I have a differential equations final in 18 minutes. You just explained this better than 2 TAs and 2 Professors managed to in all of my time studying. Bless you bless you bless you.
By far the best video on the topic I could find on the internet. I watched this when I was learning it, and now that I'm reviewing for my final tomorrow I spent a good chunk of time searching for this video specifically just because of how good it is. Thank you so much
here is a wonderful tip to make your life easier: the matrix will be spiraling counter clockwise if the lower left value of the matrix is positive, and clockwise if it is negative.
Another way to remember if it'll spin clockwise or counterclockwise with positive/negative numbers there: Think of the unit circle. Counterclockwise is positive direction around, and clockwise is the negative direction around.
@@Christian-qh5zu it is related to "twist" or "shear". You know, A12 and A21 determine how a vector is twisted with respect to A12 and A21. If A12 is larger than A21 (meaning you stretch the vector "longer" in x-direction than in y-direction) what happens next is, the vector will be twisted/sheared clockwise. However, this is a special case where both A12 and A21 are positive. Can you imagine? Think of it as a parallelogram. Actually, the more formal way to define it is, if A21 - A12 < 0 then the direction is clockwise, and if A21 - A12 > 0 then the direction is counter-clockwise.
My textbook is abominable at describing phase portraits, they just list one example for each phase portrait as their solving a system, not even bold letters to help the reader. I was hoping they would have an appendix page if they were saving on space but not even that.
Given its the season of covid, I really appreciate this. I tried to get help from my professor on our forum board but got told to rewatch the lecture. If I understood the lecture I wouldn't need to ask for help!
Thanks for this wonderful lesson. Thanks for what you do. If I may ask ,if possible can you please post a video in which you can teach us how to draw the phase portraits for "NON LINEAR SYSTEMS"?
Ellie, you are amazing. Thank you so much for this video. You made this SO much simpler than my instructor could. I'm doing well in my Differential Equations and Linear Algebra course because of people like you. You rock.
For eigenvalues that are distinct but both positive or both negative, it can be hard to remember because we may start away from the origin or start at the origin. I realize now that either way, we begin parallel to the eigenvector with the smaller eigenvalue, then as the trajectory goes toward the origin or gets further away from it, we curve in the direction of the eigenvector with the larger eigenvalue. Then for repeated eigenvalues that have an improper node, we need a test point to plug into the system to determine the orientation of the trajectories being drawn away from or toward the origin. I don't see any difficulty with the purely imaginary or complex eigenvalues. It's funny how those are more clear. Thank you for clarifying all this.
Wonderful explanation and much simpler than what I have been taught by my lecturer.
Not all heroes wear capes! Unless you're wearing a cape, are you?
she is, and does. Regularly in fact
I have a differential equations final in 18 minutes. You just explained this better than 2 TAs and 2 Professors managed to in all of my time studying. Bless you bless you bless you.
How was it
@emilgormus1556 I've since graduated so nott too bad evidently.
By far the best video on the topic I could find on the internet. I watched this when I was learning it, and now that I'm reviewing for my final tomorrow I spent a good chunk of time searching for this video specifically just because of how good it is. Thank you so much
here is a wonderful tip to make your life easier: the matrix will be spiraling counter clockwise if the lower left value of the matrix is positive, and clockwise if it is negative.
Nice one. Thanks.
What matrix are u talking about the original one or the one generated by the Eigenvector
@@ahmedtaha7348 The original matrix, that is to say "A"
Another way to remember if it'll spin clockwise or counterclockwise with positive/negative numbers there: Think of the unit circle. Counterclockwise is positive direction around, and clockwise is the negative direction around.
Why does this work?
this saved my ass
About to save mine
even for all who are in the situation to fill papers.
Yessss Lecturer aint gonna rape my ass today!!
Daaamn that's me bro, tomorrow it's this frickin exam and I finally got it
I think it just saved my ass too. I have an exam in an hour lol
You can easily know if its clockwise or counter clockwise by observing the the matrix A , if the element A21>A12 so it''s counter clockwise and if A21
That is really cool and time saving for the exam, thank you!
Can you explain why this works?
@@Christian-qh5zu No
@@Christian-qh5zu it is related to "twist" or "shear". You know, A12 and A21 determine how a vector is twisted with respect to A12 and A21.
If A12 is larger than A21 (meaning you stretch the vector "longer" in x-direction than in y-direction) what happens next is, the vector will be twisted/sheared clockwise. However, this is a special case where both A12 and A21 are positive.
Can you imagine? Think of it as a parallelogram.
Actually, the more formal way to define it is, if A21 - A12 < 0 then the direction is clockwise, and if A21 - A12 > 0 then the direction is counter-clockwise.
@@peanutbutterjelly2188 thanks
Exam in two days including this little bit and you just explained it so simply and plainly. Thanks a lot Ellie :)
take a bow professor!, not many professors can share knowledge in such a lucid manner. Thank you.
Best explanation of phase portraits I've seen online, great video
YOU ARE AMAZING!!! FROM AN ENGINEER AT UCLA, this topic was confusing, but your video made everything clear! THANKS
Studied all day to find out how to sketch these portraits and you explained so well thank you. Im glad I found your video or I would still be lost.
Thank you for showing all the different types of phase portraits!! Super helpful!
thank you! this is so much more simpler and easier to understand than just reading textbooks/listening to lecturers. Keep sharing your gift!
This is genuinely the best video on the internet thank you so much this has saved me immensely
just perfect 🤍
You've made it so much simpler, now I get it. Thank you!
way better than my professor
My textbook is abominable at describing phase portraits, they just list one example for each phase portrait as their solving a system, not even bold letters to help the reader. I was hoping they would have an appendix page if they were saving on space but not even that.
You are the boss on this topics
This is the best thing ever you are a hero you are a hero of my people
Hands down.....
best video. I've watched it multiple times while studying for my Diff Eq final
Mam i am really greatful to you!
This is godsend. Thank you. I was breaking down in the middle of the night lol. So happy I found this
this is the most clear explanation of phase potraits ive encountered thank you!
Excellent video with comprehensive explanation, such a life saver
The best video on this topic. I return to it all the time. Thank you so much!
this was actually one of the best DE videos on this topic i've found
very clear
one of the best explanation
Thank you miss Blair. you saved my scholarship in college
you presented in a very organized fashion. It was very helpful
Given its the season of covid, I really appreciate this. I tried to get help from my professor on our forum board but got told to rewatch the lecture. If I understood the lecture I wouldn't need to ask for help!
You just saved me. Thank you
Best explanation of phase diagram.
Just wonderful and very much helpful.thanks.
Thanks for this wonderful lesson. Thanks for what you do. If I may ask ,if possible can you please post a video in which you can teach us how to draw the phase portraits for "NON LINEAR SYSTEMS"?
Thanks Madam...Awesome. I like your explanation
amazingly simple explanation
At 16:55 the spiral should be counterclockwise,as the -2 down to -3 shows anti-clockwise sign and rest is fine...these lectures are treat to watch!!!!
outstanding explanation .. Thanks
awesome explanation.loved it
I spent an entire day studying on the materials of my lecturer, yet the answer was just a 20 minute video. I thank you so much
So clearly explanation
Thank you so much
The best procedure on the internet! well structured
Oh my god! You are amazing, thank you so much!
Seriously amazing. I learned more in those twenty minutes than I have in the last 4 weeks of class!
Didi bahut mazza aaya, dhanyavaad
Thank you for this clear and understandable vidio
really, no doubt best one lecture
Excellent explanation mam !!
Very useful.
you cannot explain sketching phase portrait in a simpler manner than this.Thank you so much.
Thanks for a wonderful explanation.
So simple 🤩🤩
Been having a hard time understanding these in class. Thanks a lot this really helped.
Opp ❤ nicely explained I understand pleaee upload more concept
Very clearly explained. Thank you so much.
Great video, super thorough/explains everything
What would happen if an eigenvalue was zero?
Thanks for the video
This was so clear and easy to follow. I am indebted to you forever.
Amazing explanation!! Thank you
such a good explanation
This was SUPER helpful. Excellent upload. Thank you.
OH MY GOD thank you so MUCH I have a midterm today and I didn't have time to study this portion last night
Wow
This is really good
You are the best
Wow you're amazing at explaining things
13:28 how did she conclude the direction? like how did she decide its gonna be counter clockwise?
I didn't search for this video, but I needed it. Thanks algorithm.
You are awesome. Thanks so much for posting this.
Splendidly explained you literally are the best ma'am.
Absolutely !
Ellie, you are amazing. Thank you so much for this video. You made this SO much simpler than my instructor could. I'm doing well in my Differential Equations and Linear Algebra course because of people like you. You rock.
very well explained video. It was a great help. thankyou. From INDIA
Thank you so much you made this sketching so simple
Thank you so much! Much better than my trash textbook and lame professor.
Thankyou.. Clear and wonderful explanation..
You are amazing, loved the way you made it so easy. Thank you so much
amazing explanation! such a simple way to teach differential eqns
thnak you for this wonderful explanations, you rescued a lot of people, and drew smiles on each one of us !
Amazing! Didn't understand my teacher explanation, with this video i already understood all! Thank you!
Excellent lesson. Many thanks
this is the best lecture on the topic I can finally understand I love this I love you love love love
WOW this suddenly makes sense after being confused for so long! thank you so much
Thanks for sharing this video. :)
Fantastic!
great explanation
Best explanation ever
God bless you
Just wow
This video is amazing and the best explanation I've gotten on the topic, thank you!
You are the best!!!
Excellent video - thank you.
Thank you very much, i watched other lectures but cannot understand, this video is very helpful. Now i understand all the cases easily, Thank you!!!!
Probably the best video I've watched on this concept! Thank you for this x
For eigenvalues that are distinct but both positive or both negative, it can be hard to remember because we may start away from the origin or start at the origin. I realize now that either way, we begin parallel to the eigenvector with the smaller eigenvalue, then as the trajectory goes toward the origin or gets further away from it, we curve in the direction of the eigenvector with the larger eigenvalue. Then for repeated eigenvalues that have an improper node, we need a test point to plug into the system to determine the orientation of the trajectories being drawn away from or toward the origin. I don't see any difficulty with the purely imaginary or complex eigenvalues. It's funny how those are more clear. Thank you for clarifying all this.
This is the best explanation on the web!
amazing video! my professor explains it terribly 🤮🤮 thank you so much!!
Excellent explanation!!! Thanks a lot!!!
I have a test tomorrow and this video made so many puzzle pieces fall in to place! Thank you for making this.
I really appreciate this....now I can draw the phase diagrams.....
thank you very much madam.. followed your video along with sketching by myself along and had a pretty good understanding at the end..😇😊😊
Ellie Blair, thank you for sharing your knowledge!! You're amazing
Thank you so much. This is the best explanation I’ve seen so far!