I dont generally like a video... But I cant navigate away from this page without liking it... What an excellent explanation! I have never thought about, why, or why series solution... This video really opened my eyes... Million thanks!!!
This was really neat and like the opposite of generating functions ! We used generating functions to take a recurrence relation and then attach it to an infinite power series to solve it. Here we start with an infinite power series and finish with a recurrence relation !
Thank you so much, I was so excited for this episode! I see series pop up so much in higher mathematics that I wish it wasn't just introduced as a popup in Calc 2! Really seeing the full stack of theory to example makes this topic so much more useable! Thank you!
Professor Bazett, thank you for an outstanding video/lecture on How to solve Ordinary Differential Equations with Infinite Series. This topic gets messy/problematic with higher order derivatives. Pattern recognition is also. important when solving problems in Mathematics.
Great stuff. It's crazy how often series crop up in the study of ODEs. Definitely a subject that I need to review in great detail as it's the area of Calc 2 that I have always been quite weak in. I'm not quite sure why that is, but I've always struggled with series. I'll be correcting that in the coming months for sure. Trefor, in your experience as a math prof have you found that your second semester calc students struggle more with series that other subjects in Calc 2? If so, why do you think that is? If not, what seems to be the most challenging subject for your students?
What you showed from using the Ratio Test was that the series converged for all x. However, the Ratio Test did not guarantee that it indeed converged to the function e^x. I think in order to prove the series converges to e^x, you need to show the error E_n(x) = e^x -P_n(x) , where P_n(x) is Taylor polynomial of degree n, goes to 0 as n goes to infinity. Is it correct? I might be wrong.
I’m saying that in this specific case we recognize the series as the familiar e^x but in general it will be just some weird series and then you do need to do the ratio test to know if it converges, and I only practice doing that test for e^x to show the idea even if unnecessary as we are familiar with that series.
Sir you covered very well the concepts of trigonometric integration including the powers of sin and cosine will all possible combination but sir please make a video on trigonometric integration of tan and secant . There is one case in this kind of trig integration of tan amd secant which is not discussed in any of the books of calculus I have read so far. This case is when the power of tan is even (not 2) and the power of secant is odd (not 1). I have struggled so hard to solve this problem but I can't manage to do I need your help to integrate Tan²*²(x)sec³(x)dx Note here tan is raised to the fourth power.
Trefor Bazett yes but the example he gave at the end of the video was very simple and that had tan to power zero which is pretty simple but my question was where tan had a power of 4 and secant had a power of 3 can you please make a separate video on this special case please I need this please 😭😭😭
Trefor Bazett Sir I myself tried to solve this question which I made myself and found that If power of tan is even (greater than 2) and power of secant is odd (greater than 1) then such kind of question can be solved by first using identity Tan²x =sec²x - 1 And then using integration by parts and reduction formula techniques to sovle each term. Thanks a lot for supporting me. I will be very thankful if you make a video on this and tell the whole world about this technique ; your subscribers will greatly increase.
I dont generally like a video... But I cant navigate away from this page without liking it... What an excellent explanation! I have never thought about, why, or why series solution... This video really opened my eyes... Million thanks!!!
Wow, thank you!
man how can i thank u... now i dont have money but after my exams im going to goin as a member cause u deserved it !
I am in this same situation that you kkkkkkk
This was really neat and like the opposite of generating functions !
We used generating functions to take a recurrence relation and then attach it to an infinite power series to solve it.
Here we start with an infinite power series and finish with a recurrence relation !
Thank you so much, I was so excited for this episode!
I see series pop up so much in higher mathematics that I wish it wasn't just introduced as a popup in Calc 2!
Really seeing the full stack of theory to example makes this topic so much more useable! Thank you!
Also thanks so much for using this simple ode so that its easily contrastable to other methods of solving it!
This clarified the one part I don't like and often confuse in differential equations. Thanks a lot sir
Your videos make me want to learn everything!! It's awesome!!!
Prof. Bazett, you are such an amazing instructor, I owe you my A on Math Methods course :)
Oh wow well done!
Thanks a lot dear sir❤. Watching from Bangladesh 🇧🇩
Suddenly trimmed bread surprised me as a proceeded from previous video !
Professor Bazett, thank you for an outstanding video/lecture on How to solve Ordinary Differential Equations with Infinite Series. This topic gets messy/problematic with higher order derivatives. Pattern recognition is also. important when solving problems in Mathematics.
Thank you so much!
So underrated...
Keep on making Such great videos Sir!!!
I m sure it is going to grow...👍
Great stuff. It's crazy how often series crop up in the study of ODEs. Definitely a subject that I need to review in great detail as it's the area of Calc 2 that I have always been quite weak in. I'm not quite sure why that is, but I've always struggled with series. I'll be correcting that in the coming months for sure. Trefor, in your experience as a math prof have you found that your second semester calc students struggle more with series that other subjects in Calc 2? If so, why do you think that is? If not, what seems to be the most challenging subject for your students?
@@DrTrefor that all makes sense. Glad I wasn't the only one. =)
Thank you very much sir 🔥🔥🔥
another good video as always 👍 thank you
thank you sir
Firist view. Just missed this power series method question in yesterday's exam.
The Test Fails means it is Inconclusive. I was wondering what it meant for a long time.. Thanks.. ❤
Wooow Amazing! Any videos about PDEs sir??
Coming soon!
Great videos! Thank you so much!
Nice explained sir
4:59 - I thought you said something else entirely here.
based
scrolled down looking for this comment. would really take this channel to the next level.
Oh my god LMAO that would be the most papa flammy thing ever
What you showed from using the Ratio Test was that the series converged for all x. However, the Ratio Test did not guarantee that it indeed converged to the function e^x. I think in order to prove the series converges to e^x, you need to show the error E_n(x) = e^x -P_n(x) , where P_n(x) is Taylor polynomial of degree n, goes to 0 as n goes to infinity. Is it correct? I might be wrong.
I’m saying that in this specific case we recognize the series as the familiar e^x but in general it will be just some weird series and then you do need to do the ratio test to know if it converges, and I only practice doing that test for e^x to show the idea even if unnecessary as we are familiar with that series.
Which book or books are the best for learning to write proofs? (your opinion). As always thanks for everything!
Sir you covered very well the concepts of trigonometric integration including the powers of sin and cosine will all possible combination but sir please make a video on trigonometric integration of tan and secant . There is one case in this kind of trig integration of tan amd secant which is not discussed in any of the books of calculus I have read so far. This case is when the power of tan is even (not 2) and the power of secant is odd (not 1). I have struggled so hard to solve this problem but I can't manage to do I need your help to integrate
Tan²*²(x)sec³(x)dx
Note here tan is raised to the fourth power.
Trefor Bazett yes but the example he gave at the end of the video was very simple and that had tan to power zero which is pretty simple but my question was where tan had a power of 4 and secant had a power of 3 can you please make a separate video on this special case please I need this please 😭😭😭
Trefor Bazett Sir I myself tried to solve this question which I made myself and found that
If power of tan is even (greater than 2) and power of secant is odd (greater than 1) then such kind of question can be solved by first using identity
Tan²x =sec²x - 1
And then using integration by parts and reduction formula techniques to sovle each term. Thanks a lot for supporting me. I will be very thankful if you make a video on this and tell the whole world about this technique ; your subscribers will greatly increase.
What book do you use as reference Sir?
Tnx alot sir. Gamma function nd its seirios solution. Videos post plz
Ok. Sir ill check
With real concept
❤❤
Hello, prof. Will you be making a series in about DE covering seperable,linear, homogenuous,... DE’s ?
Looks like a bunch of bull shifts to me