Hot damn, if he was my professor, I'd never miss a lecture because he is an excellent teacher and explains the material in a very clear and concise manner
@@dd92727 I think that is great and the rest of the world should model that example. The US education system lacks a fundamental drive to want to teach/learn though. It's teach to the test. Get them to pass the test and force them on into something new and harder just to be able to say you have completed it yet cannot demonstrate even a fraction of mastery. I love my country but there are countless things we do wrong here.
@@ianmatthewkline8279 I really dont know what Math they teach in the US. Was taking a class and everyone could not convert decimal to binary. Its stuff i did in high school when i was about 13 years old. Not bragging but the British system is way better. I was in Africa and i have a Bachelors in Mechanical Engineering.
@@dd92727 The US seems to be concerned about the statistics of their school systems rather than the mastery of the subject. I am in no way an expert on the educational system but it seems like they care more about how many students graduate, are not failing, etc. than if the students who are graduating can actually USE or REMEMBER what they were taught. This is especially true in math which is taught but not always used in each persons' professional field. So understandably you do forget some of this stuff. But the problem is compounded when students fail to have even a novice mastery of the subject in the first place. Se then we are left with people who can't do basic algebra
I appreciate the "Do you understand?" because there are many times when my professor seems to take the stance, "Of course you understand, this is easy" when something is *not* easy and we do *not* understand. While it's flattering when my prof clearly thinks we're as good as math as he is, he also has ten years on us (likely more) and it's nice to see a professor who takes that into account.
@@warrenyazzie9975 That can definitely be annoying when something is still new to you. However, there are also certain things that _should_ be trivial when you enter a new course, like for example the fundamentals of simple single-variable derivatives and integrals shouldn't cause any problems when you start Calculus 2, and if they do, then you should review Calculus 1. You do however of course deserve detailed explanations on everything that belongs specifically to the course that you are studying, and it is certainly strongly advisable that the teacher includes old stuff in his/her example problems as much as possible, so that you review those things while you learn the new course at the same time.
@@Peter_1986 It was a course on Mathematical Methods in the Physical Sciences using Mary L. Boas book my the same name. Everything in the book was covered in other classes IF you too them. I ended up dropping the class because I wasn't learning anything new.
i just fucking hate those professors who say "this is so basic and not hard" n it is. which makes u feel so dumb, adding to the dying feeling already being felt in the class
love you they way you visit the algebra again. A lot of teachers assume kids have a 100 percent recall of previous math no matter how long ago even if it isn't used beyond school
Jake Dassan dude Yes, this is why I love this professor, my proffesor gave us a surprise quiz the day after watching his lectures from chapter 7 and I didn't even do the assigned HW for my class yet I got all the questions right just because I did step by step following Leonard's lectures, shit I didn't even memorize the formulas it just came to me lol I guess I learned it. By just watching him do examples. But yes I am going to do the exercises from my textbook before exam comes.
Sorry to comment on your old comment but this is so true, because the other day our professor essentially said that we should be able to to divide polynomials because we "learned it in middle school" and went on with the calculus part of the problem.
I try to do just this in my videos, where I solve math and physics exercises step-by-step, explaining everything I do along the way to avoid confusion. And I have videos on every technique I use :)
Professor Leonard provides a method for learning. The problem presented with the theorem and examples. All highlighted by where you may go wrong. The lookout for and do not forget aspects of pay attention here. Professor Leonard is a gifted teacher, one who understands human nature understands he is not above it or below it showing respect for the students, the subject and teaching. Outstanding and for those other teachers who can learn from the positives of others should take notice. Thank you Professor Leonard.
I'm really glad you mentioned it, because I was starting to think that every professor assumes the student remembers everything from all of the previous math. And by the way, this video helped me a LOT (our professor, even though I have a great respect for the man, literally rushed through it in like 10 minutes) with my preparation for the final exam from Calculus that I took yesterday and I passed!!! :) Thanks a lot, really like the way you teach. Now watching your video about complex numbers as a preparation for linear algebra class that I'm taking this semester.
The physics course Dynamics is a nightmare when it comes to algebra. Always a million vector products and partial derivatives and crap everywhere, lol.
yeah for sure. we'd be living on Mars by now if they taught with his approach instead of purposefully making things harder than they need to be. a lot professors are good at math, but that's very different than being good at teaching.
Professor Leonard and Gilbert Strang lectures are the best. Both men helped me get through my lower division math requirements as an undergrad (almost 10 years ago) and the knowledge I learned from these men have helped in graduate school. Thanks a ton for help many people over the years!
"No I don't want another Jose Canseco card, I already have two!" Thank god your funny, it adds some comic relief to the absurdity of watching videos of a lecture I just went to. Cuz we can all learn integration by partial fractions in fifty minutes /sarcasm. You are seriously unreal, and mark my fucking words, I owe you big time man. I really can't believe this exists. You are going to end up so friggin successful and wealthy (not that you seem like the type to realllyy care about $$, otherwise this wouldnt be here for free, but you are building quite the brand undoubtedly.) Seriously, people who learn from this need to donate so you aren't forced to monetize this precious resource. I didn't know teachers could be this good. You are unbelievable man. You should go to bed feeling great about yourself every single day. I can't imagine how many people you have helped. You've saved my math major imo, or at least a lot of stress that I would have gone through if this didn't exist. THANK YOU!!!
You're very welcome. I am so glad that you have found the videos helpful and that they relieved some of the stress of a math major (which can get overwhelming at times). Best wishes on your education!!
i should just give this guy my tuition money. these videos just proved to me what I already knew: my calc 2 professor can't teach. now I just take my notes from here haha.. thanks for the FREE videos
I'm kind of pissed my actual professor got paid instead of him. She definitely doesn't deserve the money, and now I'm confined to giving him the meager amount left after my tuition was exchanged for the horrible quality teaching lol
Enrollment will continue to increase until everyone goes to university and gets a Bachelors degree. Then the schools will introduce a new 4-year degree that is higher than a Doctorate. Students will spend 40 years of their life in school, will work until they're 75, will retire broke, and will die shortly thereafter.
School i a tool box to do what you like. If you're enjoying your work, you will never want to retire. And if you don't know what to build, you surely don't need a tool box !
Just want to say that I'm extremely thankful for your dedication in making these videos. At the beginning of the school-year I didn't think I was going to pass my calculus course but thanks to you and your videos I'm even starting to enjoy solving the problems. I'm even thinking about taking the optional advanced calculus course!
persoanlly id disagree, because the math is easier than the physics. the physics, and workload is the real "weed out" for engineers lol. The calculus and math is simply backround language
@@fazom1707I would like to agree with you, in my opinion mathematics is like programming, it's a language, it provides the foundation to physics and a lot of subjects, just like computer science based on programming.
I started college in remedial math, a non credit baring course..thanks to Professor Leonards videos, I am now taking Calculus II!!! I WOULDN'T BE HERE WITHOUT YOU PROFESSOR THANK YOU SO MUCH
at 2:08:33 someone's phone goes off, & he handled it so perfectly LOL. Props to whoever that was for surviving that half-second glare x) Anyway, fantastic teaching! Love how he paused practically every other sentence to check if students understood & invite questions - such valuable chances to give students, especially in harder math or physics problems. this guy's so good ^.^
he would be wasted as president. I say Professor Leonard for the head of the department of education. let him make the new standards that all other teachers have to follow
Professor Leonard saved my butt. I had been trying to figure out a partial fractions problem for, literally, hours. His lecture calmed me down and I did it correctly in about 5 minutes. I will never make that mistake again.
I am taking calc 2 online over the summer. Having these videos make me feel like I am in the classroom. What is better? Well, the professor is amazing.
I am running short of words to describe how good ur teaching is.. U explain each and everything very very clearly, u even go back to basic algebra if u have to. Whereas my professor expects us to know all of the basic stuff and she'll skip a step or two without even mentioning what the step was.. I think u are one of the best professors I have come across so far..Thank you very much.. Keep up the good work..
I had a Calculus I professor that I actually dropped after a week that would spend every single class just calling on people to work out homework problems on the board while he made fun of/criticized them in front of the entire class, mostly about the algebra/trig knowledge they lacked. Thankfully I took it later with an incredible professor that I learned so much from. She was very similar to Professor Leonard and would always go over the prerequisite knowledge while doing a problem, even if it was quick. Having a good/understanding professor is so important, it can literally make you love or hate a subject for the rest of your life. Thank you Professor Leonard for being one of the good ones.
I FINALLY UNDERSTAND THIS. Thank god. Your teaching style makes it easy for someone like me who takes a bit to comprehend calc concepts. Thank you prof!
Thank you so much for your videos Professor Leonard! They're literally a life saver and completely helped me understand some very important calculus concepts that I previously could not understand due to bad professors who unlike you, do not take the time and effort to teach their students the material in a thorough manner.
you're appreciated, as a neurodivergent student the way you break things down is super helpful, especially because sometimes i have to miss class, your lessons are a lifesaver
I don't understand my lectures in the school but when I watch your videos everything is so clear for me... God bless you, Leonard, you are helping so many people with these videos...thank you so much
these videos help out so much. you guys are lucky to have an instructor who is this good and knows his stuff. I have had teachers that put students down for not knowing something in class. we all forget things, it's great to be reminded and helped rather than berated and put down.
Professor Leonard, I wanted to thank you so much for posting these videos. It helped me so much and I got really good grade in Cal 2. I also shared this video with another student. Honestly, you are very talented in teaching. I literally made notes of your every class and studied for my final exam for University. Again I can't thank you enough. Best of luck with everything.
The fact that there is 381,000+ views on this tells me how sorry college professors are doing their job. Thank you for the in depth detail on this video and many more you have posted.
Man the amount of effort he puts to make sure every student in the class getting the idea is phenomenal. My lecture doesn't even give a damn about any of the students in class
Professor Leonard thank you for an impressive video/lecture on Integration by Partial Fractions in Calculus Two. Partial Fraction Integration is a simple Technique of integration to breakdown; however, the algebra can be messy from start to finish in some cases. All Techniques of Integration works together with substitution /change of variables in Calculus.
Professor Leonard you are absolutely gifted. If it wasn't for your videos online i wouldn't be half the math student I am today. All of these crazy concepts seem so easy after watching your videos. Thankyou Thankyou Thankyou so much!!!
Saving the bacon once again! the CU math department should watch these lectures to learn how to teach the material they expect us to master in a day. Thank you so much for spending HOURS teaching this material rather than a brief 30 minutes. We don't all remember how to do polynomial long division and fraction decomposition off the top of our heads.
It has not been long since I started watching your calculus lecture videos but am really getting a great relief that my study of mathematics will be at ease. Thank you so much prof and be blessed all the time in Jesus name....
[6 years later during COVID-19 pandemic] *20 minute online class periods 5 days a week* *No office hours or contact outside of "class"* *One week per chapter* *One weekend to watch all of Professor Leonard's videos to ACTUALLY learn the content* Thank you, Professor Leonard, your lectures have been more useful now than ever before. It makes me question why I'm paying nearly $75,000 a year to get a college education when the education I get from you on RUclips far surpasses what I'm paying for...
I would transfer to wherever just to take this man's class 😂😂😂 I just can't help but love the way he teaches. He teaches with his own style. He adds ✨personality✨ to the way he teaches and it makes all of the difference.
For the last problem you can go a step further by combining the two natural log terms. You would end up with ln(x^2/(x^2+1)). Absolute value bars can be omitted since the expression in the logarithm is always positive.
You're a savior. I am in my calc 2 w/ analytical geo. and it is just relentless. On top of that, my teacher moves faster than the speed force. Thank you!
omg these lectures are great ! I'm gonna watch them before my calc lectures and will probably study ahead through these cause my professor is not bad tbh but she goes suuuuper fast ! she went through 7.4 in less than 40 minutes which I don't think is fair. Thank you so much for posting these !
My math teacher in Linear Analysis was really boring, he sounded almost like he was talking to himself or something. He also managed to make everything overly complicated and sound all formal all the time instead of getting to the point. The cool thing about professor Leonard is that he focuses a lot on intuition - he doesn't spend entire lectures on writing down tedious proofs (which you can follow in detail in the textbooks anyway), he actually shows examples and speaks in normal English while explaining things.
Now this is how a Professor should teach. Making sure Students are understanding before he moves on. He asks the class for the answer before he writes it down. That is how he knows the class is following. This tuition would be worth every dime.
Wow. I left class still entirely unsure about this, my instructor regurgitates everything word for word from the book with no explanation, no stopping, no asking if we understand, etc. After watching this I completely understand.
I vote you as top math teacher mate.. Excellent job, i was hesitant about PFD but now after these videos I feel like I get it.. I wish I understood the proofs, so that I can get a better idea of the bind blowing abstraction that is going on in the background
Thank you from the bottom of the hearts of all past, present and future calculus students. I can honestly say, I'd take calculus 3 if by some stroke of luck I find that you also have those lessons here because who needs a real professor, when you have a badass virtual one.
im not sure if he acknowledges this, but for the first example you do not need to do the series of equations he did. just use the trick by making factors equal zero and save yourself 30 minutes
Atlas Slates Yep, you're absolutely correct. I believe I show that in another example. I showed this first so that when factors can't be made zero (such as irreducible quadratics) students have a method to use. But good looking out!
+Atlas Slates In the goal of getting the work done you are correct. In the goal of teaching someone the method, the how to aspect of mathematics requires skill of patience, understanding of the struggle therefore being careful and clearly taking each step to its conclusion. This what makes this teacher Professor Leonard outstanding. I have been taught by those gifted people who think everyone who is a right brain thinker is stupid. Everyone one is different everyone needs to be taught differently, some need all four of the methods applied. See it , speak it, say it, write it. To those who can get it seeing it good for you. Those of us who see the world from all sides need all sides shown to us.
Hot damn, if he was my professor, I'd never miss a lecture
because he is an excellent teacher and explains the material in a very clear and concise manner
This stuff is taught in high school in british commonwealth countries. Nothing spectacular he is doing
Salt
@@dd92727 I think that is great and the rest of the world should model that example. The US education system lacks a fundamental drive to want to teach/learn though. It's teach to the test. Get them to pass the test and force them on into something new and harder just to be able to say you have completed it yet cannot demonstrate even a fraction of mastery. I love my country but there are countless things we do wrong here.
@@ianmatthewkline8279 I really dont know what Math they teach in the US. Was taking a class and everyone could not convert decimal to binary. Its stuff i did in high school when i was about 13 years old. Not bragging but the British system is way better. I was in Africa and i have a Bachelors in Mechanical Engineering.
@@dd92727 The US seems to be concerned about the statistics of their school systems rather than the mastery of the subject. I am in no way an expert on the educational system but it seems like they care more about how many students graduate, are not failing, etc. than if the students who are graduating can actually USE or REMEMBER what they were taught. This is especially true in math which is taught but not always used in each persons' professional field. So understandably you do forget some of this stuff. But the problem is compounded when students fail to have even a novice mastery of the subject in the first place. Se then we are left with people who can't do basic algebra
THIS is what true passion for teaching looks and sounds like. Great work, Prof. Leonard!
I appreciate the "Do you understand?" because there are many times when my professor seems to take the stance, "Of course you understand, this is easy" when something is *not* easy and we do *not* understand. While it's flattering when my prof clearly thinks we're as good as math as he is, he also has ten years on us (likely more) and it's nice to see a professor who takes that into account.
One of my physics professor who graduated from MIT was always saying "This is trivial." 🙄
Some teachers have been given instructions with time restraints
@@warrenyazzie9975
That can definitely be annoying when something is still new to you.
However, there are also certain things that _should_ be trivial when you enter a new course, like for example the fundamentals of simple single-variable derivatives and integrals shouldn't cause any problems when you start Calculus 2, and if they do, then you should review Calculus 1.
You do however of course deserve detailed explanations on everything that belongs specifically to the course that you are studying, and it is certainly strongly advisable that the teacher includes old stuff in his/her example problems as much as possible, so that you review those things while you learn the new course at the same time.
@@Peter_1986 It was a course on Mathematical Methods in the Physical Sciences using Mary L. Boas book my the same name. Everything in the book was covered in other classes IF you too them. I ended up dropping the class because I wasn't learning anything new.
i just fucking hate those professors who say "this is so basic and not hard" n it is. which makes u feel so dumb, adding to the dying feeling already being felt in the class
love you they way you visit the algebra again. A lot of teachers assume kids have a 100 percent recall of previous math no matter how long ago even if it isn't used beyond school
Jake Dassan dude Yes, this is why I love this professor, my proffesor gave us a surprise quiz the day after watching his lectures from chapter 7 and I didn't even do the assigned HW for my class yet I got all the questions right just because I did step by step following Leonard's lectures, shit I didn't even memorize the formulas it just came to me lol I guess I learned it. By just watching him do examples. But yes I am going to do the exercises from my textbook before exam comes.
Sorry to comment on your old comment but this is so true, because the other day our professor essentially said that we should be able to to divide polynomials because we "learned it in middle school" and went on with the calculus part of the problem.
my professor just skips it, and is like this is the answer. SHOW ME GODDAMIT lol
I try to do just this in my videos, where I solve math and physics exercises step-by-step, explaining everything I do along the way to avoid confusion. And I have videos on every technique I use :)
I actually find that part the only annoying part of his teaching.
Professor Leonard provides a method for learning. The problem presented with the theorem and examples. All highlighted by where you may go wrong. The lookout for and do not forget aspects of pay attention here. Professor Leonard is a gifted teacher, one who understands human nature understands he is not above it or below it showing respect for the students, the subject and teaching. Outstanding and for those other teachers who can learn from the positives of others should take notice. Thank you Professor Leonard.
so accurately put!
1:13:00 for the second case
1:35:00 for the third case
2:15:00 for the fouth case
To learn this part start at 0:00:00
Means
THANK YOU
Helpful! Thanks
1:31:34 third case
* 9:00 - The first case.
Amazing how touching the camera changes his shirt instantly!
"People take calculus to finally fail algebra" that is my favorite quote now :D
how sadly true it is!!!! :)
I'm really glad you mentioned it, because I was starting to think that every professor assumes the student remembers everything from all of the previous math. And by the way, this video helped me a LOT (our professor, even though I have a great respect for the man, literally rushed through it in like 10 minutes) with my preparation for the final exam from Calculus that I took yesterday and I passed!!! :) Thanks a lot, really like the way you teach. Now watching your video about complex numbers as a preparation for linear algebra class that I'm taking this semester.
The physics course Dynamics is a nightmare when it comes to algebra.
Always a million vector products and partial derivatives and crap everywhere, lol.
@@ProfessorLeonard love you dawg
@@Peter_1986 did you pass?
Leo is a legend for making calc 2 look like algebra. Imagine him teaching in MIT or Harvard school. I mean, he deserve to be math head department.
Nah, schools like that love to make topics unnecessarily hard
yeah for sure. we'd be living on Mars by now if they taught with his approach instead of purposefully making things harder than they need to be. a lot professors are good at math, but that's very different than being good at teaching.
I wouldn’t wish HOD on any soul. It’s AWFUL for minimal pay increase
41 dislike from teachers who can't teach
"2b or not 2b, that is the question" smooth as fuck
fax
Professor Leonard and Gilbert Strang lectures are the best. Both men helped me get through my lower division math requirements as an undergrad (almost 10 years ago) and the knowledge I learned from these men have helped in graduate school. Thanks a ton for help many people over the years!
Show hands if you're okey with this one
"Show of hands if you follow me." *Raises hand in front of computer*
My girlfriend thinks I am a crazy ass but I get really into these lectures.
EagleLogic my kids were laughing at me too! He's really good.
Lmao that's what I did too
So did I
"No I don't want another Jose Canseco card, I already have two!" Thank god your funny, it adds some comic relief to the absurdity of watching videos of a lecture I just went to. Cuz we can all learn integration by partial fractions in fifty minutes /sarcasm. You are seriously unreal, and mark my fucking words, I owe you big time man. I really can't believe this exists. You are going to end up so friggin successful and wealthy (not that you seem like the type to realllyy care about $$, otherwise this wouldnt be here for free, but you are building quite the brand undoubtedly.) Seriously, people who learn from this need to donate so you aren't forced to monetize this precious resource. I didn't know teachers could be this good. You are unbelievable man. You should go to bed feeling great about yourself every single day. I can't imagine how many people you have helped. You've saved my math major imo, or at least a lot of stress that I would have gone through if this didn't exist. THANK YOU!!!
You're very welcome. I am so glad that you have found the videos helpful and that they relieved some of the stress of a math major (which can get overwhelming at times). Best wishes on your education!!
i should just give this guy my tuition money.
these videos just proved to me what I already knew: my calc 2 professor can't teach. now I just take my notes from here haha..
thanks for the FREE videos
I'm kind of pissed my actual professor got paid instead of him. She definitely doesn't deserve the money, and now I'm confined to giving him the meager amount left after my tuition was exchanged for the horrible quality teaching lol
Isn't that just amazing?!
When the student loan bubble collapses and enrollment falls drastically this man will definitely be one of the last ones standing.
I'm really thinking hard to figure out what your comment means exactly, but all I can think about are partial fractions.
Enrollment will continue to increase until everyone goes to university and gets a Bachelors degree. Then the schools will introduce a new 4-year degree that is higher than a Doctorate. Students will spend 40 years of their life in school, will work until they're 75, will retire broke, and will die shortly thereafter.
School i a tool box to do what you like. If you're enjoying your work, you will never want to retire. And if you don't know what to build, you surely don't need a tool box !
THIS COMMENT IS STILL RELEVENT
My professor went through all of this in 45 minutes and never talked about it again.
ruclips.net/video/Ti8G7SSFlJE/видео.html
Just want to say that I'm extremely thankful for your dedication in making these videos. At the beginning of the school-year I didn't think I was going to pass my calculus course but thanks to you and your videos I'm even starting to enjoy solving the problems. I'm even thinking about taking the optional advanced calculus course!
That's Great!!! Good luck in the advanced course
If every calculus teacher was like him, the world would have a lot of engineers
persoanlly id disagree, because the math is easier than the physics. the physics, and workload is the real "weed out" for engineers lol. The calculus and math is simply backround language
@@marcelelliott9952 calculus is math
@@Sam-zi6gb "all calculus is math but not all math is calculus" - master oogway
@@marcelelliott9952 But higher mathematical aptitude translates to easier understanding of physics, because physics is very mathematically founded.
@@fazom1707I would like to agree with you, in my opinion mathematics is like programming, it's a language, it provides the foundation to physics and a lot of subjects, just like computer science based on programming.
I started college in remedial math, a non credit baring course..thanks to Professor Leonards videos, I am now taking Calculus II!!! I WOULDN'T BE HERE WITHOUT YOU PROFESSOR THANK YOU SO MUCH
how did calc 3 go?
Professor Leonard you're a god amongst men. The 2B and not 2B joke was GOLD.
When you gotta teach a class at 3 but hit the house of gains at 6
Fr
This man is singlehandedly carrying my entire fucking Calculus career
at 2:08:33 someone's phone goes off, & he handled it so perfectly LOL. Props to whoever that was for surviving that half-second glare x)
Anyway, fantastic teaching! Love how he paused practically every other sentence to check if students understood & invite questions - such valuable chances to give students, especially in harder math or physics problems. this guy's so good ^.^
That's the moment when Clark Kent was about to turn into Superman.
It happens again at 2:15:01 and, that time, he makes his displeasure known.
Joseph Smith I’d be so scared😂
shit I'm not even there and I got scared
Thanks professor leanord. You taught me in 2 hours what my actual prof couldn’t teach in a weeks worth of lecture in such depth.
I don't know how I would survive without Professor Leo. He is a Universal professor. Keep up the good work.
29:15 relating Shakespeare to systems of equations... brilliant.
Thank you!
I dont understand how someone can be this good at teaching
You're the epitome of a great educator. #LeonardForPrez
he sets the golden standard
he would be wasted as president. I say Professor Leonard for the head of the department of education. let him make the new standards that all other teachers have to follow
Professor Leonard saved my butt. I had been trying to figure out a partial fractions problem for, literally, hours. His lecture calmed me down and I did it correctly in about 5 minutes. I will never make that mistake again.
I am taking calc 2 online over the summer. Having these videos make me feel like I am in the classroom. What is better? Well, the professor is amazing.
I love this channel so much. This guy has carried me through both of my Cal 1 and 2 courses with great grades and I've actually enjoyed learning it!
I attend to class because of attendance..
All my cal lessons are taught here by the best prof ever...thanks
Imagine if Professor Leonard taught college physics and chemistry
This video may be 8 years old, but I'm still watching it preparing for my Calc 2 exam tomorrow, this man is a God
I am running short of words to describe how good ur teaching is.. U explain each and everything very very clearly, u even go back to basic algebra if u have to. Whereas my professor expects us to know all of the basic stuff and she'll skip a step or two without even mentioning what the step was.. I think u are one of the best professors I have come across so far..Thank you very much.. Keep up the good work..
Professor Leonard
I made A in cal I & II just because of your videos . Please post videos for DE. You are amazing . Thank you!
I am lover of Prof. Leonard
He teaches in the best understandable way!
The mysteries of mathematics systematically broken down into understandable chunks. First class teaching with a caring attitude. Thankyou
Honestly, you're the best teacher that I ever saw in my life. I learn more with you than with my own teachers. Thank you very much for your videos!
Prof Leonard actually is a legend . I've never attended any calculus lecture but now I can do my best . May your work of hands be fruitful
I had a Calculus I professor that I actually dropped after a week that would spend every single class just calling on people to work out homework problems on the board while he made fun of/criticized them in front of the entire class, mostly about the algebra/trig knowledge they lacked. Thankfully I took it later with an incredible professor that I learned so much from. She was very similar to Professor Leonard and would always go over the prerequisite knowledge while doing a problem, even if it was quick. Having a good/understanding professor is so important, it can literally make you love or hate a subject for the rest of your life. Thank you Professor Leonard for being one of the good ones.
Professor Leonard indisputably has the best explanations for calculus concepts out there. Thank you!
I FINALLY UNDERSTAND THIS. Thank god. Your teaching style makes it easy for someone like me who takes a bit to comprehend calc concepts. Thank you prof!
Thank you so much for your videos Professor Leonard! They're literally a life saver and completely helped me understand some very important calculus concepts that I previously could not understand due to bad professors who unlike you, do not take the time and effort to teach their students the material in a thorough manner.
I wish you were my professor, very detailed. Wow!!!! Thanks a lot for saving us. I have recommended you a lot!!!!
you're appreciated, as a neurodivergent student the way you break things down is super helpful, especially because sometimes i have to miss class, your lessons are a lifesaver
I don't understand my lectures in the school but when I watch your videos everything is so clear for me... God bless you, Leonard, you are helping so many people with these videos...thank you so much
OMG. I watch a lot of math video lectures on youtube and yours are the best by far! Please don't stop. ❤
these videos help out so much. you guys are lucky to have an instructor who is this good and knows his stuff. I have had teachers that put students down for not knowing something in class. we all forget things, it's great to be reminded and helped rather than berated and put down.
video posted 7 years ago but still the best , you are the best prof.
The BEST math lecture omg
Like…this is making me like math. This is crazy 😭❤️
Professor Leonard, I wanted to thank you so much for posting these videos. It helped me so much and I got really good grade in Cal 2. I also shared this video with another student. Honestly, you are very talented in teaching. I literally made notes of your every class and studied for my final exam for University. Again I can't thank you enough. Best of luck with everything.
this prof swole asf
+Propane TreeFiddy Professor swole professor swol, he teaches math and moistenes holes....
The fact that there is 381,000+ views on this tells me how sorry college professors are doing their job. Thank you for the in depth detail on this video and many more you have posted.
I'm watching this like a series and my god I would recommend it to anyone doing calc 2 fantastic!!
Man the amount of effort he puts to make sure every student in the class getting the idea is phenomenal. My lecture doesn't even give a damn about any of the students in class
Man, been struggling with calculus this whole time and this teacher just makes me enjoy studying calculus even more. Love this!
YOU'RE THE BEST my university is too big and I feel an elitism from my school so I tend not to speak up. I need to watch more of your videos!
extremely helpful. I never really understood Partial Fractions but I know I will Ace it in the exam. Thanks a lot Professor.
Got a test today. I always find myself on your videos before a test because it’s just so well explained. Thank you professor
You are an awesome teacher, keep up the good work. Calc 2 is my favorite class.
Thank you Professor Leonard! This material is very complex and tricky but you explain it in a way that it makes sense! God Bless!
Watched over 30 hours of this man for free. THANK YOU SIR!
Professor Leonard thank you for an impressive video/lecture on Integration by Partial Fractions in Calculus Two. Partial Fraction Integration is a simple Technique of integration to breakdown; however, the algebra can be messy from start to finish in some cases. All Techniques of Integration works together with substitution /change of variables in Calculus.
you have literally been saving my life since calc 1. thank you for these amazing videos!
Best professor ever. Swear to god I had no idea about these stuff ‘till I watched his video. Highly recommended.
This professor is really detailed oriented, loving his style of teaching.
Superman is my savior. He's not just a powerful man fighting off villains but also a good teacher. Damn!!
Professor Leonard you are absolutely gifted. If it wasn't for your videos online i wouldn't be half the math student I am today. All of these crazy concepts seem so easy after watching your videos. Thankyou Thankyou Thankyou so much!!!
Saving the bacon once again! the CU math department should watch these lectures to learn how to teach the material they expect us to master in a day. Thank you so much for spending HOURS teaching this material rather than a brief 30 minutes. We don't all remember how to do polynomial long division and fraction decomposition off the top of our heads.
u are just amazing professor and not like my professor who just read the script all the time in class. Hats off to u
At last integration is making sense. I took a similar class years ago. Looking at this makes me aware of how little I learned back then.
why can't he be my teacher...😩😩. I love his lectures
It has not been long since I started watching your calculus lecture videos but am really getting a great relief that my study of mathematics will be at ease. Thank you so much prof and be blessed all the time in Jesus name....
[6 years later during COVID-19 pandemic]
*20 minute online class periods 5 days a week*
*No office hours or contact outside of "class"*
*One week per chapter*
*One weekend to watch all of Professor Leonard's videos to ACTUALLY learn the content*
Thank you, Professor Leonard, your lectures have been more useful now than ever before. It makes me question why I'm paying nearly $75,000 a year to get a college education when the education I get from you on RUclips far surpasses what I'm paying for...
My professor went over this section in less than an Hour. You spent like 3 hours on this.
FUCKEN AMAZINGGGGGGGG.
Thank you
I would transfer to wherever just to take this man's class 😂😂😂 I just can't help but love the way he teaches. He teaches with his own style. He adds ✨personality✨ to the way he teaches and it makes all of the difference.
For the last problem you can go a step further by combining the two natural log terms. You would end up with ln(x^2/(x^2+1)). Absolute value bars can be omitted since the expression in the logarithm is always positive.
You're a savior. I am in my calc 2 w/ analytical geo. and it is just relentless. On top of that, my teacher moves faster than the speed force. Thank you!
In 30 minutes I understood the concept better than a full week of class. Thank you so much Prof, really saved my bacon.
Who else is here goes to BCC and in professor Watkins' Calc 2 night class?
Haha all that work on the last example just to forget the "+ C" much sadness.
omg these lectures are great ! I'm gonna watch them before my calc lectures and will probably study ahead through these cause my professor is not bad tbh but she goes suuuuper fast ! she went through 7.4 in less than 40 minutes which I don't think is fair. Thank you so much for posting these !
Thank you so much all of your lecture video🙏🙏
Professor leonard is definitely a savior of math, he helps me to get an A on cal1, and now I'm here for cal2
This man is a mad good teacher. He actually wants to teach
My math teacher in Linear Analysis was really boring, he sounded almost like he was talking to himself or something.
He also managed to make everything overly complicated and sound all formal all the time instead of getting to the point.
The cool thing about professor Leonard is that he focuses a lot on intuition - he doesn't spend entire lectures on writing down tedious proofs (which you can follow in detail in the textbooks anyway), he actually shows examples and speaks in normal English while explaining things.
2:55:41 Not done. You forgot to put "+" C in the end.
Shut up!
44 dislikes are from kids who found this video after they had failed their calc test already
Now this is how a Professor should teach. Making sure Students are understanding before he moves on. He asks the class for the answer before he writes it down. That is how he knows the class is following. This tuition would be worth every dime.
Wow. I left class still entirely unsure about this, my instructor regurgitates everything word for word from the book with no explanation, no stopping, no asking if we understand, etc. After watching this I completely understand.
I vote you as top math teacher mate.. Excellent job, i was hesitant about PFD but now after these videos I feel like I get it.. I wish I understood the proofs, so that I can get a better idea of the bind blowing abstraction that is going on in the background
My heart almost stopped, when something rang the second time after prof told a guy to turn it off!
Thank you from the bottom of the hearts of all past, present and future calculus students. I can honestly say, I'd take calculus 3 if by some stroke of luck I find that you also have those lessons here because who needs a real professor, when you have a badass virtual one.
when he forgets the +C at the very end of the last question
wish i had a teacher like this back in the days
im not sure if he acknowledges this, but for the first example you do not need to do the series of equations he did. just use the trick by making factors equal zero and save yourself 30 minutes
Atlas Slates Yep, you're absolutely correct. I believe I show that in another example. I showed this first so that when factors can't be made zero (such as irreducible quadratics) students have a method to use. But good looking out!
+Atlas Slates
In the goal of getting the work done you are correct. In the goal of teaching someone the method, the how to aspect of mathematics requires skill of patience, understanding of the struggle therefore being careful and clearly taking each step to its conclusion. This what makes this teacher Professor Leonard outstanding. I have been taught by those gifted people who think everyone who is a right brain thinker is stupid. Everyone one is different everyone needs to be taught differently, some need all four of the methods applied. See it , speak it, say it, write it. To those who can get it seeing it good for you. Those of us who see the world from all sides need all sides shown to us.
You mean like at 38:00?
Holy fuck, thank you.
finished watching the vid at 1:46 am and I wanna say thanks. Time to start my homework now
He actually teaches...!? How amazing is that?