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!
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
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 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.
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.
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.
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.
+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!
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!
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!
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.
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.
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.
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 TH-cam.
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!
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!
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 :(((
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.
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.
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
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
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 🤣
This guy knows how to teach.
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.
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 :)
You've done the impossible, you've made calculus easy. Props to you good sir.
I literally watch your lectures instead of attending my own. Unsurprisingly, I don't struggle on the tests at all as a result.
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
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!
Bro you're so good at explaining this. When you summed it up around 27min I finally understood it a little more.
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
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
You have a gift, and use it very well. Thank you Mr. Leonard.
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 all your hard work, which allows me to passively watch it while i do dishes...jp
But i am doing dishes right now
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. :)
You are the best professor I have ever had by a long shot!
thank you so much for doing this.
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.
Thank you so much who ever placed and popup on you tube right now, Thank you Prof Leonard
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.
What this man posted online is priceless. Better than any shit I ever paid for.
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!
please post Linear algebra vidoes
professor Leonard thank you so much for making calculus seem so explicit and understandable.
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.
I LOVE YOOUUU SO FUCKING MUCH YOU HAVE NOOOOO IDEAA, YOU SAVED MY LIFE I LOVE YOU
One of the more challenging topics in Calc II made very clear. Very nice job!!
Thank you sir for all you effort...Now finally I understand approx of taylor polynomial
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.
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
+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
Always brings the quality
thank u so muuuuuuuuuuuuch prof. best ever.....looking forward to calculus 3
It's amazing that I understand a calculus professor in English better than a professor at my university in my native language. Thank you
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
awesome am a kenyan engineering student ......prof Leornard you are the best .....i learn my engineering course in Kenya USA .....THANKS
45:57 part 2
Why did you stop uploading😢
it is 2024 and still the bast professor ever you saved a lot of students
passed all my calc and diff courses in CC thanks to your videos. Now in university I'm back to review! Thank you!!
Always helping bro
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!
dude you just gave me so much knowledge in this one lecture, this is insane. thank you so much.
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!
I didn't see any comments for this but if you are studying for Taylor's Inequality (Taylor's Remainder Theorem)
- 5:28
Prof Leonard: What's our C?
Class: One
Prof Leonard: Si 😃
God bless prof. Leonard for eternity !
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 so much
Thanks from India 🇨🇮
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.
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.
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 TH-cam.
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!
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!
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 :(((
thank you so much! because of you my test grades improved from 75 to 93!
thank you for this video needed it for my numerical analysis class
Everything you do is gold!
Thank You Professor Leonard! Thanks A Lot!
wonderfully well explaination
Omg thank you soo much for posting your teaching. Lesson you make everything magical so clear 😭😭
this z really cool Teaching....
i giv you a high 5 Sir
Thank you Professor Leonard
You have amazing method for teach
Thank you again and again ...
Aaaah just 26 subscribers more and he has the silver play button! He really deserves that!
Guys
So does Z not have to be bigger than C if the given interval gives us a smaller error value??
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
you're a blessing on my life, thankyou
great sir
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 ?
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
Thank you for making calculus enjoyable
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 when are you uploading, double and triple integral videos?
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.
Great lecture! Thank you.
I don't like many videos but I like this video to increase the worlds awareness of how a teacher is supposed to teach
My A- on my midterm is all thanks to you!
God bless. Our professor always managed to get across topics but this chapter he just fell off. Thank you so much!
Nice work..
48:40
can you use any series to calculate logarithms outside the traditional radius of convergence? like ln5?
Is there mistake at 45:10 in which he writes "around X = 4" instead of "around C = 4" ??
Thank you for the explanation, Professor Leonard!
Thank you! That was great! I appreciate how you explain everything
Dealed very well with questions.
Thanks smart guy
@kashmir
you are Just a blessing prof
Does anyone know a good physics channel?
I'm trying to be in this guy's class, easy and simple to understand
Thank you for all labors.
Definitely watching your calc 3 course before second year
Oh man thnx! I wish u were my professor. Your teaching style is great.
professor leonard is the best professor in the world.
Awesome explanation!
Thanks Again 💗💝💛😘😘😘😘