In case it is helpful, here are all my calculus videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE.html. All my control theory videos are at ua-cam.com/play/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o.html . You can support this channel via Patreon at www.patreon.com/christopherwlum or by clicking on the 'Thanks' button underneath the video. Please let me know what you think in the comments. Thanks for watching!
AE 512: You made the Jacobian a lot simpler to understand, especially with the point that it's basically just multiple gradients stacked on top of each other. Thanks.
Yep, just a matrix of gradients…as a simplification. And it is used outside (traditional) engineering 😮 in economics too! I have used it in credit scoring! Then obviously in machine learning…
AE501: Learning that the Jacobian was the total sensitivity of all possible outputs was completely new to me. I never knew the true applications of a Jacobian, it was so abstract before.. Thank you!
AE501 This is the most clear explanation of the Jacobian I have ever heard. I knew what it was mathematically, but conceptually I was never sure what it was used for or "means". Thank you!
I'm glad it was helpful. I have several related videos on the channel, please feel free to check them out and let me know what you think. Thanks for watching!
What a video abput Jacobian matrix. I have been searching a simple explanation for this topic. But I found more than what I have been searching for. Everyone can understand what you are teaching without getting into a stuck. Thank you Christoper Lum
Professor Lum, I am not saying this for any other reason than you deserve praise for how well you teach. I am sure that you were born just about the time that I received my BSEE but if at that time, my teachers had been able to explain the material that you teach (aerodynamics, calculus, vector calculus, etc.) as well as you teach it, then I think that I would really have learned it!
Thanks for the kind words, I'm glad you find the videos engaging and interesting. Please let me know if you have any thoughts or feedback on any of these topics or if you have suggestions for future content. Thanks for watching!
@@ChristopherLum Hi Professor, I do have some suggestions as to future content and I am a patrion member. Having watched this video to the end, I caught where you said that you were going to approach machine learning from a control systems point of view (neural networks). I am looking forward to this. About two years ago, I took my first step in the direction of machine learning with a video that I made concerning Augmented Reality, and here is the link. ua-cam.com/video/XKi0TFinFhg/v-deo.html . I used a fairly generic software algorithm at the time called YOLO (you only look once). I look forward to a deeper understanding of the back propogation path which I am sure that you will show in terms of neural networks, which is a level "deeper" than machine learning.Training the algorithm took about two days...could have been better but I had had enough. At present, I am learning Python for DSP applications, which one could just call mathematical python. Most of machine learning, other than those that program their GPU's in CUDA are done in Python. BTW, my first programming language that I learned as an EE was Fortran, which I programmed with "punch cards", which, was kind of a nightmare. I also did a video, when I was getting my A&P on explaining why a propeller needs a twist, which you can see here. ua-cam.com/video/ohcwMSK_Yfs/v-deo.html. That was done in Solidworks. Looking forward to these lectures.
@@theminertom11551 Tom, thanks for the detailed discussion. I watched your video on the smart glasses, that is pretty cool! I'm actually surprised that you had to program this yourself. Did the glasses not come with an API that enables this functionality natively? Thanks for following up on Patreon as I just discovered that because we're having this discussion on a thread of a comment in which I already responded to earlier, UA-cam doesn't notify me when subsequent posts/discussions are made.
Love coming upon amazing lectures like Christopher Lum. Clearly explaining concepts with images included and also in an engaging manner. Keep up the good work. Look forward to watching more videos!
AE 501: Might be unrelated, but I wonder if the "Jacobian Quality" when discussing mesh quality in a fea analysis has anything to do with this lecture..... I know that solidworks uses this as one of the values to evaluate your mesh.
Haha, I know it seems unfair :) I had the same question so I did some digging to try and find his history. Checkout timestamp 23:00 for some discussion/background.
In case it is helpful, here are all my calculus videos in a single playlist ua-cam.com/play/PLxdnSsBqCrrGHwNWnP5XVhytcGL9ExuPE.html. All my control theory videos are at ua-cam.com/play/PLxdnSsBqCrrF9KOQRB9ByfB0EUMwnLO9o.html . You can support this channel via Patreon at www.patreon.com/christopherwlum or by clicking on the 'Thanks' button underneath the video. Please let me know what you think in the comments. Thanks for watching!
Thank you so much!
AE 512: You made the Jacobian a lot simpler to understand, especially with the point that it's basically just multiple gradients stacked on top of each other. Thanks.
Yep, just a matrix of gradients…as a simplification.
And it is used outside (traditional) engineering 😮 in economics too!
I have used it in credit scoring!
Then obviously in machine learning…
Multi variable calculus is the subject to study
This is a very well timed video for my graduation project which is designing 6DoF robotic manipulator. Thank you Dr. Lum. 🥳
AE501: Learning that the Jacobian was the total sensitivity of all possible outputs was completely new to me. I never knew the true applications of a Jacobian, it was so abstract before.. Thank you!
AE501: Great refresher on the Jacobian matrix. The examples really helped me here.
I'm happy the Jacobian matrix review was useful!
AE 501: It was super interesting to see how the Jacobian matrix can be implemented in knowing the sensitivity in dynamic systems!
AE501 This is the most clear explanation of the Jacobian I have ever heard. I knew what it was mathematically, but conceptually I was never sure what it was used for or "means". Thank you!
Glad you found the conceptual explanation helpful!
Please dear professor never stop doing this invaluable video-lectures. Also can't wait for your Kalman filters & Pontryagin's max principle lectures
AE501: It's nice to finally be able to connect the Jacobian to a less abstract concept for me. Thanks for this explanation!
This is probably one of the best mathematical tutorial i have ever came across! Thanks for your efforts @ChristopherLum
I'm glad it was helpful. I have several related videos on the channel, please feel free to check them out and let me know what you think. Thanks for watching!
What a video abput Jacobian matrix. I have been searching a simple explanation for this topic. But I found more than what I have been searching for. Everyone can understand what you are teaching without getting into a stuck. Thank you Christoper Lum
Professor Lum, I am not saying this for any other reason than you deserve praise for how well you teach. I am sure that you were born just about the time that I received my BSEE but if at that time, my teachers had been able to explain the material that you teach (aerodynamics, calculus, vector calculus, etc.) as well as you teach it, then I think that I would really have learned it!
Thanks for the kind words, I'm glad you find the videos engaging and interesting. Please let me know if you have any thoughts or feedback on any of these topics or if you have suggestions for future content. Thanks for watching!
@@ChristopherLum Hi Professor, I do have some suggestions as to future content and I am a patrion member. Having watched this video to the end, I caught where you said that you were going to approach machine learning from a control systems point of view (neural networks). I am looking forward to this. About two years ago, I took my first step in the direction of machine learning with a video that I made concerning Augmented Reality, and here is the link. ua-cam.com/video/XKi0TFinFhg/v-deo.html . I used a fairly generic software algorithm at the time called YOLO (you only look once). I look forward to a deeper understanding of the back propogation path which I am sure that you will show in terms of neural networks, which is a level "deeper" than machine learning.Training the algorithm took about two days...could have been better but I had had enough. At present, I am learning Python for DSP applications, which one could just call mathematical python. Most of machine learning, other than those that program their GPU's in CUDA are done in Python. BTW, my first programming language that I learned as an EE was Fortran, which I programmed with "punch cards", which, was kind of a nightmare. I also did a video, when I was getting my A&P on explaining why a propeller needs a twist, which you can see here. ua-cam.com/video/ohcwMSK_Yfs/v-deo.html. That was done in Solidworks. Looking forward to these lectures.
@@theminertom11551 Tom, thanks for the detailed discussion. I watched your video on the smart glasses, that is pretty cool! I'm actually surprised that you had to program this yourself. Did the glasses not come with an API that enables this functionality natively? Thanks for following up on Patreon as I just discovered that because we're having this discussion on a thread of a comment in which I already responded to earlier, UA-cam doesn't notify me when subsequent posts/discussions are made.
AE 512: Showing how this all connects with higher order topics like neural networks was eye opening, thank you!
AE501 : A good crawl-walk-run approach from the derivative to gradient vector to jacobian matrix
Great review of this stuff for me. I haven't dealt with Jacobians in a very long time....
Love coming upon amazing lectures like Christopher Lum. Clearly explaining concepts with images included and also in an engaging manner. Keep up the good work. Look forward to watching more videos!
Awesome stuff once again Dr Lum, thank you so much.
Great to hear from you Wil, glad you enjoyed it!
i havent watched the video yet but i know itll be another banger thanks bro
AE512: Watching this video as a refresher was the right choice :)
I'm glad it was helpful! Keep me posted on how the linearization code goes.
Thank you so much for these videos, i really enjoy every single video you have on your channel its very useful and informative, thank you sir.
AE 501 Thanks for the information!
Thanks for the video. Great explanation of a Jacobian Matrix. :)
Amazing explanation, appreciate it
Great overview.
AE50`: First time I have had the Jacobian explained.
Extremely well done, thank you! 🙂
AE 501: Might be unrelated, but I wonder if the "Jacobian Quality" when discussing mesh quality in a fea analysis has anything to do with this lecture..... I know that solidworks uses this as one of the values to evaluate your mesh.
I use arrow instead of bar to denote vector. It is same thing right ?
It’s already 6 months, where’s the chain rule video?
Jason-AE512: Even though this is a optional video, but I still learn a lot.
AE 501: Bryce Foland
AE501, Cody Smith.
AE501: Arda Cetken - Who's Jacob and why does he get his own Matrix?
Haha, I know it seems unfair :) I had the same question so I did some digging to try and find his history. Checkout timestamp 23:00 for some discussion/background.
AE501 - Malachi Morris
[A E 501 student] watched - CW
amaIng!
Thank you so much Dr
Aasome videoooo.
Bagi skrip manimnya bang
TY つ ◕_◕༽つ
Just wastage of time. Where is the intuition behind Jacobian matrix ? Just a rubbish content !!!
not his fault you're too slow to figure it out