Ciao Trefor, I need your help , seriously: do you know anybody of your caliber teaching physics on youtube ? I am having some difficukties with subject and can't find a teacher I like - probably I'm to used to your wonderful maths classes that I simply can't settle for anything with lower standard! Again you are the best!
Professor, please tell me which will yield me a better result for a function evaluated at a point, Runge kutta method or Taylor series.. Your response will be appreciated. Thanks
I don't know, if anyone needs the answer for this now, but I think it's an interesting question. I would say it mainly depends on how far are you from the point, where you know the value of the function. But it also depends on the function itself. From the Lagrangian form of the remainder you can see how well it converges the taylor polynomial to the actual function. The Runge-Kutta method will have an error proportional to the size of the step (for example the RK4 will have a 16 times smaller error for 2 times smaller step). So you can see approximately which of the methods work better for the given case. (If I'm wrong, someone can correct me)
I replayed many sections to hear what was said as your voice trailed off at the end of a sentence, then gave up. Work on keeping your clear, and not speeding up, as you finish each sentence.
thank you for explaining the "why though" that always burns in the back of my mind when learning. you're the best!
Great explanation, your enthusiasm at the end is infectious
This is helping me understand the theorem, especially visualizing it. Thank you!
You are a gift sent from god to math enthusiasts. Thank you.
An excellent explanation on taylor's inequality. Thank you!
this guy is a god sent
Your videos are awesome. Keep up the good work!
You are so good. Excellent teaching. Please continue making such good videos. By the way Happy Holi.
Amazing job , respect
Your explanation is always very helful in answering why I learn.
Ciao Trefor, I need your help , seriously: do you know anybody of your caliber teaching physics on youtube ? I am having some difficukties with subject and can't find a teacher I like - probably I'm to used to your wonderful maths classes that I simply can't settle for anything with lower standard! Again you are the best!
Professor, please tell me which will yield me a better result for a function evaluated at a point, Runge kutta method or Taylor series..
Your response will be appreciated.
Thanks
I don't know, if anyone needs the answer for this now, but I think it's an interesting question.
I would say it mainly depends on how far are you from the point, where you know the value of the function. But it also depends on the function itself.
From the Lagrangian form of the remainder you can see how well it converges the taylor polynomial to the actual function.
The Runge-Kutta method will have an error proportional to the size of the step (for example the RK4 will have a 16 times smaller error for 2 times smaller step).
So you can see approximately which of the methods work better for the given case.
(If I'm wrong, someone can correct me)
Understood! Thank you
The sigma notation for the Taylor series, shouldn't 'i' start at 0?
It is just an index, so as long a you are consistent it doesn't matter
Amazing video, thank you!
Glad you liked it!
Great one mann♥️
Hello, professor. Can you explain why are you omitting -a term for interval in example with f(x) = e^x ?
Because we are taking the power series centered at 0, so a = 0 in this case
Great Video!
Glad you enjoyed it
what M, and d at 5:10 mean?
M is an upper bound (possibly the LEAST upper bound) for the given derivative, and d represents the distance from your starting point.
This was a great explanation, thank you!
Seems like all the good male calculus tutors like plaid shirts.
FACT
U r a blessing!
great vid
Gold
Nifty!
I replayed many sections to hear what was said as your voice trailed off at the end of a sentence, then gave up. Work on keeping your clear, and not speeding up, as you finish each sentence.
i can understand him perfectly. Try slowing down the video if you need. Hope this helps!
Sounds fine to me