most math channels on youtube spend like 25 minutes rambling before they get to the actual point, this dude always keeps it concise and straightforward and it boggles my mind how much easier it for me to learn with his vids than anyone else's. cheers mate
I started from lesson 1 and finished now. I couldn't even solve the simplest algebraic equation and even had trouble doing some arithmetic. Now I can even do calculus. I am planning to study physics so I decided to go through the math playlist first, and then the physics playlist. Thank you so much Dave, you are a really awesome person. :)
cant thank you enough for this video. I went to khan academy, and 3blue1brown and didn't understand a thing, finally, before I gave up on it, I came to your video and understood everything. You made it way easier and simple to understand. You are a very talented man !! thank you. !!!
3blue1brown is for people that have already some prior knowledge on the topic or have slightly above average intuition skills, clearly you aren't one of them.
I have my final exam in about three hours, the air and water show is in town and there are F-16 fighter jets with full throttle roaring overhead, my neighbor is blasting loud music so I can barely hear anything, and yet your video somehow managed to help me understand this concept while all that was going on. I love you, Dave.
I can still remember the first day I watched your videos, it was when my school chemistry teacher suggested your videos. And now after three years I got selected to engineering faculty and still watching your videos to improve my knowledge in uni.
I watched this video 2 years ago and untill watching this video now, I was unable to understand this simple concept (maybe my overthinking was making it difficult for me to understand this) but now, that I am watching this one day before exam, I don't know why but this just feels like a piece of cake. Your teaching style is excellent and I don't know, the pressure of exams really makes me go on flow state then i guess...
I’ve watched a lot of videos from other sites struggling to get an intuitive understanding of the Taylor series. After watching this, I’m finally getting it, and finding Dave’s other videos just as great.Really helpful, thanks so much!
Searching for this topic in the German TH-cam Math space didn't do me much, I found the explanations of the Taylorreihe too confusing. So I decided to search for the Taylor Series in English, and thankfully, Professor Dave covered it, and I can finally understand the concept now.
Oh Dang, this was the last topic of the series? That's bittersweet. I'm happy that I have finished this Calculus playlist but I'm sad that I would need to find other channels now for even more advanced Math. But hey, it was still a fun ride. I'm glad and happy that I was able to finish this playlist.
This is a stupendous , marvelous job. You wouldnt imagine how many materials I have been looking for MGF with taylor series also why e^x was used generally as the RVS.Thank you so much.
Very splendid explanation sir. Some always start a topic with examples without delving into the real issue. You started it from the very beginning of inception of Taylor series from power series. That is derivation of Taylor series from first principle
I've done well in studying Calculus so far, but I find this topic quite challenging. Thankfully, it is finally starting to make sense to me, due to Professor Dave's more streamlined approach. Too many instructors think you must know the entire history of China before they can show you how to make a cup of tea.
Glad to be of service! You can go to www.patreon.com/professordaveexplains or feel free to send any amount you wish to the PayPal account associated with professordaveexplains@gmail.com thanks for your support!
Great video Prof. Dave I've learned a lot , but there's something you forget with the Checking Comprehension (number 2 problem) There's no , P_0(x)= f(1)=2 🌺💗
We evaluated that its derivatives are: f'(x) = 4*x^3 + 1 f"(x) = 12*x^2 f'"(x) = 24*x f""(x) = 24 Evaluate all of these at x=1: f'(1) = 4*1^3 + 1 = 5 f"(1) = 12*1^2 = 12 f'"(1) = 24*1 = 24 f""(1) = 24 Now divide each of these by their corresponding factorials: f'(1)/1! = 5 f"(1)/2! = 12/2 = 6 f'"(1)/3! = 24/6 = 4 f""(1)/4!= 24/24 = 1 It's zeroth derivative at x=1, is zero, because the original function is x^4 + x - 2, which evaluates to zero Thus, we get: T(x) = 5*(x - 1) + 6*(x - 1)^2 + 4*(x - 1)^3 + 1*(x - 1)^4
Since this already is a polynomial, it's really redundant to do a Taylor series. Any application of a Taylor series, could easily be done directly with the original function. All we need to do is shift the original function, so its input is centered on x=1. Given: f(x) = x^4 + x - 2 Let X = x - 1, and rewrite it in terms of capital X. Thus: x = X +1 (X + 1)^4 + (X + 1) - 2 Expand & simplify: X^4 + 4*X^3 + 6*X^2 + 4*X + 1 + (X + 1) - 2 X^4 + 4*X^3 + 6*X^2 +5*X Replace X with (x - 1), and reverse the order: (x - 1)^4 + 4*(x - 1)^3 + 6*(x - 1)^2 + 5*(x - 1) Result: f(x) = 5*(x - 1) + 6*(x - 1)^2 + 4*(x - 1)^3 + (x - 1)^4
Basically it's f(a) and as it says centered at 1 so f(1) so like it says nth derivative of f(a) so first you find the derivatives then plug in the value
i am at 8:53. you have made a mistake, you showed the message the Taylor series is expanding with expansion about x=0, at (5:55) the grammar of the message is wrong, it is not the taylor series and the sentence should be saying a Taylor series is expanding through expansion and x is about 0. unless you meant at that point where x=0 or at the point where x is about 0. 6:14 (definitions) 6:35(maclurin series and base e) you also did not explain why the top terms can go away properly. the proper explanation is: the maclurin series is the wrong type of maclurin series on its own is wrong and doesn't have all the right terms for it. hence we correct it, to get the right maclurin series and to get the right maclaurin series expression we must work from e^0=1 and e^x=1, thus x=0. we cancel 0 from e^0 from e^0=1 and from sigma where the end point is infinity and n=0 and the rule given is f^n)(0/2!. f gets replaced by e since f^2=1 when n=0 and e^0 this replaces 0 with x since x=0 thus getting the right type of maclurin series that represents f(x)=e^x i.e the sigma where infinity is the end point and n=0 is the starting point and x/2! and x^n is on the right of the fraction.. also you have not explained how to get the Taylor series for the last questions. the explanation seemed to be: do f(x)=1/ x, f"(x)=-1/x^2, f"'(x)=2/x^3, F(4)x=-6/x^4, fx=x-1-(x-1)^2/2+x-1^3/3-x-1^4/4 since n gets substituded for a, and that we also must be do that because the limit approaches infinity and adding 3 side way dots after saves you time since the dots means what comes after and that adding 3 dots after takes hardly any time compared to including the rest of the fractions. for problems like that substidue n for x making f(x). for finding the taylor series for x^4+x-2 centered at a=1, we subtract the power 4 by 1thus gettung the power 3 and substituting x for 1 or whatever the value of a is given for.
excellent way of explaining. I got amazed with your explanation and did lot of calculus sums. Sir I will be sending very special 4 questions through email to you. Please be kind enough to reply. Interestingly waiting for your explanation . Thanks
most math channels on youtube spend like 25 minutes rambling before they get to the actual point, this dude always keeps it concise and straightforward and it boggles my mind how much easier it for me to learn with his vids than anyone else's. cheers mate
Thanks for the teaching
I started from lesson 1 and finished now. I couldn't even solve the simplest algebraic equation and even had trouble doing some arithmetic. Now I can even do calculus. I am planning to study physics so I decided to go through the math playlist first, and then the physics playlist. Thank you so much Dave, you are a really awesome person. :)
yes and it feels like completing other side quest and then go fight the boss
cant thank you enough for this video. I went to khan academy, and 3blue1brown and didn't understand a thing, finally, before I gave up on it, I came to your video and understood everything. You made it way easier and simple to understand. You are a very talented man !! thank you. !!!
Hamid Alrawi I did the same and agree completely
The 3blue1brown video is aimed at people who already have some prior knowledge about Taylor series.
3blue1brown was teaching philosophy not mathematics
3blue1brown is for people that have already some prior knowledge on the topic or have slightly above average intuition skills, clearly you aren't one of them.
@@ayushdugar1698 whom are you intending?
I have my final exam in about three hours, the air and water show is in town and there are F-16 fighter jets with full throttle roaring overhead, my neighbor is blasting loud music so I can barely hear anything, and yet your video somehow managed to help me understand this concept while all that was going on. I love you, Dave.
nah the dick eating is crazy
Are u still alive?
How was the exam?
let me tell you, your videos are crystal clear and very helpful. never stop man. you are great. PEACE
deeppatel9623
Fortunately, it seems like he's going strong as ever now!
These knowledge gains can be. 👌🏾
I can still remember the first day I watched your videos, it was when my school chemistry teacher suggested your videos. And now after three years I got selected to engineering faculty and still watching your videos to improve my knowledge in uni.
Your layout is soooo clean. So simple and straight to the point. Thanks so much
Coincidentally, I just thought about this series this evening.
And now open youtube with your video.
Thank you so much.
It's not coincidence, it's called surveillance
Well, I think I found my new favorite tutoring channel. This helped me catch the concepts I couldn't quite grasp, and I really appreciate it.
I watched this video 2 years ago and untill watching this video now, I was unable to understand this simple concept (maybe my overthinking was making it difficult for me to understand this) but now, that I am watching this one day before exam, I don't know why but this just feels like a piece of cake. Your teaching style is excellent and I don't know, the pressure of exams really makes me go on flow state then i guess...
I’ve watched a lot of videos from other sites struggling to get an intuitive understanding of the Taylor series. After watching this, I’m finally getting it, and finding Dave’s other videos just as great.Really helpful, thanks so much!
Searching for this topic in the German TH-cam Math space didn't do me much, I found the explanations of the Taylorreihe too confusing. So I decided to search for the Taylor Series in English, and thankfully, Professor Dave covered it, and I can finally understand the concept now.
I think man you are god gifted teacher. The world needs your lectures, keep it up bro!
I don't find any words in telling u how clear and simple u make the videos .. lots of respect and love to u !!
ohh professor dave you are naturally ahead.... this video makes me clear understand about taylor's and maclaurin series
Oh Dang, this was the last topic of the series? That's bittersweet. I'm happy that I have finished this Calculus playlist but I'm sad that I would need to find other channels now for even more advanced Math. But hey, it was still a fun ride. I'm glad and happy that I was able to finish this playlist.
This video has given me some hope to not give up just yet.
Professor Dave you really save my life!
This is a stupendous , marvelous job. You wouldnt imagine how many materials I have been looking for MGF with taylor series also why e^x was used generally as the RVS.Thank you so much.
This is excellent! Simple and concise explanation to a tricky concept
Truly a legend, thank you lots ❤
Great video, thanks, wanted to point out at 6:01, it should be a=0 and not x=0 for Maclaurin series.
Very splendid explanation sir. Some always start a topic with examples without delving into the real issue. You started it from the very beginning of inception of Taylor series from power series. That is derivation of Taylor series from first principle
Professor Dave, this was amazingly helpful! Thanks so much!
Thanks man. Only video that explains this topic clearly.
Thank you sir for your dedication! 🙏
I've done well in studying Calculus so far, but I find this topic quite challenging. Thankfully, it is finally starting to make sense to me, due to Professor Dave's more streamlined approach. Too many instructors think you must know the entire history of China before they can show you how to make a cup of tea.
A full 2h Course down to Just 9 Mins , a tip of the hat to you , thank you
Thanks a lot professor you’re literally the only reason I understood this topic
Great Video! It really helped me understand the rationale behind the Taylor and Maclaurin series. I really appreciate the content.
wow, a month later i finally get this
this is so intuitive! thanks a lot
I'm sending this to my whole class, I just found a new knowledge Bank, thanks professor 🙏🏿
Really helped out. Thank you so much
Where do I donate? You've made a significant difference on my understanding of calculus and physics. Keep pushing out videos please!
Glad to be of service! You can go to www.patreon.com/professordaveexplains or feel free to send any amount you wish to the PayPal account associated with professordaveexplains@gmail.com thanks for your support!
@@ProfessorDaveExplains done! I'll be sure to spread the word about your channel. I appreciate you!
At first thanks to you. I did understood this topic before i saw your video.. Now this topic is very clear as like as water. Thnaks again sir..
i have a test in the next 70 minutes, thanks for this so much!!!!
Very easy-to-understand lecture! Thanks!
Helped me understand it precisely. Thanks 😘😊☺️
Great work professor,you helped me understand
Thank you
3:54 Do you really want any C4 in your series?
thank you sir, I love the way u explain mathematics...
👌👌👌👌👍👍👍
This taught me the logic!! Thank you so much
Derivative to e^x is e^x yes this fact we know from Maclaurin series, but we want derive e^x by using Maclaurin series we get infinite loop logic.
We were taught this in College on this Thursday 😃
Mine today
i like how everyone is saying you make this simple and easier to understand yet im still extremely lost
Been watching you as my guide for my class discussion. Great job Prof. Dave. GBU
Thank you for this
Very beautiful. Thank you.
Great video Prof. Dave
I've learned a lot , but there's something you forget with the Checking Comprehension (number 2 problem)
There's no , P_0(x)= f(1)=2 🌺💗
Thank you. Dave is amazing
Well explained sir.Thankyou
Fantastic explanation, thank you.
Thank you professor, that was quite helpful ❤
amazing! finally understood this
You explain very clearly!
So clearly explained. Please also cover Laurent series. I have the bell icon on
8:50 hi everyone. Where do coefficients 5 6 4 1 come from?
We evaluated that its derivatives are:
f'(x) = 4*x^3 + 1
f"(x) = 12*x^2
f'"(x) = 24*x
f""(x) = 24
Evaluate all of these at x=1:
f'(1) = 4*1^3 + 1 = 5
f"(1) = 12*1^2 = 12
f'"(1) = 24*1 = 24
f""(1) = 24
Now divide each of these by their corresponding factorials:
f'(1)/1! = 5
f"(1)/2! = 12/2 = 6
f'"(1)/3! = 24/6 = 4
f""(1)/4!= 24/24 = 1
It's zeroth derivative at x=1, is zero, because the original function is x^4 + x - 2, which evaluates to zero
Thus, we get:
T(x) = 5*(x - 1) + 6*(x - 1)^2 + 4*(x - 1)^3 + 1*(x - 1)^4
Since this already is a polynomial, it's really redundant to do a Taylor series. Any application of a Taylor series, could easily be done directly with the original function. All we need to do is shift the original function, so its input is centered on x=1.
Given:
f(x) = x^4 + x - 2
Let X = x - 1, and rewrite it in terms of capital X.
Thus: x = X +1
(X + 1)^4 + (X + 1) - 2
Expand & simplify:
X^4 + 4*X^3 + 6*X^2 + 4*X + 1 + (X + 1) - 2
X^4 + 4*X^3 + 6*X^2 +5*X
Replace X with (x - 1), and reverse the order:
(x - 1)^4 + 4*(x - 1)^3 + 6*(x - 1)^2 + 5*(x - 1)
Result:
f(x) = 5*(x - 1) + 6*(x - 1)^2 + 4*(x - 1)^3 + (x - 1)^4
Thank you so much, this video was a lifesaver!
thank you so much!
8:10 I need the reason why the radius of convergence is infinite not negative infinite as it is less than 1
Waaao sir great demonstration, u hv made it clear and easy for students. thank you very much
Thank-you pro it's very helpful
Thank you
really helpful, thanks
Thanx Prof. Dave! 😊
OMG this video explain the whole thing incredible clear🎉
Lot's of love man. You are the bomb! When I was watching your video, I couldn't help nodding. I was just like "mmmm Math makes sense after all".
Thank you so much
Thanks a lot sir 🎉
I love this video. Very clear. Nice job. 👍👍
Brilliant explanation, but also how do we call "a" in this topic, when we say function is centered at a=1?
Basically it's f(a) and as it says centered at 1 so f(1) so like it says nth derivative of f(a) so first you find the derivatives then plug in the value
OMG this is so much helpful
finally understood thank you so much
Super helpful video!
i think i love you professor dave
concise video❤
i am at 8:53.
you have made a mistake, you showed the message the Taylor series is expanding with expansion about x=0, at (5:55) the grammar of the message is wrong, it is not the taylor series and the sentence should be saying a Taylor series is expanding through expansion and x is about 0. unless you meant at that point where x=0 or at the point where x is about 0.
6:14 (definitions)
6:35(maclurin series and base e)
you also did not explain why the top terms can go away properly. the proper explanation is: the maclurin series is the wrong type of maclurin series on its own is wrong and doesn't have all the right terms for it. hence we correct it, to get the right maclurin series and to get the right maclaurin series expression we must work from e^0=1 and e^x=1, thus x=0. we cancel 0 from e^0 from e^0=1 and from sigma where the end point is infinity and n=0 and the rule given is f^n)(0/2!. f gets replaced by e since f^2=1 when n=0 and e^0 this replaces 0 with x since x=0 thus getting the right type of maclurin series that represents f(x)=e^x i.e the sigma where infinity is the end point and n=0 is the starting point and x/2! and x^n is on the right of the fraction..
also you have not explained how to get the Taylor series for the last questions. the explanation seemed to be: do f(x)=1/ x, f"(x)=-1/x^2, f"'(x)=2/x^3, F(4)x=-6/x^4, fx=x-1-(x-1)^2/2+x-1^3/3-x-1^4/4 since n gets substituded for a, and that we also must be do that because the limit approaches infinity and adding 3 side way dots after saves you time since the dots means what comes after and that adding 3 dots after takes hardly any time compared to including the rest of the fractions. for problems like that substidue n for x making f(x). for finding the taylor series for x^4+x-2 centered at a=1, we subtract the power 4 by 1thus gettung the power 3 and substituting x for 1 or whatever the value of a is given for.
excellent way of explaining. I got amazed with your explanation and did lot of calculus sums. Sir I will be sending very special 4 questions through email to you. Please be kind enough to reply. Interestingly waiting for your explanation . Thanks
Thanks so much!
My undergrad courses made me hate calculus you made me propose to it!
This hit different
thx prof dave
Thank you man
Thank you sir
Thankyou sir
better than the calc prof i pay 1.5k a semeseter for smh
I'm Sri Lankan .....you are a really great professor...i really appreciate it..... Don't you like to visit sri Lanka
i would love to! if your school will pay for me to come out and speak, i'm there!
this is the same way we get all trigonometry series mostly used sin and cos
Very good
dude said: "lets check comprehension" and I thought he was gonna give us a comprehension check for all of calculus ... phew.
Thank u so much
Omg thanks Math Jesus
Dont understand at all, all these numbers seem like Harry Potter magic.
thank you soo much!
you are an absolute LIFESAVER, God bless 🤍
Do you have a video tutorial on Lorentz series?
Well done sir 👍👍👍
finding this before my calculus exam being like, wait this isnt discovery institute but its still Dave
Namaste
It is very easy to understand you