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.
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.
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
@@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.
The video is really informative, precise to the point and really easy to understand! Thanks a lot for this, definitely one of the best ones on plotting phase plots by far! Keep up the good work :D
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"?
Ma'am, you just explained it so well 💯. I was struggling the whole day just to understand one problem given in strogartz . This video helped me a lot . Thank you ma'am ❤️
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!
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.
Not all heroes wear capes! Unless you're wearing a cape, are you?
she is, and does. Regularly in fact
Wonderful explanation and much simpler than what I have been taught by my lecturer.
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.
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?
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
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
Exam in two days including this little bit and you just explained it so simply and plainly. Thanks a lot Ellie :)
Thank you for showing all the different types of phase portraits!! Super helpful!
Best explanation of phase portraits I've seen online, great video
take a bow professor!, not many professors can share knowledge in such a lucid manner. Thank you.
this was actually one of the best DE videos on this topic i've found
This is genuinely the best video on the internet thank you so much this has saved me immensely
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 the best thing ever you are a hero you are a hero of my people
You've made it so much simpler, now I get it. Thank you!
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.
Oh my god! You are amazing, thank you so much!
Hands down.....
best video. I've watched it multiple times while studying for my Diff Eq final
This is godsend. Thank you. I was breaking down in the middle of the night lol. So happy I found this
YOU ARE AMAZING!!! FROM AN ENGINEER AT UCLA, this topic was confusing, but your video made everything clear! THANKS
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
this is the most clear explanation of phase potraits ive encountered thank you!
WOW this suddenly makes sense after being confused for so long! thank you so much
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
The best video on this topic. I return to it all the time. Thank you so much!
you cannot explain sketching phase portrait in a simpler manner than this.Thank you so much.
The video is really informative, precise to the point and really easy to understand! Thanks a lot for this, definitely one of the best ones on plotting phase plots by far! Keep up the good work :D
Probably the best video I've watched on this concept! Thank you for this x
Excellent video with comprehensive explanation, such a life saver
This was SUPER helpful. Excellent upload. Thank you.
Oh my gosh thank you so much!! Very informative! I would be so much further in life if every teacher I ever had was like you!
You are amazing, loved the way you made it so easy. Thank you so much
You are awesome. Thanks so much for posting this.
Ellie Blair, thank you for sharing your knowledge!! You're amazing
I have a test tomorrow and this video made so many puzzle pieces fall in to place! Thank you for making this.
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"?
This was so clear and easy to follow. I am indebted to you forever.
Thanks for a wonderful explanation.
So simple 🤩🤩
just perfect 🤍
This video is amazing and the best explanation I've gotten on the topic, thank you!
awesome explanation.loved it
Been having a hard time understanding these in class. Thanks a lot this really helped.
Ma'am, you just explained it so well 💯. I was struggling the whole day just to understand one problem given in strogartz . This video helped me a lot . Thank you ma'am ❤️
Really great explanation! Easy to understand and includes all the possibilities may occurs.
thnak you for this wonderful explanations, you rescued a lot of people, and drew smiles on each one of us !
Thank for your effort. A very concrete and well structured lesson!
Nice, simple and straight to the point! Thanks a lot for the help.
Thanks Madam...Awesome. I like your explanation
Thank you! Your explanation is very clear as well. This helps me a lot.
Lifesaver!!!!! THANK YOU!
really, no doubt best one lecture
very clear
one of the best explanation
you presented in a very organized fashion. It was very helpful
Amazing explanation!! Thank you
amazingly simple explanation
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!
Wow you're amazing at explaining things
amazing explanation! such a simple way to teach differential eqns
Excellent explanation mam !!
Very useful.
You just saved a life. Thanks and I love you!
way thorough than my lecturer explained, Thank you so much.
I love this explanation Ellie. It is really good
The best procedure on the internet! well structured
I cannot thank you enough this video was amazing
life saver, much appreciation from Math 216 gang here in Ann Arbor!!!
Thank you so much you made this sketching so simple
Great video, super thorough/explains everything
Seriously amazing. I learned more in those twenty minutes than I have in the last 4 weeks of class!
You are the best!!!
Just wonderful and very much helpful.thanks.
your are the best! you were born to teach
such a good explanation
Didi bahut mazza aaya, dhanyavaad
very well explained video. It was a great help. thankyou. From INDIA
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.
Great video. Much easier to understand and apply. Thank you so much.
So clearly explanation
Thank you so much
Lifesaver ig, no words😌
Awesome and straight to the point, great vid
I've watched this so many times already (preparing for my exam) , I think it's my favourite video on UA-cam now haha
Very clearly explained. Thank you so much.
You are the boss on this topics
Love you Ma'am.. You made it so easy :-)
OH MY GOD thank you so MUCH I have a midterm today and I didn't have time to study this portion last night
HOLY MOLY THIS IS AMAZING....THANK YOU SO MUCH!!
Thank you so much. This is the best explanation I’ve seen so far!
Thankyou.. Clear and wonderful explanation..
This video is fkn so wonderful, u wont regret to watch this
You're amazing! Super helpful. Thank you so much!
This is so helpful. I had trouble drawing solution curves but your explanation really helped me!
Splendidly explained you literally are the best ma'am.
Absolutely !
Great! Way simpler and more intuitive than how I was taught.
Mam i am really greatful to you!
U are amazing I cannot thank you enough
Very well explained, helped me a lot with my exam. Thanks!
Best explanation of phase diagram.
Thanku miss!! Nicely explained..
Lifesaver!
Thank you for this clear and understandable vidio
Perfect, greetings from Peru!