Missed a Calc class and my professor recommended we all watch this video. Insanely informative and my professor wasn't lying when he said "If you see a jacked dude with glasses, you're on the right video." Thank you for these videos.
I should be paying my tuition fees to Professor Leonard, his style of teaching is vastly superior to the robot that teaches me. All my teacher does is equation after equation after equation, never explaining the concept of it. This channel is a serious help to me.
Using Integration by Substitution Methodology w/examples 8:00 Two Substitutions in One 1:08:30 Difficulty finding u: Trial and Error (1:19:42) - Algebraic manipulation to get a dx = du/? which cancels out the remaining x terms in the function .. because we only want terms involving u. Substitution involving a trig function 1:25:00 recognise that this will not work the way it is currently written. Take advantage of known trig identities within each component of the major function. The focus is still getting rid of all the x terms.
Your videos saved me. I had no hope in calculus until I found your channel. Thanks for making the difficult things less difficult. AMAZING. Keep it up. Your students are SO lucky to have you! GOD BLESS!
There's never been a better time to be a student. Free access to content like this is a game changer. With access to a computer and the desire to learn there's nothing to stop you!
5 years and 10 years from now when students like me are gonna discover these lectures, they'll cry out tears of happiness literally when they could understand what calculus is about. I assume these videos are gonna hit millions and millions of views in the upcoming years =)
I don't just know why online teachers are teaching more better than the ones that are being payed to teach in colleges. I always understand online lectures more than the classroom.
Professor Leonard is teaching at a college, he just uploads videos of his lectures. The reason it is easier to find great online lectures is due to TH-cam being a meritocracy, and usually the better videos get more views, in tern making them easier to find.
This guy's just special. He's an excellent teacher. My guess is that he developed his math skills while determining a formula for the perfect amount of whey protein, in combination with the perfect exercise routine, which would inevitably result in the biggest muscles.
I've listened to a lot of Prof. Leonard's videos, and here's what I've gathered. It seems he's had his fair share of bad teachers when he was coming up, and may even have had some classes that he really struggled with. But he persevered, finally learned the material in a way that made sense, and got a masters in math. He also seems to be a very empathetic guy who cares about his students. So he has devoted a lot of effort to figuring out how to explain what he eventually learned in a way that most people (with the sufficient prerequisite background) can understand. And even then, he realizes that we are sometimes rusty on those prerequisites, so part of his instructional approach is to patiently remind us of what we need to know to get the new stuff.
well at least you are in college , i am taking this in school and it's so easy for us because i have two great teachers ,one online and one in my class .
Professor Leonard Being a older person & having taught maths myself I find your teaching method very informative & easy to follow Thanks for the High School that you work at for the uploads.
+AliAA I have already finished Calculus 1-3 a few years ago, but I still re-watch these videos just to refresh my memory of various topics, lol. I crammed his Calculus 3 playlist a while ago as a preparation for Mathematical Physics, which at least here in Sweden is a lot about vector calculus, partial differential equations and Fourier/Laplace Transforms.
Seriously, these lectures are saving my life. I am taking Calc II and it's been 7 years since Calc I, my currently professor is rushing through all the calc I review with little to now examples. Thank you SO much for posting these lectures.
I know I'm most likely the 200,000th person to really bring this up Professor Leonard, but thank you. I failed algebra 2 in high school three times, so math has never been my strong point. I have been struggling along my Calc 2 Class so far until I stumbled across the videos you have posted on the subject matters I have had issues on. I, and my fellow peers who have viewed your videos in the past, are viewing them now, and the ones who have yet stumbled across them on the internet are ALL thankful for your teaching style, and how you make the explanations so down to earth of such a complex math class. I truly believe that if math was taught like this from the basics of Pre algebra, all the way to D.E; across the nation there would never be such a thing as someone who doesn't understand math.
I'm currently taking calc II. On the first day of class, we went straight into integrations. I took calc I a year ago so I was completely lost; seriously forgot everything I learned. I considered dropping the class. I'm currently reviewing with your videos and OH MY GOD the hope to succeed in Calc II has been restored. Seriously, thank you for sharing these videos. You're helping future STEM students around the world :)
My uni lecturer: Today we're doing integration by substitution 5min later: Here's the fundamental theorem of calculus. And one more equation origin story you need to know... Test: Just integ by substitution
Professor L, you've helped me immensely by providing a second lecture to run parallel to my class to see what I miss. Thank you so very much for all the effort. You've helped me come from a low C at the start to scoring the top A on test 3. You're the man. You embody what it means to teach. A grateful student
These kids are so lucky to have such a charismatic and well-spoken professor to teach them calc. I am watching these videos because I am taking calc 2 online and my teacher gives us the textbook and just says "go nuts" like we can teach ourselves out of a textbook
Best video for integration ever. It can be a bit time consuming to find a video on TH-cam that is easy for me to understand because some people will skip the steps and I'll be lost. Thank you so much for this.
Thank you so much for uploading this. Substitution is one of the three concepts or applications I couldn't grasp for my calc one final coming up this week, and you showing all the steps in detail really helped me. My teacher and the book skip steps all the time and don't give any tips on assigning 'u'. You have restored my faith that I will pass the class. I can't thank you enough.
Thank you. After Getting 38% on a calculus test (I am usually an 'A' student) I have vowed to ace the course inspite of that. Your channel will make me do it.
me and my boy chase use your video's for our study groups in calculus 2 and generally just to brush up on stuff through courses current and previous. Like now, where I need a refresh on integration as a whole. Thank you for doing what you do for without which we'd be screwed in our respective fields :)
you are the best ever sir! Words cannot describe the joy, relief, and satisfaction i feel after watching these videos. Sure am not the only one who leaves my calculus class more confused than when i entered! thanks so much for what you do. God bless you
you're really the best man. you saved me from the beginning of cal 2 because i didnt pay attention much in cal 1 so so spent the past 5 days watching all of your cal 1 videos and i'm rocking my cal 2 rn. tbh, i will eventually rather watch your lec to understand cal 2 than watching or listen to my teacher cus she does not know how to entertain their students like you do
You are a legend! I’m in 9th grade and my honors geometry class is so easy, that I finished my 18 page packet while I was only supposed to have 7 pages complete. Thanks for giving my brain a challenge!
*TIP:* By the time you finish his courses on Calc 1/2/3, if you're not already an "A+" student in Algebra, you WILL be. It's astonishing just how good you become at algebra when you're crunching derivatives and integrals every day and moving numbers around in the equations (something that used to give me problems). It becomes so easy that you won't even have to think about it any more. :)
I'm really grateful for your videos. You break it down into simple terms that anyone could understand. I'm quite slow to connect the dots on how the operations works and the way my current professor taught it just went by me as she taught it too fast. (being taught online doesn't help either).
got taught this and came across problems like the ones you teach after 1:08 and thank you so much for making me understand, honestly ur a great teacher , wishhhhh i had you u rlly know what ur doing and ur not boring XD
my parents always slam the doors so hard so the constant background of a door being slammed in these videos kind of keep be on alert of my surroundings IRL.
The universities should not hire teachers and take money from us who can't make us learn a single thing. Just take a test from us and give us our degree we have got far better teachers on internet who actually knows how to teach although we can't interact with him but still all my concepts are now vivid clear. Professor Leonard is the the best calculus teacher I ever had.
100% absolutely agree. My professor has a doctorate in mathematics but doesn't know how to lay things out in a way students can understand. Learning instead through this channel now
This is saving my life right now. Could never get u-sub down in Calc I, and it came back to bite me in the ass in Calc II. But this is really helpful and well explained
I would be screwed without your videos! I wish my school would take a cue from you and simply post a teacher giving a lecture, instead they choose to focus on production value and flashy images when making videos with very little useful content.
+Chance Hope One thing that I have always disliked about certain math teachers is that they spend way too much time deriving theorems and proofs. It would've been much better if they gave the students an intuition for what in the world was happening and gave examples on how to solve simple problems instead of talking forever about abstract proofs which don't mean anything to complete beginners anyway, especially when those proofs are always derived in detail in the course literature. Professor Leonard instead focuses a lot on intuition and example problems, which is awesome.
Missed a Calc class and my professor recommended we all watch this video. Insanely informative and my professor wasn't lying when he said "If you see a jacked dude with glasses, you're on the right video." Thank you for these videos.
The comment of the Professor though. hhahaha
@@mussawarahmed8530 agreed lmao
I should be paying my tuition fees to Professor Leonard, his style of teaching is vastly superior to the robot that teaches me. All my teacher does is equation after equation after equation, never explaining the concept of it. This channel is a serious help to me.
Using Integration by Substitution Methodology w/examples 8:00
Two Substitutions in One 1:08:30
Difficulty finding u: Trial and Error (1:19:42) - Algebraic manipulation to get a dx = du/? which cancels out the remaining x terms in the function .. because we only want terms involving u.
Substitution involving a trig function 1:25:00 recognise that this will not work the way it is currently written. Take advantage of known trig identities within each component of the major function. The focus is still getting rid of all the x terms.
Bless you!
Your videos saved me. I had no hope in calculus until I found your channel. Thanks for making the difficult things less difficult. AMAZING. Keep it up. Your students are SO lucky to have you! GOD BLESS!
Pa
M n. N
The best Math teacher in the WORLD!!! Thank you for existing Professor Leonard. I could not have gone this far without your videos.
The goat fr
There's never been a better time to be a student. Free access to content like this is a game changer. With access to a computer and the desire to learn there's nothing to stop you!
5 years and 10 years from now when students like me are gonna discover these lectures, they'll cry out tears of happiness literally when they could understand what calculus is about. I assume these videos are gonna hit millions and millions of views in the upcoming years =)
you'r right, this could be the beginning , take like
Try one year
well this is exactly me
Its been eight years from when I last took a calculus class and I only discovered this now (2022)
So very true
I don't just know why online teachers are teaching more better than the ones that are being payed to teach in colleges. I always understand online lectures more than the classroom.
Professor Leonard is teaching at a college, he just uploads videos of his lectures. The reason it is easier to find great online lectures is due to TH-cam being a meritocracy, and usually the better videos get more views, in tern making them easier to find.
This guy's just special. He's an excellent teacher. My guess is that he developed his math skills while determining a formula for the perfect amount of whey protein, in combination with the perfect exercise routine, which would inevitably result in the biggest muscles.
I've listened to a lot of Prof. Leonard's videos, and here's what I've gathered.
It seems he's had his fair share of bad teachers when he was coming up, and may even have had some classes that he really struggled with. But he persevered, finally learned the material in a way that made sense, and got a masters in math.
He also seems to be a very empathetic guy who cares about his students. So he has devoted a lot of effort to figuring out how to explain what he eventually learned in a way that most people (with the sufficient prerequisite background) can understand. And even then, he realizes that we are sometimes rusty on those prerequisites, so part of his instructional approach is to patiently remind us of what we need to know to get the new stuff.
@S Green And, you're a mentalist!
well at least you are in college , i am taking this in school and it's so easy for us
because i have two great teachers ,one online and one in my class
.
Professor Leonard
Being a older person & having taught maths myself I find your teaching method very informative & easy to follow
Thanks for the High School that you work at for the uploads.
I think he works at UC Merced
bro tried to gaslight uni and collage students
@@christianatanasov 😂😂
literally cramming all his videos for finals.
Me too
+AliAA
I have already finished Calculus 1-3 a few years ago, but I still re-watch these videos just to refresh my memory of various topics, lol.
I crammed his Calculus 3 playlist a while ago as a preparation for Mathematical Physics, which at least here in Sweden is a lot about vector calculus, partial differential equations and Fourier/Laplace Transforms.
Seriously, these lectures are saving my life. I am taking Calc II and it's been 7 years since Calc I, my currently professor is rushing through all the calc I review with little to now examples. Thank you SO much for posting these lectures.
same boat now!
@Wesley Richardson You still have notes from 7 years ago?
I know I'm most likely the 200,000th person to really bring this up Professor Leonard, but thank you. I failed algebra 2 in high school three times, so math has never been my strong point. I have been struggling along my Calc 2 Class so far until I stumbled across the videos you have posted on the subject matters I have had issues on. I, and my fellow peers who have viewed your videos in the past, are viewing them now, and the ones who have yet stumbled across them on the internet are ALL thankful for your teaching style, and how you make the explanations so down to earth of such a complex math class. I truly believe that if math was taught like this from the basics of Pre algebra, all the way to D.E; across the nation there would never be such a thing as someone who doesn't understand math.
Same here, barely passed algebra 1 with a D and failed every other math class. I now have an A+ in calc 1 with my eyes on calc 2,3 and physics 1,2
I'm currently taking calc II. On the first day of class, we went straight into integrations. I took calc I a year ago so I was completely lost; seriously forgot everything I learned. I considered dropping the class. I'm currently reviewing with your videos and OH MY GOD the hope to succeed in Calc II has been restored.
Seriously, thank you for sharing these videos. You're helping future STEM students around the world :)
My uni lecturer: Today we're doing integration by substitution
5min later: Here's the fundamental theorem of calculus. And one more equation origin story you need to know...
Test: Just integ by substitution
GOAT Math TH-cam teacher
Professor L, you've helped me immensely by providing a second lecture to run parallel to my class to see what I miss. Thank you so very much for all the effort. You've helped me come from a low C at the start to scoring the top A on test 3. You're the man. You embody what it means to teach.
A grateful student
I wish I had found these videos sooner than 5 days before my final. Looks like I'll be using them when I take Calc 1 again next semester.
You teach so much better than the professors I have. I can always rely on these videos to inform me when I'm lost.
You are really a blessing to me here in Nigeria . The way your teaching sinks into my head is amazing...THANKS 4 THE GOOD JOB
I really follow your teachings very understandable you really saved me.
This man is single handedly getting me through calculus
Professor, you are a life saver!!
These kids are so lucky to have such a charismatic and well-spoken professor to teach them calc.
I am watching these videos because I am taking calc 2 online and my teacher gives us the textbook and just says "go nuts" like we can teach ourselves out of a textbook
thumbs up to professor leonard, he is one of the mathematics legend lecturer
I really appreciate your effort professor. Keep uploading those videos and God bless you
Prof Leonard, you are amazing. Thank you so much!!
Thank you. your explanation really increases my passion for Maths. You make Maths enjoyable. Keep the good work up. :D
Again, Professor Leonard to the rescue!!! This is way better than my online prof videos. Thank you for teaching so calmly and methodically!
Best video for integration ever. It can be a bit time consuming to find a video on TH-cam that is easy for me to understand because some people will skip the steps and I'll be lost. Thank you so much for this.
Thank you for posting all of these videos!!! You're saving my grade in calculus this summer! You do great job of explaining difficult concepts.
Thank you so much for uploading this. Substitution is one of the three concepts or applications I couldn't grasp for my calc one final coming up this week, and you showing all the steps in detail really helped me. My teacher and the book skip steps all the time and don't give any tips on assigning 'u'. You have restored my faith that I will pass the class. I can't thank you enough.
Amazing and professional teaching Sir
teachers like you should be in our university
literately i wasn't understand the integ. substitution and now i understood it how to solve it . thank u very much really
By far the best math teacher alive today. Thank you so much for making your lectures public!
Thank you. After Getting 38% on a calculus test (I am usually an 'A' student) I have vowed to ace the course inspite of that. Your channel will make me do it.
good bless you pro, i'm from Saudi Arabia, and I found your high skills helpful. thank you :)
me and my boy chase use your video's for our study groups in calculus 2 and generally just to brush up on stuff through courses current and previous. Like now, where I need a refresh on integration as a whole.
Thank you for doing what you do for without which we'd be screwed in our respective fields :)
You are an amazing Professor! Thank you for sharing your videos.
you are the best ever sir! Words cannot describe the joy, relief, and satisfaction i feel after watching these videos. Sure am not the only one who leaves my calculus class more confused than when i entered! thanks so much for what you do. God bless you
Thanks Leonard, you are just the best
you're really the best man. you saved me from the beginning of cal 2 because i didnt pay attention much in cal 1 so so spent the past 5 days watching all of your cal 1 videos and i'm rocking my cal 2 rn. tbh, i will eventually rather watch your lec to understand cal 2 than watching or listen to my teacher cus she does not know how to entertain their students like you do
YOU ARE JUST GREAT
THANK YOU SO MUCH FOR MAKING MY LIFE EASIER
You sir are amazing! Totally worth the time!
يعطيك العافية ياشيخ ليونارد .. والله انك وحش يارجل ساعدتني وبقوة
عاش
You are a legend! I’m in 9th grade and my honors geometry class is so easy, that I finished my 18 page packet while I was only supposed to have 7 pages complete. Thanks for giving my brain a challenge!
You are literally my life saviour, thank youuu!!!
This man is the real MVP, Thanks so much for helping me through Calculus!
So far ur the best math teacher ive had come to know of
When I hear this man's voice I know everything is going to be okay
*TIP:* By the time you finish his courses on Calc 1/2/3, if you're not already an "A+" student in Algebra, you WILL be. It's astonishing just how good you become at algebra when you're crunching derivatives and integrals every day and moving numbers around in the equations (something that used to give me problems). It becomes so easy that you won't even have to think about it any more. :)
Thank you sir for your great help in making me understand about the substitution method
In Calc 2 right now and am just now understanding u-subs. Thank you, Mr. Leonard!
You have to make the force flowwww...Youre the best teacher man, God bless you
live long man the way you taught was super great (Y)
I remember watching this during my university days. Thank you for your assistance. 🐐
This man is an awesome teacher.
You explained in few seconds and I get it. My teacher take 10 year to explain and all the students still lost....God bless you
here is a real professor. thank your sir.
Professor, you are literally saving my life.
my favourite Proffessor in the whole world.🤗
HS student here THANK YOU SO MUCH FOR THIS my calc1/2 final is in three weeks and this was explained perfectly!!!
the length of the videos kills me........yet every time i leave feeling like a math pro.......THANK YOU!
Looking for enhanced understanding of quantum mechanics via calculus. Your class and your style makes the process rewarding.!
Thanks
Thank you!!!! You are the reason I'm not failing my business calculus course right now.
you're one of the greatest teacher i have ever seen.!!
I'm really grateful for your videos.
You break it down into simple terms that anyone could understand.
I'm quite slow to connect the dots on how the operations works and the way my current professor taught it just went by me as she taught it too fast.
(being taught online doesn't help either).
got taught this and came across problems like the ones you teach after 1:08 and thank you so much for making me understand, honestly ur a great teacher , wishhhhh i had you u rlly know what ur doing and ur not boring XD
AN ABSOLUTE LEGEND. MY CALC FINAL IS TOMORROW!
haven't gone to class in weeks! THANK YOU SO MUCH
Wow...the lecture was well presented... I didn't catch up with my lec but thanks I now have the content on calculus
This man is the world's greatest math teacher. Not even joking.
King Leonard carrying me through uni
Big thanks from Russian student!!!
Your video just saved me on my Calc test. Thank you
amazing actually one of the best lecture ever i ve seen in integration
and funny moment
1:08:17 because i said so best answer :D
Really appreciate the videos, man. Very in-depth. Thanks.
very good sir , keep working on it ... God bless you.....
leonard sir you rock .i wish i had a sir like u......
my parents always slam the doors so hard so the constant background of a door being slammed in these videos kind of keep be on alert of my surroundings IRL.
The best lecturer ever👍
great song, vocals are very powerful!
Great teaching and interesting relationship advice!
I can't believe this is free
thank you professor leonard. you dont know me, but youve made a positive impact on my life
Thank you Professor Leonard this help alot
This was an amazing explanation of this topic.
Thanks it made integration clear like water instead of mud.
broke up with my girl before her birthday and then got back with her a week later. Thanks for all the money I saved
Genius
The universities should not hire teachers and take money from us who can't make us learn a single thing. Just take a test from us and give us our degree we have got far better teachers on internet who actually knows how to teach although we can't interact with him but still all my concepts are now vivid clear. Professor Leonard is the the best calculus teacher I ever had.
100% absolutely agree. My professor has a doctorate in mathematics but doesn't know how to lay things out in a way students can understand. Learning instead through this channel now
thank you sir , your videos are so useful for me. I'm a college student and i really needed to understand the lesson for my quiz
sir I have no words ...to apreciate u .....u r a really great teacher ,,fantastic ....I wish to take ur classess
Thank you very much, Professor big love from Iraq ❤
This is saving my life right now. Could never get u-sub down in Calc I, and it came back to bite me in the ass in Calc II. But this is really helpful and well explained
Who hits the dislike button for such a great class 🤔
probably all of our resentful teachers who are jealous of him, hahaha
They don't dislike the video, they dislike the subject :)
@@viviang37 I know u
🌟 Simply A Legend 🔥
u r life saver
the best of the best
This guy is AMAZING, thank your mr buff sir
I would be screwed without your videos! I wish my school would take a cue from you and simply post a teacher giving a lecture, instead they choose to focus on production value and flashy images when making videos with very little useful content.
+Chance Hope
One thing that I have always disliked about certain math teachers is that they spend way too much time deriving theorems and proofs.
It would've been much better if they gave the students an intuition for what in the world was happening and gave examples on how to solve simple problems instead of talking forever about abstract proofs which don't mean anything to complete beginners anyway, especially when those proofs are always derived in detail in the course literature.
Professor Leonard instead focuses a lot on intuition and example problems, which is awesome.
amazing prof.
he's better than my own calculus instructor 😩
Many such cases