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. :)
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.
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 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’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!
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...
Searching for this topic in the German RUclips 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.
Wow. Currently, I'm studying in a nuclear bunker while outside are bomber planes and tanks rolling into the city while a crowd of people gathered outside the street to watch a Taylor Swift concert while the GameStop near my house just released GTA6 and people are flooding into my house thinking its a GameStop and still I hear every concept in your videos loud and clear. I LOVE THIS CHANNEL
Just finished calculus, will head towards Advanced Math series. My suggestion would be to show one example per math concept where and how it could be applied in real life situation (a playlist with application of these concepts). For example how you can apply Taylor series. This is how I understood what it really does. Basically applied math is where I truly understand and memorize concepts, without real case scenarios it's harder for me to grasp these concepts.
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.
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
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.
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!
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.
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
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 🌺💗
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.
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
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
The n=0 term is a constant. Take the Taylor series of cos(x) as an example: cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ... Implicit in the zeroth term of this series (i.e. 1), which equals 1, is 1*x^0. For all x's other than zero, this of course reduces to 1*1. For x=0, the 0^0 term in this context, is its limit, which approaches 1 from both sides.
Everything looks good to me. Don’t forget that we need to plug in the a or the number where the series is centered, and then use that to find the coefficient or the c sub n. You would need to divide each derivative evaluated at a point by n!
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
That’s incredible man. You learned algebra all the way through calculus from just this channel 🤯. Hats off to you
@ xD
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?
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?
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’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!
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...
Searching for this topic in the German RUclips 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.
Wow. Currently, I'm studying in a nuclear bunker while outside are bomber planes and tanks rolling into the city while a crowd of people gathered outside the street to watch a Taylor Swift concert while the GameStop near my house just released GTA6 and people are flooding into my house thinking its a GameStop and still I hear every concept in your videos loud and clear. I LOVE THIS CHANNEL
I don't find any words in telling u how clear and simple u make the videos .. lots of respect and love to u !!
Just finished calculus, will head towards Advanced Math series. My suggestion would be to show one example per math concept where and how it could be applied in real life situation (a playlist with application of these concepts). For example how you can apply Taylor series. This is how I understood what it really does. Basically applied math is where I truly understand and memorize concepts, without real case scenarios it's harder for me to grasp these concepts.
I think man you are god gifted teacher. The world needs your lectures, keep it up bro!
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.
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
This video has given me some hope to not give up just yet.
ohh professor dave you are naturally ahead.... this video makes me clear understand about taylor's and maclaurin series
Great video, thanks, wanted to point out at 6:01, it should be a=0 and not x=0 for Maclaurin series.
Professor Dave you really save my life!
Truly a legend, thank you lots ❤
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
A full 2h Course down to Just 9 Mins , a tip of the hat to you , thank you
wow, a month later i finally get this
Thanks a lot professor you’re literally the only reason I understood this topic
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!
Thanks man. Only video that explains this topic clearly.
I'm sending this to my whole class, I just found a new knowledge Bank, thanks professor 🙏🏿
Professor Dave, this was amazingly helpful! Thanks so much!
Great Video! It really helped me understand the rationale behind the Taylor and Maclaurin series. I really appreciate the content.
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..
such a goated explanation you deserve a million dollars goat
i like how everyone is saying you make this simple and easier to understand yet im still extremely lost
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.
i have a test in the next 70 minutes, thanks for this 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.
Very easy-to-understand lecture! Thanks!
8:10 I need the reason why the radius of convergence is infinite not negative infinite as it is less than 1
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".
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. Dave is amazing
this is so intuitive! thanks a lot
3:54 Do you really want any C4 in your series?
This taught me the logic!! Thank you so much
finding this before my calculus exam being like, wait this isnt discovery institute but its still Dave
Helped me understand it precisely. Thanks 😘😊☺️
Really helped out. Thank you so much
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 professor, that was quite helpful ❤
We were taught this in College on this Thursday 😃
Mine today
Been watching you as my guide for my class discussion. Great job Prof. Dave. GBU
Great work professor,you helped me understand
Thank you
thank you sir, I love the way u explain mathematics...
👌👌👌👌👍👍👍
My undergrad courses made me hate calculus you made me propose to it!
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.
dude said: "lets check comprehension" and I thought he was gonna give us a comprehension check for all of calculus ... phew.
Well explained sir.Thankyou
better than the calc prof i pay 1.5k a semeseter for smh
Waaao sir great demonstration, u hv made it clear and easy for students. thank you very much
Fantastic explanation, thank you.
So clearly explained. Please also cover Laurent series. I have the bell icon on
In the second comprehensive problem why we did not evaluated f of a in the first term
OMG this video explain the whole thing incredible clear🎉
amazing! finally understood this
Thank you so much, this video was a lifesaver!
You explain so much better than my teacher
You explain very clearly!
Omg thanks Math Jesus
Dude i respect you just like my dad
Dont understand at all, all these numbers seem like Harry Potter magic.
I love this video. Very clear. Nice job. 👍👍
Thanx Prof. Dave! 😊
Do you have a video tutorial on Lorentz series?
Isn’t the coefficient of c4 supposed to be 24 for the second derivative instead of 12? The coefficients are virtually factorials, aren’t they?
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!
Very beautiful. Thank you.
Thank you for this
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
this is the same way we get all trigonometry series mostly used sin and cos
Why can we plugin 0 as a to generalize to the cases when a equals other numbers?
concise video❤
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
Super helpful video!
should the Taylor series in the first checking comprehension drill be just ln x?? because of the zeroth derivative
Well done sir 👍👍👍
you are an absolute LIFESAVER, God bless 🤍
But when you put x = 0 , then the whole series become zero because x^n = 0^n = 0 . Why putting x = 0 in only one step and not further step?
The n=0 term is a constant.
Take the Taylor series of cos(x) as an example:
cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! + ...
Implicit in the zeroth term of this series (i.e. 1), which equals 1, is 1*x^0. For all x's other than zero, this of course reduces to 1*1. For x=0, the 0^0 term in this context, is its limit, which approaches 1 from both sides.
Thank-you pro it's very helpful
I didn't fully understood this video. He should have been more specific when making the substitutions of variables.
8:49 how can this be even possible where's f''' and f''
Everything looks good to me. Don’t forget that we need to plug in the a or the number where the series is centered, and then use that to find the coefficient or the c sub n. You would need to divide each derivative evaluated at a point by n!
OMG this is so much helpful
i think i love you professor dave
I have an exam in 10 minutes, thanks
I got sigma (-1)^n-1 * (x-1)^n / n for f(x) = lnx Taylor series at a=1?
I got sigma (-1)^n-1 * (x-1)^n / n x^n
Thank you
finally understood thank you so much