In case it is helpful, here are all my ODE videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrHHvoFPxWq4l9D93jkCNIFN.html. Please let me know what you think in the comments. Thanks for watching!
Bring on the math jokes! I appreciate the fun you add to these videos. This video does a nice job demystifying jargon I saw in my controls classes and Diffeq classes. Thanks again!
[AE501] 54:11 I like that you are very explicit in your derivations and explanations. It makes it easier to follow. I also like the visualization of the complex numbers in a 2d plot, it helps make an abstract concept a bit more tangible.
I dont understand the joke but it was quite good. You can understand if an instructor really knows about the topic they tell by how simple the explanations are. He explains the topic like it is a simple thing to understand, so get it. Liked it very much :)
Hi Turku, 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
AE 501. this video helps me to refresh Complex numbers concept which between Imaginary and Real. if we can learn more about how to solve example problem use Matlab or Mathematica, it will be great. However, the video is great explanation and clear for me. thank you Chris
AE501: "Read the fine manual" hahaha. very helpful, it summarizes complex numbers. it was refreshing for me at least, looking forward to Laplace Transform.
Professor Lum/AE501, I think it would’ve helped me out personally if the video had started out with maybe a quick reason of why I care about Euler’s formula. For example: in the previous ODE video, if I recall correctly you quickly showed what an ODE was and how it might be used. THEN went into more complex topics and derivation. I have spent a good portion of this video so far trying to figure out why I need to care about Euler and am over halfway through. I’m sure you’ll get there eventually... just some feedback for those who think like me.
Seth, thanks for the feedback, you make a very good point. To answer your question, the reason we need Euler's Formula is that we'll use it down the road when working with underdamped/oscillatory systems which introduce sin/cos terms. Just hang on for 1 or 2 more videos and hopefully it will become clear why we need it.
I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!
AE501 Student Good discussion on complex variables, complex numbers, Euler's equation, complex conjugates and complex algebra. Looks to be good applications coming up in future videos.
AE501. Another great review video. Imaginary numbers are definitely interesting to imagine about.. I've always thought it was also interesting that one could write out sin and cos in a summation. Great explanation on how complex numbers can be mathematically manipulated.
AE 501. Hi Chris, at time 51:46 you explain that for a pole the function comes out of the page. Maybe I missed it but I am having trouble understanding what this third dimension is on the real and complex plane. Also, does this mean that for the zeros the function is on the plane? I am sure I am misunderstanding something. By the way, this is Austin, I just realized my account name doesn't match.
AE 501 At around 19:10, how do you get the i on the cos portion of the equation? Also, should the signs be alternating for both the real and imaginary portions?
@@ChristopherLum I guess I don't see how the "i" from the cos(theta)+sin(theta)i (around 19:10 in the video) gets distributed to the cos(theta) portion of the equation. Not sure if that helps or not.
AE501 So just to clarify, for powers and roots formulas, the thetas have to be in radians? The choice between positive or negative theta in those formulas shouldn't matter right?
Hi, 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 or via the 'Thanks' button underneath the video. 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. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching! -Chris
AE 501. Great video on complex numbers but I guess I'm a little confused towards the end about complex functions/poles. It was still a little tricky understanding at poles F(s) is infinity and therefore sticks out of the plane. Its almost like F(s) acts like a z value (on a real plane) and sticks out of the page, but how does that pertain to the complex plane? I really think a 3D plot of a complex function would be helpful to visualize, because for most of the video I was thinking in 2D until you introduced F(s).
Zane, sorry, I realized the motion I made seemed to imply that poles stick out of the plane but this isn't really a useful way to think of it. Just think of poles as values of s that lead to the function F(s) going to infinity.
AE501: Very useful video in doing homework problem 1. I was not familar with the method of writing complex functions in terms of zeros, poles, and gain. -Natalia Ermolaeva
Hi, 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! -Chris
AE501: Professor Lum, thank you for the helpful video. If complex numbers can be represented on a plane, can the idea of a graphic representation be extended to complex functions? While it's easy to imagine functions like y = x, it's not very easy to imagine y = s where s might be a complex variable. Not sure if this is a legitimate question, but I just had this thought as I watching the last part of your video. Thanks!
Karina, that is a good observation. Yes, you can think of complex functions in the same fashion as you think of vector functions. With vector functions, the vector might be changing with some independent parameter and the same is true with complex functions/variables.
HI Christopher. Love all your lectures. Can you please upload the remaining videos on ardupilot! A lot of people are really looking forward to it! If you cant put in a video, can you please at least share some slides or lecture notes here?
AE 501. Overall very helpful! 1 comment, a few of the equations at the top of the board get cut off when you are explaining multiplication and division.
Hi John, do you have a timestamp of when this occurs? I usually try to setup the camera to cover the whole board but I may have missed something. Please let me know if you notice anything odd like this in the future, thanks!
AE501: Never once have a I heard why poles are named the way they are! Also, thinking about a transfer function as a type of complex function is new to me.
Haha, yes, keep your eyes out for them as I've got a few more math jokes sprinkled around the lectures. Also be in the look out for my dog as he'll make a few appearances soon.
In case it is helpful, here are all my ODE videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrHHvoFPxWq4l9D93jkCNIFN.html. Please let me know what you think in the comments. Thanks for watching!
AE501: The crickets at 11:28 were hilarious lmaoo. Thank you for a great refresher video professor!
AE501: Thank you for this great video! The Eulers formula exaplanation was straightforward and easy to follow!
Bring on the math jokes! I appreciate the fun you add to these videos. This video does a nice job demystifying jargon I saw in my controls classes and Diffeq classes. Thanks again!
Glad you like them, I've got a few other math jokes up my sleeve so be on the lookout for more corny jokes in future videos.
AE 501: Great review of complex variables! I really like the graphical representations of the complex vectors
AE501: That imaginary number telephone joke definitely landed with me. Thanks for the review on complex numbers and complex functions!
Glad you enjoyed the joke!
AE501: This was a great review on complex numbers and complex variables! A lot of this information was foreign to me but well explained
AE501: Great refresher to understanding the relations of complex operations as well as back to basics with Euler's, super useful and goes a long way!
[AE501] 54:11
I like that you are very explicit in your derivations and explanations. It makes it easier to follow. I also like the visualization of the complex numbers in a 2d plot, it helps make an abstract concept a bit more tangible.
AE501: Much need refresher! Thanks for the great review!
Complex numbers/variables/functions don't seem quite so complex anymore - very easy to understand thanks to this video!
AE501: This is a very excellent explanation on complex numbers. Thank you, Professor!
I dont understand the joke but it was quite good. You can understand if an instructor really knows about the topic they tell by how simple the explanations are. He explains the topic like it is a simple thing to understand, so get it. Liked it very much :)
Hi Turku,
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
[AE501] It's great to see when a professor's humor comes through in lectures, makes it entertaining!
AE501: Great explanation of Euler's formula
AE501: Quick review of complex numbers and I like the math joke. Thanks for keeping me interested in learning.
I'm glad you enjoyed the math joke!
AE 501. this video helps me to refresh Complex numbers concept which between Imaginary and Real. if we can learn more about how to solve example problem use Matlab or Mathematica, it will be great. However, the video is great explanation and clear for me. thank you Chris
AE501: Hey Chris! I really liked your explanation of poles! It was a great visual to think about it sticking out of the board like a pole!
AE501. Thanks, Dr.Lum for these videos, very easy to follow. Great explanations.
AE501: "Read the fine manual" hahaha. very helpful, it summarizes complex numbers. it was refreshing for me at least, looking forward to Laplace Transform.
Professor Lum/AE501,
I think it would’ve helped me out personally if the video had started out with maybe a quick reason of why I care about Euler’s formula. For example: in the previous ODE video, if I recall correctly you quickly showed what an ODE was and how it might be used. THEN went into more complex topics and derivation. I have spent a good portion of this video so far trying to figure out why I need to care about Euler and am over halfway through. I’m sure you’ll get there eventually... just some feedback for those who think like me.
Seth, thanks for the feedback, you make a very good point. To answer your question, the reason we need Euler's Formula is that we'll use it down the road when working with underdamped/oscillatory systems which introduce sin/cos terms. Just hang on for 1 or 2 more videos and hopefully it will become clear why we need it.
AE 501. Thanks again for this tutorial. A great refresher on the topic of complex numbers.
AE501: Great explanation of poles and simple zeros at the end of the video.
AE501: Great fresher on complex numbers and Euler’s Theorem.
Thanks for these videos, very easy to follow. Great explanations sir.
I'm glad it was helpful. There are several related videos on the channel. Please feel free to check them out and I would love to hear what you think in the comments. Thanks for watching!
AE501 Student Good discussion on complex variables, complex numbers, Euler's equation, complex conjugates and complex algebra. Looks to be good applications coming up in future videos.
AE501. Another great review video. Imaginary numbers are definitely interesting to imagine about.. I've always thought it was also interesting that one could write out sin and cos in a summation. Great explanation on how complex numbers can be mathematically manipulated.
AE 501. Hi Chris, at time 51:46 you explain that for a pole the function comes out of the page. Maybe I missed it but I am having trouble understanding what this third dimension is on the real and complex plane. Also, does this mean that for the zeros the function is on the plane? I am sure I am misunderstanding something. By the way, this is Austin, I just realized my account name doesn't match.
AE501: Thanks for the review on Euler's Theorem!
Good refresher on complex numbers, and thanks for the warning on not using i and j as counters in MatLab!
AE501: Thank you for the video. Easy to follow and understand.
AE501: Good review of Euler's theorem as well as Complex Functions!
[AE501]
I like the energy you bring to your lectures, makes them a lot more engaging.
Great Video, to the point and explains it in very informative way.
So so oxm oxm lectures thank you sir for giving us time and we needs more lectures.
Good refresher on complex numbers
AE501 - thank you for the clear explanations.
AE501: Good class and review.
[AE 501 JENNIFER JOHNSON] This video so far is answering some questions I had prior to watching.
AE501: Arda Cetken. Video is 5 years old when I'm watching... Good thing Math doesn't change!
AE501, I enjoy the joke. it makes the lesson more enjoyable!
Great coverage of the various complex concepts.
Hi Uncle Chris awesome video it’s me Ethan & Maddy I learned a lot thanks remember calming background music 👌👌😀
Hi guys, thanks for watching! Did you check out my video on the van? I'm going to be putting a lot more adventure van videos up soon!
AE 501 At around 19:10, how do you get the i on the cos portion of the equation? Also, should the signs be alternating for both the real and imaginary portions?
Ryan, I'm not sure i understand the question, can you provide more exposition?
@@ChristopherLum I guess I don't see how the "i" from the cos(theta)+sin(theta)i (around 19:10 in the video) gets distributed to the cos(theta) portion of the equation. Not sure if that helps or not.
Thank you for the post
This help me to refreser about complex numbers.
Thanks
Sam
I forgot about Euler's theorem, so this video was a great review of this topic.
AE501: A good review on complex function, I hope it does not get too complex because 'i' can't be in an complex space :)
AE501
Chris, in your version of polar notation that doesn't use e^jtheta, but z
Ben, let's chat a bit at office hours, it is probably easier given the details of this particular question.
@@ChristopherLum Sounds good, Chris! I'll be there on Monday.
AE501 So just to clarify, for powers and roots formulas, the thetas have to be in radians? The choice between positive or negative theta in those formulas shouldn't matter right?
Correct on both accounts
Thank you so much!!!
Hi,
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 or via the 'Thanks' button underneath the video. 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. I can also answer any questions, provide code, notes, downloads, etc. on Patreon. Thanks for watching!
-Chris
AE 501. Great video on complex numbers but I guess I'm a little confused towards the end about complex functions/poles. It was still a little tricky understanding at poles F(s) is infinity and therefore sticks out of the plane. Its almost like F(s) acts like a z value (on a real plane) and sticks out of the page, but how does that pertain to the complex plane? I really think a 3D plot of a complex function would be helpful to visualize, because for most of the video I was thinking in 2D until you introduced F(s).
Zane, sorry, I realized the motion I made seemed to imply that poles stick out of the plane but this isn't really a useful way to think of it. Just think of poles as values of s that lead to the function F(s) going to infinity.
[AE 501] loved the math joke!!🤣
Buckle up, I've got a few more coming up :)
AE501: Very useful video in doing homework problem 1. I was not familar with the method of writing complex functions in terms of zeros, poles, and gain. -Natalia Ermolaeva
AE501 Good refresher on handling components of complex numbers.
AE501: petition for a dedicated video just for math jokes!
Buckle up, I've got a few more coming up :)
Great refresher!
Is the pole just a pulse in signal procession. Great discussion. Enjoyed the video. (AE501)
Great video as per usual!
Thanks for the helpful video!
I love his explanations...The maths joke though😂...
Hi,
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!
-Chris
thank you for sharing. So, what’s the Complex plane? what’s means of z=x+iy? what’s its physics means?
AE501: Professor Lum, thank you for the helpful video. If complex numbers can be represented on a plane, can the idea of a graphic representation be extended to complex functions? While it's easy to imagine functions like y = x, it's not very easy to imagine y = s where s might be a complex variable. Not sure if this is a legitimate question, but I just had this thought as I watching the last part of your video. Thanks!
Karina, that is a good observation. Yes, you can think of complex functions in the same fashion as you think of vector functions. With vector functions, the vector might be changing with some independent parameter and the same is true with complex functions/variables.
HI Christopher. Love all your lectures. Can you please upload the remaining videos on ardupilot! A lot of people are really looking forward to it! If you cant put in a video, can you please at least share some slides or lecture notes here?
Great video
I definitely appreciate the math jokes
I'm glad to hear that because I have a bunch 🙂
Hello Doctor, I need this lecture in PDF format
AE 501. Overall very helpful! 1 comment, a few of the equations at the top of the board get cut off when you are explaining multiplication and division.
Hi John, do you have a timestamp of when this occurs? I usually try to setup the camera to cover the whole board but I may have missed something. Please let me know if you notice anything odd like this in the future, thanks!
@@ChristopherLum i watched it again and nothing was cut off. Something must have been messed up on my computer last night.
finally understand eulers theorem!
AE501: Never once have a I heard why poles are named the way they are! Also, thinking about a transfer function as a type of complex function is new to me.
[AE501] I'm going to need at least one math joke section in every video going forward 😂
Haha, yes, keep your eyes out for them as I've got a few more math jokes sprinkled around the lectures. Also be in the look out for my dog as he'll make a few appearances soon.
AE501 Great Video
Loved the joke : )
Thanks for watching!
nice vid prof lum
how imaginary number i is square root -1, how to think it
AE511: I studied in last year for AE501.
ae501 for problem 1! hw2
AE 501 - Malachi Morris
AE501, Cody Smith
AE 501 Bryce Foland
[A E 501 student] watched - CW
AE501
Talking to the board.....