. Re-learning vs first time learning is so different.

[@atruon17uw]

[AE501] I like having the Mathematica examples, it seems like they will be very useful for homeworks.

[@elijahleonen198]

AE501: Great review of Taylor series. Thank you for the great lecture professor!

[@ThienNguyen-vx1td]

AE501: Thank you for making these helpful videos.

[@AadyaGoel-kr9lv]

21:27 but since x=0 wouldn't f'(0) /2! * x be 0 ? since x is 0. And how did we get x^n instead of e^x for the maculerian series of the function? Woudn't it all just become 0?

[@ChristopherLum]

Hi Aadya, Thanks for reaching out, I'm glad you enjoyed the video. Unfortunately I'm unable to respond to questions on KZbin due to the sheer volume of inquiries that I receive. That being said, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum or via the 'Thanks' button underneath the video as I'll be able to answer questions there. Given your interest in the topic, I'd love to have you as a Patron as I'm able to talk/interact personally with Patrons. Thanks for watching! -Chris

[@ruttorobert]

AE501: great lecture as usual.

[@ecotive]

I don't like your videos, I LOVE them all. :-) Thank you, Christopher!

[@ChristopherLum]

Hi Behnam, Thanks for the kind words, I'm glad you enjoyed the video. If you find these videos helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@KarolOrtizSolar]

AE 501: great video!

[@tonykuenzli2182]

AE501 - Very straighforward explanation of Taylor Series

[@yopenzo]

Min 34:30 and ahead. The green Taylor line for P=1 is not linear because it's doesn't go through the origin?😅 But sure the green line is straight! Is a linear function of x^1 with angular coefficient e^2/2!

[@Tamanaaaa1]

AE501: Great video thank you!

[@thefoxcatch]

I feel pretty good. I calculated the 2nd order with the Hessian by hand. Woohoo.

[@sethwhittington28]

AE501: I wasn't aware that a function is non-linear if it does not cross through the origin. You alluded to this in the lecture, but didn't expand on it and it was pretty big news to me. Is there anything more to this?

[@ChristopherLum]

Seth, this is a common place of confusion. y = m*x+b is not linear. It is affine. y = m*x is linear. The non-zero y-intercept is what changes a mapping/function/transformation from being linear to affine.

[@AbhishekSharma-oq6in]

@@ChristopherLum I'm confused as to what actually linearity is. Like if we go by standard definition then both of them are linear aren't they? Could you please help me out here?

[@carlydunford2546]

AE 501: To make sure I am understanding correctly, we would only use the techniques taught in the 20ish minutes if we are working in 3 dimensions? not in two dimensions?

[@BeniSnow]

AE501: Since the math for Maclaurin series is always simpler than a Taylor series, why would anyone use a Taylor over a Maclaurin? You can always just use more terms to get a good enough approximation. Also, thanks, for a great term. Happy holidays!

[@ChristopherLum]

Beni, good observation. However in many situations you are at a specific point other than the origin and you will need to approximate the function at this location. As such, it is actually better to just learn the Taylor Series as the Maclaurin is just a special case of the Taylor Series.

[@vahidengineer7303]

Thank you so much. can you make videos about integrating numerically and also discrete control?

[@rowellcastro2683]

AA516: Watching Taylor Series get utilized to approximate multivariable functions such as a surface was very very interesting. I have one question though. Let's say you have a gradient function in matlab that computes the gradient. How would I implement the gradient function to calculate a hessian? I just now learned about Matlab's Symbolic Math Toolbox that has funtions gradc and hessc; can we use that instead?

[@maggiesplantgirl]

AE501: I remember taylor/McLaurin from undergrad but we never did the cool vector format version! -Maggie Shelton

[@ChaseSnow-w9f]

AE501: Great video.

[@AshleyMush-v9m]

Hello guys, whats the program or software being used to plot

[@Richard_Le]

AE501 Why is Taylor series preferred in optimization over Fourier series when both are just different ways of approximating a function?

[@ChristopherLum]

You'll see that in optimization we want the gradient/derivative of the function and this is what Taylor is good at.

[@RahulSharma-oc2qd]

how to linearise y''(y+2) using taylor series?

[@AG-cx1ug]

What is |x-a| < R?

[@marcosszmania5874]

AE 501: Hey professor Lum, can every continuous function be described by a Taylor series? Thanks!

[@Gholdoian]

AE 512: I didn't realize the nuance between a linear approximation vs an affine approximation and the need to keep in mind delta units vs. absolute

[@ChristopherLum]

Yes this delta issue is important and well need to use it shortly

[@mike_field]

Thank you so much 👍

[@ChristopherLum]

Hi Akpam, Thanks for the kind words, I'm glad you enjoyed the videos. If the find the these videos to be helpful, I hope you'll consider supporting the channel via Patreon at www.patreon.com/christopherwlum. Given your interest in this topic, I'd love to have you a as a Patron as I'm able to talk/interact personally with all Patrons. Thanks for watching! -Chris

[@tranpham7120]

AE501: I calculated the 2nd order with the Hessian by hand

[@KanwarjitSingh88]

AE 501 nice video to learn

[@meavbeer]

Another great video lol

[@rowellcastro2683]

45:30 100% agreed

[@malachimorris1649]

AE501 - Malachi Morris

[@CodySmith]

AE501 Cody Smith

[@shavykashyap]

AA516

[@changlongwang5201]

[A E 501 student] watched - CW

[@davidtelgen8114]

AE 512