Ok, gals and guys, these videos definitely work. I quit my textbook and stopped paying attention in class and took the risk of learning all the theory for the integral techniques test (everything from integration by parts up to improper integrals) using just these videos (of course I still used the text for the practice problems and I practiced A LOT). Yesterday I got my test and aced it with a perfect score. Thanks, Professor Leonard, for such an excellent job! Onward to series now...! By the way, please DO pay attention in class and don't do like me. :)
I got the finals results today and guess what? I passed calc 1 and 2 thanks to your videos!! Thank you so much, professor Leonard! These lectures have been a great help throughout the semester.
Jesus christ I watched this entire thing and I actually understand it...I'm debating on whether I should even bother going to my lecture next week when I can learn it 10x better here
I feel the same way sometimes. For Calculus I enjoy professor Leonard's style as well as others to learn, and for other topics such as physics I listen to Michel Van Biezen. It literally feels like a waste of time attending lecture at the brick and mortar school. I only go because of the occasional pop quiz and in class homework that is part of my grade.
@@animeshmajumdar66 Im going to be honest I'm not the best at calc so I don't know if I'm right, but he said something about at pi/2 its asymptotic, but if you look at the line you can see that it goes on up forever (infinity). This is similar when we were talking about e(infinity) which equaled infinity. Again I'm not 100 percent certain I'm correct, but this is what gets me through calc 2.
The only thing I can say is i love you. Calc 1 final got 98%, taking calc 2 right now and thanks to YOU I am acing my tests!!!! I hope you win the lottery or something..Thanks again!
This guy is really talented. I am a math tutor myself, but he's just on top of the game. I wish my teachers at the University had at least half of the teaching skills of this Professor !!
He said they would spend 3 days on improper integrals.... My calc 2 prof did it in one day.... moving way too fast. Luckily with superman here I can review/relearn some topics. Thanks for the videos!
After 3 days, it is my final, and I still rely on you. You saved my academic life. Thanks for everything in Calculus1. I hope, we will continue the path in Calculus 2 as well
I’m older and went back to school last year to work on an engineering degree. Even though I’d already taken calculus for my business degree, I had to retake it due to how long ago I took it because engineering requires calc 2, 3, and a couple more advanced math classes. I will say I would love to have a professor like this one. So far after calc 1 and into calc 2 this year, all my professors do is write a problem, work it out, and move on. No clear explanations, no sort of interaction. It’s just watching someone do algebra, trig, and then calculus. After class I come here, look up the section, pretend I’m in this class and have a way better understanding and sharper tools in the tool box to take on the homework. Thank you for these recordings. You are a great teacher.
Oh my god you have saved me.... I just discovered you and I’m taking calc right now and has a professor who doesn’t show up to lecture 50% of the time and can’t teach for heck. Thank god😭😭😭😭
I am quarantined at home from work due to the fact of the Coronavirus and that I have a wife that is 8 months pregnant ,two kids (3 and 2), and school is shut down here in Colorado. No, I do not have the virus but my work is awesome and let me stay home to take care of my wife and kids. While they are resting, do I just game and waste my time? NO!!!! I am relearning Calculus 2 so I can move on to Calculus 3 and DE so I can start my math and physics degree double major. I took a weird path, I have a bachelors degree and a masters already but I want one in math and physics now. I am taking full advantage of my situation! Update: I completed a math degree last week (April 25, 2021). I give all the credit to Professor Leonard!!! Without him, it would not have been possible. Instead of a physics degree, I am instead applying to a PhD program in Aerospace Science at the University of North Dakota.
Because I usually lose my focus in class, thinking about other things, your lectures were extremely helpful for me. Because I can pause and rewind if i lost my focus. Thank you prof. Leonard.
You have an amazing gift for teaching. Thank you so much for all your help!! I have been watching all your calc two videos and this has given me the opportunity to be caught up with all the other kids. Thank you Professor Leonard!!
Professor Leonard, You helped me get an A in my calculus class last quarter. I wouldn't have been able to do it without you. The average grade on the final was a D and I got an A. I can't wait to watch your videos next quarter as well.
Professor Leonard, thank you for a well-organized and excellent explanation of Improper Integrals in Calculus Two. The examples/problems and graphs increase my overall knowledge and understanding of this important topic in Calculus. Remembering to check for infinite discontinuities at the interior points as well as the end points is important when determining an integral is improper. Pattern recognition is also important when solving problems in Mathematics.
The examples at 42:00 are closely related to the concept of power series, for which if p > 1 then the series (hence the integral) converges and if p ≤ 1 the series diverges (hence the integral diverges). The concepts of power series and integrals who involve power series are indeed closely realted to one another.
I'm so proud of me. I was just literally with nothing to do in my life and my mind just thinked... ''I don't know nothing about improper integrals, let me check some nice video'' I thought I won't stand almost 3 hours... And I just not watch all, as I liked all the video and the explanations. So, I'm so thankful for your videos, Professor Leonard!!! I liked this video as if someone liked watching Avengers: Infinity War!
Eventhough your classes are long, the examples are really important for us to understand all the situations that happens in each subject. Please dont change the way you teach. I know that a lot of students dont like it but I think it's really necessary
One little intricacy of his videos is the way he gestures with his arms - when motioning to negative infinite, he motions using his right hand rightward, which is interesting because that's actually, based on a first-person perspective visioning a cartesian, positive infinite. But since his students are facing him (as is the camera), he needs to do everything in reverse from his perspective to make it representative to our perspective. Really neat.
I didn't show up to class 3 times in 3 weeks (9 classes). I made 97 in Calc 2 first test last week, everyone who showed up made 80 and below. My Professor was surprised, but technically I showed up to class (Professor Leonard's UA-cam class) haha
Thanks for all the help. I don't have as much time to watch your videos now since I'm in school (thanks to you I was able to test into Calc 1 last semester) but when I really need help with a subject that wasn't covered well in a lecture I come right back here.
Hello professor!! I just want to hugely thank you for pushing me to face my fear of calculus. I have been cramming your calc 1 and calc 2 playlists and you have no idea how much I depended on you. Your effort in making us understand is applaudable truly, and I have been recommending you to all the ppl I know. I just hope my exam that's in a couple of weeks goes well, but either way, you have been a HUMONGOUS aid to me. Thank you sir once more! Have a nice day
prof Leonard you went beyond my expectations....i am in china struggling with vpn's but still i am able follow you clearly...thank you for saving me...you are super smart.
The world needs more math teachers like you keep up the great work u do make a difference in students life by building confidence in a students belief that they can do it!!!!!!!👍
An amazing teacher aside, you are very humble too, Professor. (see at 49 mins around when you remembered to put the value of "u" back. I have been enjoying your classes on youtube and benefiting from them. :)
Honestly, Professor Leonard makes me fall in love with math a little more every time. I am so happy he makes these videos and I can actually study these concepts. I am so grateful I can understand it.
My Calc 2 class = this video on 1.5 speed with most of the helpful explanations deleted out And its sad because my teacher is awesome, but he rushes through material so fast, and skips over steps that HE CONSIDERS easy or trivial, so you end up lost and have to go on youtube to learn stuff for free that you paid thousands of dollars to learn at university
I have learned more in these 3 hours than I did for a whole week of my professor... Thank you so much! I have a quiz soon and this saved me! I understand it now!
Thank you Professor Leonard, you make these concepts so clear and make sure that class understands what you're doing as opposed to some professors who just throw theorems at you without explanations.
I love this lecture, sadly in my university the part on improper integrals in an exam is only on the comparison test, so I'll actually only use the last 20 mins of the 3-hrs lecture I just saw, but the review on all the integration techniques was invaluable, and even though the explanation was kinda slow, it very precise and accurate, thank you so much.
Learning is beautiful, thank you professor. My teacher literally gave us notes and I didn't know what the hell was going on but this video makes me understand what's actually happening
Thank you so much. You are doing such a great job in teaching, and I understood everything so well, thanks to you. you are such a great teacher. wish you all the very best for everything you do and may the triple gem bless you sir.
dude. these lectures are insanely helpful. I can't imagine passing calculus without the internet and I feel bad for anyone who took calculus 2 before the internet.
1:50:45 It actually makes sense that you cannot account for an infinite amount of removable discontinuities in your integral: since holes have no area, a finite amount of them would be fine (0 * anything is still 0), but an infinite amount of them would be 0 * infinity, which is undefined.
At time 1:14:16, when applying L'Hopital's rule, he says "the derivative of "a" is 1. Isn't "a" a constant, and therefore the derivative is 0 ? At the beginning we selected "a" to "be some number"; it is not a variable. When we apply L'Hopital's, we are strictly taking a derivative, not substituting in infinity, at this point. Similarly, if "a" is a constant, the denominator would be 0 also. And we'd be back to 0/0....My comments here are similar to Ted Chirvasiu's comments below.
When you replace u with x at about 47:30, technically shouldn't you change your limits of integration? So as a general method , wouldn't be better to figure out the indefinite integral separately and then substitute it in? I think this is what is done with the integration by parts at about 1:05:25
weird fact: at 23:24 when he says "smaller and smaller and smaller", his hand motion is nearly perfectly lined with the function on the board behind him which is getting smaller and smaller and smaller
You're the first teacher who put me in this situation. I have to find reasons to watch your videos because I'm preparing for GATE and I wish you taught EVERYTHING. unfortunately I don't have lot of things to revise in maths otherwise would have watched your entire playlist. Loved your lectures sir! You're an amazing teacher. Just try to do more videos on probabilities (conditional and all) because that's bugging me...
awesome, fantastic, fantabulous..... I don't have words to describe your teaching. I become really big fan of yours. We are students of Qatar University (QU) are looking forward for your courses. Thank you very much for your hard working. love you
I wish that math teachers would put _short_ problems in their exams more often; exams at this level shouldn't be a huge drill in arithmetic and algebra, they should be about understanding and solving integrals (for example). Even a simple integral like ∫[x/(x² + 1)⋅dx] would be a perfectly good exam problem.
Love your videos Professor Leonard/ I'm a college student and your videos help strengthen my understanding of calculus and doing the problems assign and one the text book easier.
30 minutes in, you are amazing. Learning by my teacher sucks. She is a nice person but I find that its too much mathspeak for me. I hate mathspeak and your teaching style is in layman terms. Thank you. U are a blessing.
Thank you Sir !!! You are an excellent teacher !!! It is very easy for me to understand the way that you present the material. Please do a series on Calc 3 if you have a chance .
Definitely putting this guy to the top of my list of "people who are gonna help me get through engineering".
+David m and understand it as well.
+David m me 2
+David m Well, your engineering classes are going to be what you do everyday for work...you should enjoy doing them!
+Caleb Harrison I never said I didn't.. And even though I enjoy it its still hard stuff to learn.
+David m Right there with ya.
Time Stamps:
1. Difference between Proper & Improper integrals 0:00-2:02
2. 2 types of improper integrals 2:02-7:38
3. Infinite Intervals example (has 1 ∞) (Pretend its Definite, then approach limit, PD-AL) 7:38-18:07
4. Summary of PD-AL method 18:38-21:40
5. Convergence & Divergence 21:40 - 24:15
6. Infinite interval example (divergent case) 24:40- 31:00
7. How to check if the form 1/x^n is divergent or convergent? 31:15 - 43:45
8. Infinite interval example (has 1 ∞) (convergent case)) 43:50 - 53:20
9. Infinite interval example (has 1 ∞) (divergent case) 53:40 - 59:50
10. Infinite interval example (has 1 -∞) 59:50 - 1:16:12
11. Infinite interval example (has 2 ∞) (Break interval then PD-AL)1:16:12 - 1:33:18
12. Infinite Discontinuities example (left discontinuity) () 1:33:18 - 1:43:01
13. 3 types of infinite discontinuities 1:43:01-1:53:49
14. Infinite discontinuity (right discontinuity) 1:53:49 - 2:03:13
15. Infinite discontinuity (left discontinuity) 2:03:13 - 2:13:46
16. Infinite discontinuity (middle discontinuity) 2:14:36 - 2:16:25
17. Infinite interval (1 ∞) & Infinite discontinuity (left discontinuity)(Break interval then PD-AL at ∞ & discontinuity) 2:16:25 - 2:27:02
18. Comparison test to check for convergence & divergence 2:27:02 - 2:34:26
19. Comparison test example 2:34:26
thank you friend, you are a friend
Much appreciated my man
Thanks mate, amazing job
The best lecturer in calculus
Literally goated
Ok, gals and guys, these videos definitely work. I quit my textbook and stopped paying attention in class and took the risk of learning all the theory for the integral techniques test (everything from integration by parts up to improper integrals) using just these videos (of course I still used the text for the practice problems and I practiced A LOT). Yesterday I got my test and aced it with a perfect score. Thanks, Professor Leonard, for such an excellent job! Onward to series now...!
By the way, please DO pay attention in class and don't do like me. :)
belated congratss
That's what I've been doing since Algebra 1
thats amazinggg anyways hope ur doing well now cuz ur comments from such a long time ago lol
Might have to binge these calc videos Bc I am drowning in my calc II class and it’s only week 5🥲
@@SMARTT3CH bro same. Professor Superman is the only person keeping me afloat right now
Quick show of hands if you're okay with that one
*raises hand and realizes I'm not in the class*
i solve that problem by never being okay with anything
I read that at 15 minutes right when it happened lol
And raised my hand just for fun
every single time...
Same here buddy. It Fucking pains to have to see this cool teacher through phone and not being able to go there..
I got the finals results today and guess what? I passed calc 1 and 2 thanks to your videos!! Thank you so much, professor Leonard! These lectures have been a great help throughout the semester.
Jesus christ I watched this entire thing and I actually understand it...I'm debating on whether I should even bother going to my lecture next week when I can learn it 10x better here
I feel the same way sometimes. For Calculus I enjoy professor Leonard's style as well as others to learn, and for other topics such as physics I listen to Michel Van Biezen. It literally feels like a waste of time attending lecture at the brick and mortar school. I only go because of the occasional pop quiz and in class homework that is part of my grade.
A range of sources is best never stick to one source for a topic if you can...
@@dildobaggins2759 even when the professor never fails to confuse you?
At 1:33:25 sir wrote π/2 but π/2 does not belong to the domain of tan inverse x
@@animeshmajumdar66 Im going to be honest I'm not the best at calc so I don't know if I'm right, but he said something about at pi/2 its asymptotic, but if you look at the line you can see that it goes on up forever (infinity). This is similar when we were talking about e(infinity) which equaled infinity. Again I'm not 100 percent certain I'm correct, but this is what gets me through calc 2.
Comparison Theorem starts at 2:27:00 for anyone else looking specifically for that.
Thank you SO MUCH
You're a true lad
year late but damn thanks
your the man
Thanks!
I don't know if you noticed, but at 23:32 he did something magical with his back to the board as he explained convergence.
Rafael Montecristo LOL he followed the curve hahaha
lmao only he would do something so perfect without even realizing it
dude, i just noticed that too!
LOL! Great catch!
The only thing I can say is i love you.
Calc 1 final got 98%, taking calc 2 right now and thanks to YOU I am acing my tests!!!!
I hope you win the lottery or something..Thanks again!
This guy is really talented. I am a math tutor myself, but he's just on top of the game. I wish my teachers at the University had at least half of the teaching skills of this Professor !!
He said they would spend 3 days on improper integrals.... My calc 2 prof did it in one day.... moving way too fast.
Luckily with superman here I can review/relearn some topics.
Thanks for the videos!
+lukas wood Sometimes I will do one lesson twice. No small feat when they are 3 hours long in some cases. An outstanding teacher!
Mine did it in 15 mins.
@@mathewmiller730 Yeah i do like 2 lessons per day
Mine did it in 4sec
@@lseansiamz4251 mine did it in 3.5 femtoseconds.
is that a calc instructor? why don't we have professors with biceps like that around campus?
DID YOU GRADUATE COLLEGE, HOW ARE YOU, WHAT ARE YOU DOING NOW? Sorry I felt like it was a cool thing to think about hold long ago your comment was
@@youniic9665 she dead lmao
@@jacktheiss4085 so we all just here lmaooo
Nah, thats Clark Kent.
@@youniic9665 did YOU???
I wish he did physics
23:33 his hand perfectly matches up with the graph behind him when he says it gets “smaller and smaller and smaller”.
LOL IT DOES
crystal clear, nuanced, organized, engaging. rare find in STEM education. 11/10 . thank you
This man is the most reassuring calculus teacher ever, I love it =).
You're an amazing teacher its unbelievable! You're making engineering calculus so much easier for me. Thank you so much!
You are the most helpful teacher I've ever seen. watching your videos makes me like maths even more.
This man saved my life, my GPA and possibly my admission into my major!
After 3 days, it is my final, and I still rely on you. You saved my academic life. Thanks for everything in Calculus1. I hope, we will continue the path in Calculus 2 as well
I’m older and went back to school last year to work on an engineering degree. Even though I’d already taken calculus for my business degree, I had to retake it due to how long ago I took it because engineering requires calc 2, 3, and a couple more advanced math classes. I will say I would love to have a professor like this one. So far after calc 1 and into calc 2 this year, all my professors do is write a problem, work it out, and move on. No clear explanations, no sort of interaction. It’s just watching someone do algebra, trig, and then calculus. After class I come here, look up the section, pretend I’m in this class and have a way better understanding and sharper tools in the tool box to take on the homework. Thank you for these recordings. You are a great teacher.
Oh my god you have saved me.... I just discovered you and I’m taking calc right now and has a professor who doesn’t show up to lecture 50% of the time and can’t teach for heck. Thank god😭😭😭😭
Have*
I am quarantined at home from work due to the fact of the Coronavirus and that I have a wife that is 8 months pregnant ,two kids (3 and 2), and school is shut down here in Colorado. No, I do not have the virus but my work is awesome and let me stay home to take care of my wife and kids. While they are resting, do I just game and waste my time? NO!!!! I am relearning Calculus 2 so I can move on to Calculus 3 and DE so I can start my math and physics degree double major. I took a weird path, I have a bachelors degree and a masters already but I want one in math and physics now. I am taking full advantage of my situation!
Update: I completed a math degree last week (April 25, 2021). I give all the credit to Professor Leonard!!! Without him, it would not have been possible. Instead of a physics degree, I am instead applying to a PhD program in Aerospace Science at the University of North Dakota.
What do you do for a living if i may ask?
@@ahmedfaris26 I’m in the Army
Because I usually lose my focus in class, thinking about other things, your lectures were extremely helpful for me. Because I can pause and rewind if i lost my focus.
Thank you prof. Leonard.
You have an amazing gift for teaching. Thank you so much for all your help!! I have been watching all your calc two videos and this has given me the opportunity to be caught up with all the other kids. Thank you Professor Leonard!!
The way we walk into that example of divergence using the integral sin(x) is masterfully done.
This man is a legend, I wish I had more professors like him. He has single handedly helped me grasp these concepts. Thank you 🙏
You're my Calc hero 👍🙂
You have saved me from failing Calculus :-)
You've got some fortunate students, thank you for posting your classes :-)
Professor Leonard,
You helped me get an A in my calculus class last quarter. I wouldn't have been able to do it without you. The average grade on the final was a D and I got an A. I can't wait to watch your videos next quarter as well.
Professor Leonard, thank you for a well-organized and excellent explanation of Improper Integrals in Calculus Two. The examples/problems and graphs increase my overall knowledge and understanding of this important topic in Calculus. Remembering to check for infinite discontinuities at the interior points as well as the end points is important when determining an integral is improper. Pattern recognition is also important when solving problems in Mathematics.
The examples at 42:00 are closely related to the concept of power series, for which if p > 1 then the series (hence the integral) converges and if p ≤ 1 the series diverges (hence the integral diverges). The concepts of power series and integrals who involve power series are indeed closely realted to one another.
I'm so proud of me.
I was just literally with nothing to do in my life and my mind just thinked... ''I don't know nothing about improper integrals, let me check some nice video''
I thought I won't stand almost 3 hours... And I just not watch all, as I liked all the video and the explanations.
So, I'm so thankful for your videos, Professor Leonard!!! I liked this video as if someone liked watching Avengers: Infinity War!
Eventhough your classes are long, the examples are really important for us to understand all the situations that happens in each subject. Please dont change the way you teach. I know that a lot of students dont like it but I think it's really necessary
May God bless you for making me understand this concept.
One little intricacy of his videos is the way he gestures with his arms - when motioning to negative infinite, he motions using his right hand rightward, which is interesting because that's actually, based on a first-person perspective visioning a cartesian, positive infinite. But since his students are facing him (as is the camera), he needs to do everything in reverse from his perspective to make it representative to our perspective. Really neat.
I didn't show up to class 3 times in 3 weeks (9 classes). I made 97 in Calc 2 first test last week, everyone who showed up made 80 and below. My Professor was surprised, but technically I showed up to class (Professor Leonard's UA-cam class) haha
will you ever do calculus 3 course? Your teaching skills are beyond awesome
Shahin Sateei Yes, Calculus 3 is in the planning phase right now and should be filmed during the Spring 2016 Semester!
great! Anything on Linear Algebra as well? More specifically Linear Algebra 2 (university level)? :)
+Professor Leonard That's gonna be great! I hope you post the videos throughout your semester!
+Professor Leonard That works out!! I'll be hopefully taking Calc 3 next semester. First step is to pass calc 2...
+Professor Leonard the videos will be released spring 2016? or the filming will start spring 2016?
Thanks for all the help. I don't have as much time to watch your videos now since I'm in school (thanks to you I was able to test into Calc 1 last semester) but when I really need help with a subject that wasn't covered well in a lecture I come right back here.
Hello professor!! I just want to hugely thank you for pushing me to face my fear of calculus. I have been cramming your calc 1 and calc 2 playlists and you have no idea how much I depended on you. Your effort in making us understand is applaudable truly, and I have been recommending you to all the ppl I know. I just hope my exam that's in a couple of weeks goes well, but either way, you have been a HUMONGOUS aid to me. Thank you sir once more! Have a nice day
This man literally saved the grades of the tens of thousands of calc ii students with incompetent teachers. Professor Leonard sir, you are a saint.
I was getting really confused in my math class and your videos are helped me!! your teaching skills are incredible
You are such an amazing instructor! I even want to skip my lecture so that I can watch your lessons online! That really helps me a lot!
Professor Leonard, thank you so much for being an awesome human being and posting these amazing videos. You actually made me love calculus even more!
prof Leonard you went beyond my expectations....i am in china struggling with vpn's but still i am able follow you clearly...thank you for saving me...you are super smart.
The world needs more math teachers like you keep up the great work u do make a difference in students life by building confidence in a students belief that they can do it!!!!!!!👍
1:34:30 is roughly where the second type of improper integral starts.
I love the full length videos. They're always well thought out and I appreciate the great content!
I got a 100% on my first Calc 2 exam thanks to your lectures!!!
An amazing teacher aside, you are very humble too, Professor. (see at 49 mins around when you remembered to put the value of "u" back. I have been enjoying your classes on youtube and benefiting from them. :)
Honestly, Professor Leonard makes me fall in love with math a little more every time. I am so happy he makes these videos and I can actually study these concepts. I am so grateful I can understand it.
My Calc 2 class = this video on 1.5 speed with most of the helpful explanations deleted out
And its sad because my teacher is awesome, but he rushes through material so fast, and skips over steps that HE CONSIDERS easy or trivial, so you end up lost and have to go on youtube to learn stuff for free that you paid thousands of dollars to learn at university
Yeah professors haven't been in your spot for a really long time. So they don't know what is considered hard or easy to a student.
I have learned more in these 3 hours than I did for a whole week of my professor... Thank you so much! I have a quiz soon and this saved me! I understand it now!
53:40 when b is approaching ♾ means e^0=1 which means 1/e^0 =1,that means 1/1 =1 then *-1/2
I think this guy is actually superman, saving us from failing courses due to bad profss...
Thanks Professor Leonard!
thank you so much. i passed my midterm by a good bit by strictly watching your lectures, then redoing the problems on my own.
literally hope this man gets anything he wants in life. Saving my life
You really saved me , I do my bachelor's degree here in china but I literally don’t understand anything, thank you so much professor leonard
Somebody put a f***in medal on this guy I'm skipping lectures and still acing Calc!
I have never watched a more educational and engaging math tutorial!
You should do a video of your workout routine. Sick gainz, dawg. Also, very helpful math lectures.
Thank you Professor Leonard, you make these concepts so clear and make sure that class understands what you're doing as opposed to some professors who just throw theorems at you without explanations.
You really help to many Students Proff. Leo , we really appreciate your videos. Thanks for teaching me even you do not know me
I love this lecture, sadly in my university the part on improper integrals in an exam is only on the comparison test, so I'll actually only use the last 20 mins of the 3-hrs lecture I just saw, but the review on all the integration techniques was invaluable, and even though the explanation was kinda slow, it very precise and accurate, thank you so much.
Grateful for all your videos. They helped me through Cal 1 & now Cal 2. Thank you and keep doing what you’re doing
You're very welcome! Best of luck :)
I don't know what college he is teaching but these students are getting an S tier professor.
Learning is beautiful, thank you professor. My teacher literally gave us notes and I didn't know what the hell was going on but this video makes me understand what's actually happening
I actually really enjoyed learning math right now. I wish all teachers were like that. Having to teach yourself often sucks
Thank you so much. You are doing such a great job in teaching, and I understood everything so well, thanks to you. you are such a great teacher. wish you all the very best for everything you do and may the triple gem bless you sir.
dude. these lectures are insanely helpful. I can't imagine passing calculus without the internet and I feel bad for anyone who took calculus 2 before the internet.
1:50:45 It actually makes sense that you cannot account for an infinite amount of removable discontinuities in your integral: since holes have no area, a finite amount of them would be fine (0 * anything is still 0), but an infinite amount of them would be 0 * infinity, which is undefined.
At time 1:14:16, when applying L'Hopital's rule, he says "the derivative of "a" is 1. Isn't "a" a constant, and therefore the derivative is 0 ? At the beginning we selected "a" to "be some number"; it is not a variable. When we apply L'Hopital's, we are strictly taking a derivative, not substituting in infinity, at this point. Similarly, if "a" is a constant, the denominator would be 0 also. And we'd be back to 0/0....My comments here are similar to Ted Chirvasiu's comments below.
When you replace u with x at about 47:30, technically shouldn't you change your limits of integration? So as a general method , wouldn't be better to figure out the indefinite integral separately and then substitute it in? I think this is what is done with the integration by parts at about 1:05:25
1:49:50 Wait so I can create a line where it's just infinite removal discontinuities right beside each other and still have an integral?
weird fact: at 23:24 when he says "smaller and smaller and smaller", his hand motion is nearly perfectly lined with the function on the board behind him which is getting smaller and smaller and smaller
I wondered if one day I would find someone who gonna explain everything as well so that I'll understand everything
He always kills me when he does these 59:47,,,,man this is a fun class !
You're the first teacher who put me in this situation. I have to find reasons to watch your videos because I'm preparing for GATE and I wish you taught EVERYTHING. unfortunately I don't have lot of things to revise in maths otherwise would have watched your entire playlist. Loved your lectures sir! You're an amazing teacher. Just try to do more videos on probabilities (conditional and all) because that's bugging me...
I wish this man, was my calculus 2 professor....
23:33 looks like it was planned! Very smooth
you're a hero
2022, Here I am watching and learning from Professor Leonard. Recommended 110%.
May you live long Love from Pakistan dear Sir
Is it just a numbering error. ? since 7.5 is missing !! Just wondering.
Thank You So Much Professor, you made me love calculus.
best in the world my superman
awesome, fantastic, fantabulous..... I don't have words to describe your teaching. I become really big fan of yours. We are students of Qatar University (QU) are looking forward for your courses. Thank you very much for your hard working. love you
I wish that math teachers would put _short_ problems in their exams more often;
exams at this level shouldn't be a huge drill in arithmetic and algebra, they should be about understanding and solving integrals (for example).
Even a simple integral like ∫[x/(x² + 1)⋅dx] would be a perfectly good exam problem.
Watching your videos, I got a 100% on my Calc 2 Exam!!!
Love your videos Professor Leonard/ I'm a college student and your videos help strengthen my understanding of calculus and doing the problems assign and one the text book easier.
Where is exercise 7.5 ????
Upload that video bcz i really need it sir
30 minutes in, you are amazing. Learning by my teacher sucks. She is a nice person but I find that its too much mathspeak for me. I hate mathspeak and your teaching style is in layman terms. Thank you. U are a blessing.
I couldn't imagine trying to learn this stuff from a textbook! so grateful for these videos!
you are awesome.....now i understand how to deal with intergrals.......your skills are beyond
Thank you Sir !!! You are an excellent teacher !!! It is very easy for me to understand the way that you present the material. Please do a series on Calc 3 if you have a chance .
The best math professor in the world? Perhaps.
Damn bruh, you jacked af.
Thank you so much prof. A calculus teacher who's finally understandable and also funny :)
Hey Professor, I'm finding your lectures invaluable...thanks so much.
Halfway through my summer class before I realized my professor is using the same book. This is great!
What happened to lecture 7.5?