Very quickly in college you realize that there are two types of professors. Those who are there to teach, and those who are there to conduct a class. Thank you for teaching mathematics. Professors such as yourself are the reason I have always loved math. This is a wonderful explanation of Taylor polynomials. Keep it up!
My college needs professors like this... God I couldn't understand a single thing they were saying and everything this guy said is so incredibly clear. Subscribed
Hey, I just wanted to thank you so much for uploading these videos. I found out about your channel through constant searching and I decided to give you a shot to see if you would be able to help me understand the content. I watched all of the videos that you had on the series and sequences for my last exam and I got a 100! Now I just finished watching the power series and Taylor series videos and I hope that I'll do just as well as I did in my last exam. You're a phenomenal teacher and I hope that lots more people can find out about your channel, thanks again!
Laurelindo I agree. Unfortunately, my instructor just breezes through the material and the class is lost half the time. Then, he gets frustrated when we spend too much time asking questions. Thanks to Leonard for the extra clarification on what can be a very challenging subject!
There is a lot more I can say, but for now I just want to say that, your videos are very effective, they work for us, and they are awesome. Actually this is a calling for you. I like it. We thank God for you. Mr C.S. Mhlongo in South Africa
Thank you for getting me through Calculus 2! My professor doesn't provide any form of notes/lecture or guidance, he just gives daily quizzes on material we are expected to know. I appreciate all of your help!
Hey prof, I can't thank you enough failed calc 2 the first time and then i found your videos. I now passed the class with a 90, I owe you one big time.
Hey Professor, you should set up a patreon or some sort of donations box. I feel a lot of gratitude towards you and would be more than happy to donate some money.
Why he become old so fast? This is from 8 years ago and when i see him in his new videos , he changed a lot. Thanks for having amazing pple like him in this world.
thank you so much for being an excellent, hilarious, and engaging professor. if my calc professor didn't take attendance i'd skip and just watch your videos!
Tbh Taylor Polnomials are AMAZING. I might sound super nerdy, but being able to approximate ANY number without a calculator just sounds like pure genius its truly amazing.
So apparently you are a well known at my school and people directed me to your channel for help but holy hell how can i pay attention when those guns are just huge. O.O
If I ever become a minister in charge of education, then I will pass a law that all math teachers who sucks at teaching should take Math teaching course under Prof. Leonard. It will be mandatory, otherwise they will be fired from teaching, and demoted to support administration staff. Because teaching is serious business, as it is either shaping the future of students, or destroying their future. I will not allow the latter to happen !!!! Especially when we have gold standard like Prof. Leonard is around. Any body who has a problem with that please contact me directly . Thanks.
This is the best calculus 2 ever. The videos and style of teaching are so much better than the calculus class I have, plus it is really helpful for the exams! Need help for calculus 3 next semester! Thank you!
Professor Leonard, thank you for an excellent explanation on the Approximation of Functions by Taylor Polynomials in Calculus. The different examples really breakdown and analyze the Approximations of different Functions by Taylor Polynomials. All Transcendental Functions can be represented as Taylor Series/Polynomials. This is an error free video/lecture on UA-cam.
Thanks to your videos, I got an 85% on my final Calc II test. My final grade was high enough that I didn't need to retake the course. Thank you so much for these!
+Professor Leonard I live in San Diego, and your lectures are the best! They are really benefiting me. Do you happen to teach Intro to Linear Algebra, or do you have any recorded linear algebra lectures? I'm taking it next semester and I don't know how will I pass without your lectures... Thanks a million!
Thanks @professor Leonard. You just saved my semester. I'm a computer science student - sophomore. Couldn't be much better. You're really a great teacher.
You, my good sir, are unlike ALL of my professors and teachers who only portray Math and calculus as something we HAVE to learn to just "be done with our term". You make it sound interesting, and totally catch the attention of everyone in the lecture room, even that of those attending your lectures on the screen... TEACH AT OUR UNIVERSITY PLZZZZ :(((
these videos are a life saver. Only problem is, the last section of my class is solving differential equations using power series, which doesn't seem to be in this section, and none of the other sections i've looked at cover the specific problems I'm expected to solve.
I really wish I watched your videos in Calculus 1. I am in Calculus 2 and I watched the whole 9.1-9.9 series (I also missed out on integrals). I dont even go to my classes because my professor teaches from slides and it is really hard to focus. I am going to take differential equation in the summer and guess what? I am just going to watch your lectures. Thank you Professor Leonard.
I hope I could find out your video earlier bc I will have my final tomorrow, I don't have time to watch all over, so sad!! however, thank you so much for record the video, you are really a saver for college students!
If some wants a fourth degree approximation of Sine(x) centered at zero, would they have only 2 nonzero terms because the 2nd and 4th derivatives are zero when c=0 ?
I made the previous comment because to understand Taylor series (which is nothing but a Polynomial constructed by power integration of serially higher differentials) one must have 2 concepts 1) Concept of the Remainder Error (RE) and 2) How the RE requires a subsequent higher differential. For if the subsequent higher differential ever becomes finally zero, as it can with some functions, then a Taylor series, if used, does come to an end. True one may not need a Taylor series in those functions but its a matter of developing the basic concepts of what a Taylor series basically is.
Professor Leonard i am having problem with derivation of the error.in my book bartle sherbert they used relle's theorem to prove it.but why rolle's theorem is used i can't understand.please explain me .i can"t understand.
the second statement of lagranges form of remainder i.e, fn-1 is derivable on open interval (a,b)...why not on closed interval? what mistakes would occur if derivable on closed interval?
and yah what is the meaning of function is centered at c? i think that centered at c means not at centre always,but c is any point between two intervals....
True one may not need Taylor series for Functions which have a final derivative which becomes zero but in theory and conceptually we can. I mention those chiefly to emphasize the concept of Remainder Error (RE) and how the RE requires a non zero subsequently higher differential.
So you calculate the biggest possible error. The value calculated by taylor polynomials of that function is a certain number away from the actual value. Does this mean that the approximated value cannot be "more away" than the calculated error? can the approximated be closer to the actual value, thus closer than the calculated error?
Very quickly in college you realize that there are two types of professors. Those who are there to teach, and those who are there to conduct a class.
Thank you for teaching mathematics. Professors such as yourself are the reason I have always loved math. This is a wonderful explanation of Taylor polynomials. Keep it up!
finally, chapter complete. this marathon is more enjoyable than watching madame web
This guy knows how to teach.
This man is saving every college student in New York City, bless your soul!
Not only NY but all over world...
His teachings aren't just limited to us New Yorker's 😅
im in south africa being saved rn@@davida99 🤣
My college needs professors like this... God I couldn't understand a single thing they were saying and everything this guy said is so incredibly clear. Subscribed
I hear your voice in my head while I evaluate problems on my test... is that cheating? You're just that dang good dude. Keep em' coming.
I literally watch your lectures instead of attending my own. Unsurprisingly, I don't struggle on the tests at all as a result.
You've done the impossible, you've made calculus easy. Props to you good sir.
Hey, I just wanted to thank you so much for uploading these videos. I found out about your channel through constant searching and I decided to give you a shot to see if you would be able to help me understand the content. I watched all of the videos that you had on the series and sequences for my last exam and I got a 100! Now I just finished watching the power series and Taylor series videos and I hope that I'll do just as well as I did in my last exam. You're a phenomenal teacher and I hope that lots more people can find out about your channel, thanks again!
Great job!! keep up the good work :)
Prof.leonard always great keep teaching us with great enthusiasm that you have
You are awesome. Please come teach at UCLA. I wish UCLA professor's were half as good as you
Such an awesome teacher. Sounds like he always makes sure his students are completely on board before moving forward!
Laurelindo I agree. Unfortunately, my instructor just breezes through the material and the class is lost half the time. Then, he gets frustrated when we spend too much time asking questions. Thanks to Leonard for the extra clarification on what can be a very challenging subject!
You have a gift, and use it very well. Thank you Mr. Leonard.
It's amazing that I understand a calculus professor in English better than a professor at my university in my native language. Thank you
There is a lot more I can say, but for now I just want to say that, your videos are very effective, they work for us, and they are awesome.
Actually this is a calling for you. I like it.
We thank God for you.
Mr C.S. Mhlongo in South Africa
Bro you're so good at explaining this. When you summed it up around 27min I finally understood it a little more.
Thank you for getting me through Calculus 2! My professor doesn't provide any form of notes/lecture or guidance, he just gives daily quizzes on material we are expected to know. I appreciate all of your help!
Thank you so much who ever placed and popup on you tube right now, Thank you Prof Leonard
went from literally 48% on first test to 100% on my last test before the final you saved my life, can't thank you enough!
Thank you all your hard work, which allows me to passively watch it while i do dishes...jp
But i am doing dishes right now
Hey prof, I can't thank you enough failed calc 2 the first time and then i found your videos. I now passed the class with a 90, I owe you one big time.
One of the best professors I've ever been able to experience. Thanks again for all these fantastic videos!
Hey Professor, you should set up a patreon or some sort of donations box. I feel a lot of gratitude towards you and would be more than happy to donate some money.
Thanks!!! I actually do have a Patreon account set up. I am very happy to have helped you. :)
professor Leonard thank you so much for making calculus seem so explicit and understandable.
You are the best professor I have ever had by a long shot!
I thought i would be bored watching an hour plus ,but after your explain i can watch more of your hours than anyother thank very much
Why he become old so fast? This is from 8 years ago and when i see him in his new videos , he changed a lot. Thanks for having amazing pple like him in this world.
thank you so much for being an excellent, hilarious, and engaging professor. if my calc professor didn't take attendance i'd skip and just watch your videos!
Tbh Taylor Polnomials are AMAZING. I might sound super nerdy, but being able to approximate ANY number without a calculator just sounds like pure genius its truly amazing.
it is 2024 and still the bast professor ever you saved a lot of students
So apparently you are a well known at my school and people directed me to your channel for help but holy hell how can i pay attention when those guns are just huge. O.O
thank u so muuuuuuuuuuuuch prof. best ever.....looking forward to calculus 3
passed all my calc and diff courses in CC thanks to your videos. Now in university I'm back to review! Thank you!!
I didn't see any comments for this but if you are studying for Taylor's Inequality (Taylor's Remainder Theorem)
- 5:28
What this man posted online is priceless. Better than any shit I ever paid for.
One of the more challenging topics in Calc II made very clear. Very nice job!!
If I ever become a minister in charge of education, then I will pass a law that all math teachers who sucks at teaching should take Math teaching course under Prof. Leonard. It will be mandatory, otherwise they will be fired from teaching, and demoted to support administration staff. Because teaching is serious business, as it is either shaping the future of students, or destroying their future. I will not allow the latter to happen !!!! Especially when we have gold standard like Prof. Leonard is around. Any body who has a problem with that please contact me directly . Thanks.
Just replace the lectures with these youtube videos and just have the student come in for periodic exams/quizzes.
Thank you sir for all you effort...Now finally I understand approx of taylor polynomial
I'm about to have my Calc 2 final this Friday. Thank you for all the videos you have uploaded. You've helped me understand these concepts.
awesome am a kenyan engineering student ......prof Leornard you are the best .....i learn my engineering course in Kenya USA .....THANKS
This is the best calculus 2 ever. The videos and style of teaching are so much better than the calculus class I have, plus it is really helpful for the exams! Need help for calculus 3 next semester! Thank you!
please post Linear algebra vidoes
dude you just gave me so much knowledge in this one lecture, this is insane. thank you so much.
You are singlehandedly saving my engineering calc 2 class here in Utah. We just had a watch party of your lectures in our class discord XD
I LOVE YOOUUU SO FUCKING MUCH YOU HAVE NOOOOO IDEAA, YOU SAVED MY LIFE I LOVE YOU
Professor Leonard, thank you for an excellent explanation on the Approximation of Functions by Taylor Polynomials in Calculus. The different examples really breakdown and analyze the Approximations of different Functions by Taylor Polynomials. All Transcendental Functions can be represented as Taylor Series/Polynomials. This is an error free video/lecture on UA-cam.
Thanks to your videos, I got an 85% on my final Calc II test. My final grade was high enough that I didn't need to retake the course. Thank you so much for these!
thank you so much! because of you my test grades improved from 75 to 93!
I don't like many videos but I like this video to increase the worlds awareness of how a teacher is supposed to teach
+Professor Leonard I live in San Diego, and your lectures are the best! They are really benefiting me. Do you happen to teach Intro to Linear Algebra, or do you have any recorded linear algebra lectures? I'm taking it next semester and I don't know how will I pass without your lectures... Thanks a million!
find any good resources for LA? I'm needing that right now !!
@@dj1984x kimberly brehm Linear Algebrae playlist
Thanks @professor Leonard. You just saved my semester. I'm a computer science student - sophomore. Couldn't be much better. You're really a great teacher.
45:57 part 2
Thank you Professor Leonard
You have amazing method for teach
Thank you again and again ...
You, my good sir, are unlike ALL of my professors and teachers who only portray Math and calculus as something we HAVE to learn to just "be done with our term". You make it sound interesting, and totally catch the attention of everyone in the lecture room, even that of those attending your lectures on the screen... TEACH AT OUR UNIVERSITY PLZZZZ :(((
these videos are a life saver. Only problem is, the last section of my class is solving differential equations using power series, which doesn't seem to be in this section, and none of the other sections i've looked at cover the specific problems I'm expected to solve.
thank you so much for doing this.
I really wish I watched your videos in Calculus 1. I am in Calculus 2 and I watched the whole 9.1-9.9 series (I also missed out on integrals). I dont even go to my classes because my professor teaches from slides and it is really hard to focus.
I am going to take differential equation in the summer and guess what? I am just going to watch your lectures.
Thank you Professor Leonard.
Omg thank you soo much for posting your teaching. Lesson you make everything magical so clear 😭😭
Could you do a video on the gamma function. I know the basis behind it involves series, but i want to know what its linked to how to use it
Always brings the quality
I hope I could find out your video earlier bc I will have my final tomorrow, I don't have time to watch all over, so sad!! however, thank you so much for record the video, you are really a saver for college students!
can you use any series to calculate logarithms outside the traditional radius of convergence? like ln5?
thank you for this video needed it for my numerical analysis class
Thanks from India 🇨🇮
Aaaah just 26 subscribers more and he has the silver play button! He really deserves that!
God bless prof. Leonard for eternity !
God bless. Our professor always managed to get across topics but this chapter he just fell off. Thank you so much!
Thank You Professor Leonard! Thanks A Lot!
If some wants a fourth degree approximation of Sine(x) centered at zero, would they have only 2 nonzero terms because the 2nd and 4th derivatives are zero when c=0 ?
you're a blessing on my life, thankyou
Everything you do is gold!
I made the previous comment because to understand Taylor series (which is nothing but a Polynomial constructed by power integration of serially higher differentials) one must have 2 concepts 1) Concept of the Remainder Error (RE) and 2) How the RE requires a subsequent higher differential. For if the subsequent higher differential ever becomes finally zero, as it can with some functions, then a Taylor series, if used, does come to an end. True one may not need a Taylor series in those functions but its a matter of developing the basic concepts of what a Taylor series basically is.
My A- on my midterm is all thanks to you!
Thank you for making calculus enjoyable
this z really cool Teaching....
i giv you a high 5 Sir
Prof Leonard: What's our C?
Class: One
Prof Leonard: Si 😃
Guys
So does Z not have to be bigger than C if the given interval gives us a smaller error value??
Dealed very well with questions.
Thanks smart guy
@kashmir
Professor Leonard i am having problem with derivation of the error.in my book bartle sherbert they used relle's theorem to prove it.but why rolle's theorem is used i can't understand.please explain me .i can"t understand.
Can someone explain why in 1:31:06 does f^(n+1) (x) is +- sin or +- cos?
professor when are you uploading, double and triple integral videos?
I love your lecture, it’s much clear than my professor
the second statement of lagranges form of remainder i.e, fn-1 is derivable on open interval (a,b)...why not on closed interval? what mistakes would occur if derivable on closed interval?
Oh man thnx! I wish u were my professor. Your teaching style is great.
I'm trying to be in this guy's class, easy and simple to understand
Always helping bro
58:46 If x = 5 and c is 4, it doesn't make any sense to pick Z = 3. Didn't you say that Z must be between c and x?
it can be equal to either c or x too
and yah what is the meaning of function is centered at c? i think that centered at c means not at centre always,but c is any point between two intervals....
Is there mistake at 45:10 in which he writes "around X = 4" instead of "around C = 4" ??
professor leonard is the best professor in the world.
great sir
Thank you for the explanation, Professor Leonard!
Great lecture! Thank you.
Why did you stop uploading😢
wonderfully well explaination
True one may not need Taylor series for Functions which have a final derivative which becomes zero but in theory and conceptually we can. I mention those chiefly to emphasize the concept of Remainder Error (RE) and how the RE requires a non zero subsequently higher differential.
Professor, do you know what is the approximation in series that is use in calculators and computers due that the Taylor series never end?
So you calculate the biggest possible error. The value calculated by taylor polynomials of that function is a certain number away from the actual value. Does this mean that the approximated value cannot be "more away" than the calculated error? can the approximated be closer to the actual value, thus closer than the calculated error?
06:30
Isn't the remainder another infinite series from the n+1th derivative to infinity?
Why is the 7:30 Rn just a single derivative?
How is choosing c making the erorr larger in the lnx example but 1.1 isnt?