Watching these videos over the summer before my actual differential equations class starts helps so much. This world needs more people like you and PatrickJMT who can explain everything clearly instead of teachers just trying to show off how much they know.
Right now, I'm spending my summer going through your Calculus 1 playlist, and I've enjoyed it. Thank you so much for helping me rediscover my love for math. I've done practice problems on each topic and it all makes perfect sense to me thanks to you.
In principal I've gone beyond this material. Watching you vid proved to me that I've never given it enough thought and I still have a lot to learn. Thank you professor, for giving me the motivation to keep studying further. Also,thank you for your efforts!
Your video does help me a lot, after I've found a dozen videos, and no one gives me a clue about what exactly the equilibrium point is. Thank you so much!
Please continue the series professor, in any way possible! Your teaching is unmatched and would do anything in the world to get the rest of the material for DE taught under you. Wishing you and your family great health and prosperity
Sir. I just dont have words. Your teaching is just a whole other level of teaching. Domt think i have ever come across a better teacher than you. Your the reason i nailed my further calculus. And now your gonna be the reason for me to nail Mathematical Economics. Thank you sir. God Bless you and may you be blessed with the best!! ❤❤❤
Thank you professor Leonard for all your videos. They helped me succeed in Calculus 2 and Calculus 3 in college. I really enjoyed learning and watching all your lectures. They were always very interactive, especially with raising our hands :) I really appreciate the work you do. Thank you again professor.
Thank you for this video. I have an exam next week and this was exactly what I needed to watch. Your videos should be federally mandated in every educational institution
had no idea what my teacher was talking about and my book barely explains it. it doesn't seem so overwhelming now and makes sense. thank you so much for uploading these D.E. videos!!!!!!!
Thank you for being well-versed throughout all of your lessons. You've really accelerated my learning and love for math. I cannot thank you enough professor ^_^
I can't wait to see your linear algebra video lessons. I also look forward to the following courses: College Algebra Precalculus Geometry Trigonometry Probability
these could come fast enough, taking diffeq this summer at the moment, had my first exam today. you're the best!!! been watching since calc 1 and have done pretty well. now if only you did linear algebra videos!
great explaining on "stability" ! please make some higher level math courses video in the future, and I feel that I only can understand math in your class.Thank you professor!
@@ProfessorLeonardAwesome! Keep up the great work and congratulations on the new addition to your family!! I recently graduated from UC Berkeley in Physics and am preparing for grad school. Your videos are invaluable and a godsend. I just completed the entire series of differential equations so far and wrote down detailed notes of all the different techniques and examples. Also, thanks for the reply! Really nice actually hearing from you. You were my colleagues and my Calc 3 teacher because our teacher in community college didn't teach the material very well. You do such an excellent job of making difficult/higher-level concepts accessible and easy to understand and digest. Thank you for your time and energy and for everything you do!
Thank you for making these amazing lectures. If you don't mind me asking, how many videos do you plan on making for this course? Hope you have a great day 😃
Hi Sir hope you are having great time. I have a question regarding fixed point. In context of a function fixed point is defined as f(x) = x or standard notion is T(x)=x as given by Banach fixed point theorem. But in context of dynamical system when we use the word fixed point it seems that it doesn't relate to definition T(x) = x but rather we say that fixed point is where the derivative is zero. So my question is that does the word fixed point meaning differs in both contexts or is there any analogy.
How can a function like (3 - x(0)) equal plus or minus C? Shouldn't it only be able to equal one of them, at most? In addition, can an initial value that starts on one side of a critical point ever jump over to the other side of the critical point; if not, why not? Your videos are pretty awesome!
Do you have a tee spring where we could get t-shirts like the one in this video? Or hoodies that have a cool print to look like your channel profile image? I could think of a bunch of cool designs. Like a silhouette of your hair, glasses and face, but instead of the superman "S", it could be an integral symbol inside the superman shield. So many possibilities!
I think that the second derivative test for relative extrema is more reliable because you only need the critical point itself to plug in. The first derivative test needs two points around it, and one point might be far enough from the crit. pt. that it will give you an inaccurate answer because the slope to the right of the crit. pt. might be positive (for example) and if you choose a pt just beyond that, it might be negative. #secondderivativetest all tha way
Hi, did Professor Leonard ever finished the course in perhaps his patreon? He talks about making videos on linearity and other topics I can't seem to find on his youtube....
Hi! I haven't finished Differential Equations yet, but I do plan to... Life has been extremely busy with more children and career changes and house building. However, I will put out more videos in the future :)
@@ProfessorLeonard Thank you! Praise the Lord you are doing great! I am so thankful for all your help. Truly you are the best profesor I've ever had. So thankful to God because now I can study without the huge anxiety of not understanding but rather truly enjoy and look forward to taking (binged watching self studying) the courses (I've done Cal 1,2, this one and will do Cal 3). PD I've seen that some people write the logistic equation as rN(1-N) or rN (1-N/L) how does it relate to kP(M-P)? Praying for the Lord Jesus, since His riches are infinite and His will perfect, to repay all the good and help you've given to all the thousands of students around the globe so we can succeed and achieve goals. God has given you such a special gift and you've used it so brilliantly! It's so inspiring to read the comments and see how far others have reached thanks to God and your help! Greetings from Spain!
@@ProfessorLeonard By the way could you please do one on Numerical Methods?!! I am trying to get into an engineering program and it will be of inmeasurable help!
Anyone else trudging through this journey of remote learning for a year now and fighting back tears watching this after reading his shirt? lol
Watching these videos over the summer before my actual differential equations class starts helps so much. This world needs more people like you and PatrickJMT who can explain everything clearly instead of teachers just trying to show off how much they know.
That’s exactly what I said !!
doing this too five years later!
Right now, I'm spending my summer going through your Calculus 1 playlist, and I've enjoyed it. Thank you so much for helping me rediscover my love for math. I've done practice problems on each topic and it all makes perfect sense to me thanks to you.
I want to genuinely thank you for showing me the beauty of mathematics. I feel like Ramanujan after watching your playlists.
I've got my first dif eq exam tomorrow morning but I know I'm going to do well because Prof Leonard believes in me :)
In principal I've gone beyond this material. Watching you vid proved to me that I've never given it enough thought and I still have a lot to learn. Thank you professor, for giving me the motivation to keep studying further. Also,thank you for your efforts!
Your video does help me a lot, after I've found a dozen videos, and no one gives me a clue about what exactly the equilibrium point is. Thank you so much!
Thank you so much prof. Leonard. Please, never ever stop posting math vids.
Please continue the series professor, in any way possible! Your teaching is unmatched and would do anything in the world to get the rest of the material for DE taught under you. Wishing you and your family great health and prosperity
Thanks professor Leonard, you believe in me even when i dont believe in myself....
Sir. I just dont have words. Your teaching is just a whole other level of teaching. Domt think i have ever come across a better teacher than you. Your the reason i nailed my further calculus. And now your gonna be the reason for me to nail Mathematical Economics. Thank you sir. God Bless you and may you be blessed with the best!! ❤❤❤
Thank you professor Leonard for all your videos. They helped me succeed in Calculus 2 and Calculus 3 in college. I really enjoyed learning and watching all your lectures. They were always very interactive, especially with raising our hands :)
I really appreciate the work you do.
Thank you again professor.
Thank you for this video. I have an exam next week and this was exactly what I needed to watch. Your videos should be federally mandated in every educational institution
We believe Professor Leonard to be the best math teacher ever to surface online.
had no idea what my teacher was talking about and my book barely explains it. it doesn't seem so overwhelming now and makes sense. thank you so much for uploading these D.E. videos!!!!!!!
Professor Leonard!!! Thank you for continuing this series
You are one of the biggest reasons for me being able to pursue my American Dream.
Thank you for being well-versed throughout all of your lessons. You've really accelerated my learning and love for math. I cannot thank you enough professor ^_^
Best Professor ever!
I can't wait to see your linear algebra video lessons. I also look forward to the following courses:
College Algebra
Precalculus
Geometry
Trigonometry
Probability
lol
I wish he start real analysis and complex analysis too...and I wish probability too
Very clean explanation of the critical points. I have learnt a lot from this video. Thank you very much!
Best Professor....thankyou for making our concepts of Mathematics clear in a very easy way....
Please come back, Leonard! I learn so much better from you and I’m just about loving passed your posted DE videos in my class…please?!
Wow this was very helpful for conceptually grasping this concept. You’re videos are very helpful!
omg Professor Leonard you are a great teacher!
Professor Leonard I shit you not you are the greatest teacher of all time
these could come fast enough, taking diffeq this summer at the moment, had my first exam today. you're the best!!! been watching since calc 1 and have done pretty well. now if only you did linear algebra videos!
*If Professor Leonard believes in me then I can't go wrong 😤*
I did not find this awesome Differential equations tutorial, it found me !
So now that you're done with diff eq according to your patreon you gonna do linear algebra and discrete math?
great explaining on "stability" ! please make some higher level math courses video in the future, and I feel that I only can understand math in your class.Thank you professor!
Any idea on when you will start uploading this series again?
Hope we can get a Prof Leonard Linear Algebra next!!!
I'm working on it :)
I'll be finishing Diff Eq first, and then LA is next on the list!
@@ProfessorLeonardAwesome! Keep up the great work and congratulations on the new addition to your family!!
I recently graduated from UC Berkeley in Physics and am preparing for grad school. Your videos are invaluable and a godsend. I just completed the entire series of differential equations so far and wrote down detailed notes of all the different techniques and examples.
Also, thanks for the reply! Really nice actually hearing from you. You were my colleagues and my Calc 3 teacher because our teacher in community college didn't teach the material very well.
You do such an excellent job of making difficult/higher-level concepts accessible and easy to understand and digest.
Thank you for your time and energy and for everything you do!
Plz as soon as possible I need this lecture
Yahoo! He's back!
Thank you for making these amazing lectures. If you don't mind me asking, how many videos do you plan on making for this course? Hope you have a great day 😃
Hi Sir hope you are having great time. I have a question regarding fixed point. In context of a function fixed point is defined as f(x) = x or standard notion is T(x)=x as given by Banach fixed point theorem. But in context of dynamical system when we use the word fixed point it seems that it doesn't relate to definition T(x) = x but rather we say that fixed point is where the derivative is zero. So my question is that does the word fixed point meaning differs in both contexts or is there any analogy.
Awesome Stuff!!!🎓
Love ur shirt,professor!
Teacher, I have another question. What's your training routine?
Great work
I love the shirt you're wearing
It is asymptotical stability in Lyapunov sense.
How can a function like (3 - x(0)) equal plus or minus C? Shouldn't it only be able to equal one of them, at most? In addition, can an initial value that starts on one side of a critical point ever jump over to the other side of the critical point; if not, why not? Your videos are pretty awesome!
Thank you so much!
Professor Leonard > Kawhi Leonard
Lol. Truth!
Omg... How are they even in the same scentence..😂😂
@Dr. Complex Lol.
all in all this video could be summed up into
-> -> or
The shirt was motivating lol
thanks !
Do you have a tee spring where we could get t-shirts like the one in this video? Or hoodies that have a cool print to look like your channel profile image? I could think of a bunch of cool designs. Like a silhouette of your hair, glasses and face, but instead of the superman "S", it could be an integral symbol inside the superman shield. So many possibilities!
Love the superman idea!! I sell the shirts on my shopify page along with some decals and these are some great thoughts, thanks!
I think that the second derivative test for relative extrema is more reliable because you only need the critical point itself to plug in. The first derivative test needs two points around it, and one point might be far enough from the crit. pt. that it will give you an inaccurate answer because the slope to the right of the crit. pt. might be positive (for example) and if you choose a pt just beyond that, it might be negative. #secondderivativetest all tha way
So you have your original function, x(t), and then the slope function f(x)?
what's a constant solution ?
Can we get some merch? Gotta rep my actual professor on campus.
Absolutely! professor-leonard.myshopify.com/
Do you have any plans to make a matrix algebra playlist? If so that would be awesome!
Linear Algebra PLEASEEE
Plz professor share the lecture on bessel equation and legendrey equation
IS this the same as autonomous equations?
how come he only has 500k subscribers?
nice thsirt i like
Do you have any videos which incorporate mechanical vibrations?
Does anybody know if Autonomous first-order DE are the same as Equilibrium Solutions and Stability of DE?
please someone answer. what do I do with complex fixed points? f(x)= -x^3-x^5
Hi, did Professor Leonard ever finished the course in perhaps his patreon? He talks about making videos on linearity and other topics I can't seem to find on his youtube....
Hi!
I haven't finished Differential Equations yet, but I do plan to... Life has been extremely busy with more children and career changes and house building. However, I will put out more videos in the future :)
@@ProfessorLeonard Thank you! Praise the Lord you are doing great! I am so thankful for all your help. Truly you are the best profesor I've ever had. So thankful to God because now I can study without the huge anxiety of not understanding but rather truly enjoy and look forward to taking (binged watching self studying) the courses (I've done Cal 1,2, this one and will do Cal 3).
PD I've seen that some people write the logistic equation as rN(1-N) or rN (1-N/L) how does it relate to kP(M-P)?
Praying for the Lord Jesus, since His riches are infinite and His will perfect, to repay all the good and help you've given to all the thousands of students around the globe so we can succeed and achieve goals. God has given you such a special gift and you've used it so brilliantly! It's so inspiring to read the comments and see how far others have reached thanks to God and your help!
Greetings from Spain!
@@ProfessorLeonard By the way could you please do one on Numerical Methods?!! I am trying to get into an engineering program and it will be of inmeasurable help!
I wish I could believe in myself first :D
Bro thattt is ..
HOW DO I GET ONE OF THESE SHIRTS
I have more examples like this on my channel if you want more practice!
Where could I get one of these shirts?!
Stephen Colbert teaches Calculus
My guy
Is it me or does this dude look like Henry Carville
Superman 0
Prof Leonard 1
44 minutes to explain a 30 second problem... sigh
you're way too happy to do calculus, man. Calm down plz