This is the first time I feel like I understand exactly what I'm doing...why I'm doing it and I'm able to dissabmle complex problems b3cause of this brilliantly simplified tutorial....thank you.
I am a Vietnamese, not really good at English but the way u convey ur knowledge is very fantastic and approachable, That helps me understand the lesson.
Doing my HW rn and prof did not explain it too well. Isn't fun grinding on a Monday night but actually understanding the material makes it so much better. Thank you.
THANK YOU! I'm taking a numerical equations course for university and with your informal rise over run explanation I understand the formula behind euler's method.
My lecturer made this a self study unit and I've been busy with it for hours, almost gave up and went to sleep but after watching this video I finally understand what's going. Thank you so much🔥
For my Mechanical Engineering Masters thesis project I created an ICE (Internal Combustion Engine) simulation program. I ended up with 22 differential equations needing to be solved simultaneously using a numerical method. I started out using a fourth-order Runge Kutta numerical integration method. As my model got more and more complex, my program got slower and slower and eventually got to the point where it just wouldn't converge at all. Sometimes I'd run the program all night long and get up in the morning to find it eventually crashed. I'd get underflow and divide by zero error messages. I tried everything I could think of and it just wouldn't converge. I ended up switching over to a variable step size, variable order, Adam's predictor-corrector numerical integration method. The difference was incredible. I couldn't believe how fast it ran. I was using a 10 degree crank angle step size for the 4-stroke combustion cycle from a crank angle of 0 to 720 degrees.
Thank you for the very helpful explanation! I am writing a paper for my physics class on Euler's Method as it pertained to John Glenn's 3 orbits around the earth in 1962. Euler's Method solved the problem of going from an elliptical orbit to a downward parabolic descent path and safe re-entry to earth. Thank you Katherine Johnson -- brilliant African-American lady computer!
Excellent explanation of the idea of getting the slope value! Really, why don’t we use the given differential equations itself to tell us what the actual slope is in the given x! Brilliant! Thanks author for this simple explanation!
Thank you for the very clear explanation! Sometimes the not formal math symbol like ? really helps some brains out there (including mine). Appreciate the video sm ^ ^
Hi Firefly . Thanks for explnations. One small doubt How Euler method differs from Integration? since dy/dx=2x can be integrated as Integral(dy) = Integral (2x) dx y= x2 + c
wait a min. yes, dy/dx is also the rise over run, but f(x,y) is a 3 dimensional function, the graph you are showing is 2D where its just y(x), am I missing something here?
I dont understand why in these examples the calculation of the slope always requires Y. The only example I ever see is on a function like Y'=f(x,y) where both an x and y are required to calculate the slope. How would you use Euler to estimate Y=2X^2 where slope is just 4X (no Y required)? Similarly, I dont understand why the 2nd and 3rd point of RK4 would evaluate to different values with a univariate equation (Y=2X^2) since the slope at any point does not require Y. Isn't Y'=f(x,y) a very particular and rare case, which every single video on this subject uses? Why not Y'=f(x)?
WHY DO THEY CALL IT "SOLVING DIFFERENTIAL EQUATIONS BY THE EULER METHOD"??? AREN´T THEY MERELY GETTING AN APPROXIMATION OF A """"""""""""""SLOPE""""""""""""""" AT A CERTAIN POINT?????????????
This is the first time I feel like I understand exactly what I'm doing...why I'm doing it and I'm able to dissabmle complex problems b3cause of this brilliantly simplified tutorial....thank you.
Tipuuu
This is the only euler's tutorial I understood.
Thank you!
I am a Vietnamese, not really good at English but the way u convey ur knowledge is very fantastic and approachable, That helps me understand the lesson.
Once again a clear, succinct and simply excellent lecture with no obfuscating and complicated looking notation, thank you!
May God reward you for all your efforts and all the valuable information that you provide us smoothly .
The explanation of why the step size is where it is was great. Thanks for the great content!
Doing my HW rn and prof did not explain it too well. Isn't fun grinding on a Monday night but actually understanding the material makes it so much better. Thank you.
I saw a lot of videos but didn't understand anything, but your video really helped me to clear my concept.
Thank you so much sir :)
That is truly explained ! Thank you soo much. Keep doing lectures on this kind of problems .
THANK YOU! I'm taking a numerical equations course for university and with your informal rise over run explanation I understand the formula behind euler's method.
My lecturer made this a self study unit and I've been busy with it for hours, almost gave up and went to sleep but after watching this video I finally understand what's going. Thank you so much🔥
"A" star explanation...understands how human mind works!! The advice to rewind showed it all.
For my Mechanical Engineering Masters thesis project I created an ICE (Internal Combustion Engine) simulation program. I ended up with 22 differential equations needing to be solved simultaneously using a numerical method. I started out using a fourth-order Runge Kutta numerical integration method. As my model got more and more complex, my program got slower and slower and eventually got to the point where it just wouldn't converge at all. Sometimes I'd run the program all night long and get up in the morning to find it eventually crashed. I'd get underflow and divide by zero error messages. I tried everything I could think of and it just wouldn't converge. I ended up switching over to a variable step size, variable order, Adam's predictor-corrector numerical integration method. The difference was incredible. I couldn't believe how fast it ran. I was using a 10 degree crank angle step size for the 4-stroke combustion cycle from a crank angle of 0 to 720 degrees.
Seriously this is exactly what i needed! I wish the books actually explained the concept instead of just giving you an equation to memorize.
Thanks!
Astonishing, absolutely astonishing explanation!
Thank you for the very helpful explanation!
I am writing a paper for my physics class on Euler's Method as it pertained to John Glenn's 3 orbits around the earth in 1962.
Euler's Method solved the problem of going from an elliptical orbit to a downward parabolic descent path and safe re-entry to earth.
Thank you Katherine Johnson -- brilliant African-American lady computer!
Thank you so much for this video. I didn't understand this concept at all before this video. I definitely know that I'll pass my exam now
love how you introduced it , keep it up
I gave a presentation on Euler method after seeing ur video...My faculty appreciated me for my clear explanation...Thank you Sir...
Excellent Sir. Hard thing found it very simple. Thanks a lot.
the 7 dislikes are from lecturers that didnt do such a good job explaining
🤣🤣🤣🤣🤣🤣funny
Totally agreed.
Excellent explanation of the idea of getting the slope value! Really, why don’t we use the given differential equations itself to tell us what the actual slope is in the given x! Brilliant! Thanks author for this simple explanation!
Clear and concise! I subscribed! Hoping to see more videos. :)
This is more than amazing, you are second to non
Geez, finally I found someone who bothers to explain the actual process. A+++
Thank you SO SO much! I am so glad I found your video.
Your explaination is so clear !
You're welcome Karin.
Very clear explanation !!! Thank you very much sir
thes is the best introduction to this method thank you so much
Very good and clear explanation. Thank you .
This is really good, thanks. Do you have videos on other numerical methods like fixed point iteration as well?
Thank you for the very clear explanation! Sometimes the not formal math symbol like ? really helps some brains out there (including mine). Appreciate the video sm ^ ^
Thank you ...now I understand more
Very conceptual and clear video
Best video on youtube about this topic
This is good teaching ! brilliant
You are the mann sir
Thank you so much, you are a real hero!; min 10:21 was what was puzzling me for a long time!
amazing explanation thank you! Thumbs up
wonderful explanation sir,, thanks,,
Got it everywell, Nice Explanation with Graph.
Very goooood explanation, thank you
great video, you are really good at explaining math, so that you can understand it :)
thank you :)
amazing and clear video!
Thank you so much Sir! ❤
Excellent explanation.
Awesome explanation.
Great video. Thank you.
thank you for this lecture!!!!
Amazing, Well explained
Helps a lot thanks devon
This cleared it up!! thanks!!
Yep still best one in UA-cam.
Thank you 😊🙏sir. Very clear.
excellent video!
Thank you so much for basic stuffs
very make sense it all comes back from what I've learned 50+ years ago.
Thank you so much!
Excellent
you saved my life
Thank you !
Incredible
Thank you very much
Thank you
clear explanation sir
good explanation
nice.. many thanks!
Really Helpful!!!!!thx
thank u !
Hi Firefly . Thanks for explnations. One small doubt
How Euler method differs from Integration?
since dy/dx=2x can be integrated as
Integral(dy) = Integral (2x) dx
y= x2 + c
thanks a lot really.
Awesome
Super
sheldon? is that you?
good
900th like haha. im subscribing!
wait a min. yes, dy/dx is also the rise over run, but f(x,y) is a 3 dimensional function, the graph you are showing is 2D where its just y(x), am I missing something here?
Cool
I dont understand why in these examples the calculation of the slope always requires Y. The only example I ever see is on a function like Y'=f(x,y) where both an x and y are required to calculate the slope. How would you use Euler to estimate Y=2X^2 where slope is just 4X (no Y required)? Similarly, I dont understand why the 2nd and 3rd point of RK4 would evaluate to different values with a univariate equation (Y=2X^2) since the slope at any point does not require Y. Isn't Y'=f(x,y) a very particular and rare case, which every single video on this subject uses? Why not Y'=f(x)?
Wow 👍👌👌
better than khan academy!
Sheldon Cooper
handsome
Shoutout to Mr. Achille's class
AIICWYT Lol, hi Mr. Achille’s class! :) Good luck this semester!
you look like Sheldon Cooper from Big Bang Theory
🤓
9:00
its benedict cucumber
sheldon from wish
Thanks for the like, and thanks for helping me with my math excel assignment
WHY DO THEY CALL IT "SOLVING DIFFERENTIAL EQUATIONS BY THE EULER METHOD"??? AREN´T THEY MERELY GETTING AN APPROXIMATION OF A """"""""""""""SLOPE""""""""""""""" AT A CERTAIN POINT?????????????
You sound like afroamerican,
I mean the accent ¡
The explanation of why the step size is where it is was great. Thanks for the great content!
Thank you very much