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"?
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.
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!
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.
Not only this video helped me, the comments section was helpful too, that easy trick about focii being clockwise or anticlockwise was amazing! Thank you everyone 😍
![[LIVE] : ONE ลุมพินี 68 | คู่เอก "พระจันทร์ฉาย vs โจนาธาน"](http://i.ytimg.com/vi/F3IM3w-XchI/mqdefault.jpg)
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?
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
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
Thank you for showing all the different types of phase portraits!! Super helpful!
Exam in two days including this little bit and you just explained it so simply and plainly. Thanks a lot Ellie :)
Best explanation of phase portraits I've seen online, great video
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 was actually one of the best DE videos on this topic i've found
You've made it so much simpler, now I get it. Thank you!
take a bow professor!, not many professors can share knowledge in such a lucid manner. Thank 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 best thing ever you are a hero you are a hero of my people
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.
this is the most clear explanation of phase potraits ive encountered thank you!
Oh my god! You are amazing, thank you so much!
Probably the best video I've watched on this concept! Thank you for this x
WOW this suddenly makes sense after being confused for so long! thank you so much
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
Hands down.....
best video. I've watched it multiple times while studying for my Diff Eq final
YOU ARE AMAZING!!! FROM AN ENGINEER AT UCLA, this topic was confusing, but your video made everything clear! THANKS
The best video on this topic. I return to it all the time. Thank you so much!
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!
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
I have a test tomorrow and this video made so many puzzle pieces fall in to place! Thank you for making this.
you cannot explain sketching phase portrait in a simpler manner than this.Thank you so much.
Been having a hard time understanding these in class. Thanks a lot this really helped.
You are amazing, loved the way you made it so easy. Thank you so much
This was SUPER helpful. Excellent upload. Thank you.
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
You just saved a life. Thanks and I love you!
This video is amazing and the best explanation I've gotten on the topic, thank you!
Ellie Blair, thank you for sharing your knowledge!! You're amazing
Excellent video with comprehensive explanation, such a life saver
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"?
Thank you! Your explanation is very clear as well. This helps me a lot.
thnak you for this wonderful explanations, you rescued a lot of people, and drew smiles on each one of us !
Nice, simple and straight to the point! Thanks a lot for the help.
This was so clear and easy to follow. I am indebted to you forever.
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.
Thank for your effort. A very concrete and well structured lesson!
This is so helpful. I had trouble drawing solution curves but your explanation really helped me!
Thank you so much. This is the best explanation I’ve seen so far!
Seriously amazing. I learned more in those twenty minutes than I have in the last 4 weeks of class!
The best procedure on the internet! well structured
You are awesome. Thanks so much for posting this.
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!
HOLY MOLY THIS IS AMAZING....THANK YOU SO MUCH!!
way thorough than my lecturer explained, Thank you so much.
This video is fkn so wonderful, u wont regret to watch this
This saved my life the day before my final. Thank you so much. Your literally superwoman!
You're amazing! Super helpful. Thank you so much!
Great! Way simpler and more intuitive than how I was taught.
Thanks for a wonderful explanation.
So simple 🤩🤩
your are the best! you were born to teach
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.
OH MY GOD thank you so MUCH I have a midterm today and I didn't have time to study this portion last night
Really great explanation! Easy to understand and includes all the possibilities may occurs.
Have a midterm on this in less than 4 hours. Glad I found this ! =]
THANK YOU FOR SAVING MY LIFE!!!!
I've watched this so many times already (preparing for my exam) , I think it's my favourite video on TH-cam now haha
Love you Ma'am.. You made it so easy :-)
*this video came into my life at the right time*
I cannot thank you enough this video was amazing
Lifesaver!!!!! THANK YOU!
Thank you so much you made this sketching so simple
Wow you're amazing at explaining things
I love this explanation Ellie. It is really good
Not only this video helped me, the comments section was helpful too, that easy trick about focii being clockwise or anticlockwise was amazing! Thank you everyone 😍
This is awesome. Helped so much, thank you!
Thank you for making this so easy.
best video on this ive seen thank you!
life saver, much appreciation from Math 216 gang here in Ann Arbor!!!
Awesome and straight to the point, great vid
Great video, super thorough/explains everything
oh my gosh, this is so clear. save me at least an hour to work this out by myself
you presented in a very organized fashion. It was very helpful
This is amazing thank you for teaching me what my professor hasn’t
Much clearer than my professor and TA!
amazing explanation! such a simple way to teach differential eqns
best explanation video i found, gj
Very well explained, helped me a lot with my exam. Thanks!
I really appreciate this....now I can draw the phase diagrams.....
This is the best explanation on the web!
U are amazing I cannot thank you enough
Lifesaver ig, no words😌
Thanks a bunch! Really clear and easy to understand.
thank you is not enough to express my gratitude.you just saved my ass
Thank you so much! Much better than my trash textbook and lame professor.
dziękuję Pani bardzo! ratuje mi pani dupę przed egzaminem
amazingly simple explanation
just perfect 🤍
Thank you so much , i was suffering to understand how to draw the trajectories ... I appreciate that !
This REALLY helped me! Thank you!
Thank you so much!! You are awesome. 😊
You saved my life. Thank you.