+mrburns805 same, I go to a highly reputable engineering college but guess what, I learn most of my mathematics and science from youtube which is kinda sad b/c college is expensive :(
I have been frustrated past tears by my Calc II class... my professor doesn't use class time to explain anything, and my classmates and I have been spending hours and hours outside of class trying to figure it out on our own. This video GIVES ME HOPE. I actually understand this!! Professor Leonard I hope you read these, because I am so thankful for this and your other videos. I wish my tuition was going towards your salary, not my professor's. Thank you!!!!
Professor Brandon Leonard teaches at North Idaho College in Coeur d'Alene, Idaho. Take your tuition dollars there. I'm sure that Professor Leonard would be thrilled to have you in his class.
@@jpdemont hey there! If i was you i would delete that comment of where he teaches, idk but im guessing if he doesnt have it on his profile or is public about it is because he doesnt want weird people following him around, shamefully the internet can carry scary people!
What can I look for? 1:00 > Pythagorean theorem works. The function can be one side. [3:30] The idea of trigonometric substitution 7:00 Example 11:00 - x = tan(theta), dx/dtheta = tan (theta) > dx = sec^2(theta) dtheta integral of sec^3(x): ua-cam.com/video/6XlSP58u-is/v-deo.html > convert the problem back into terms of x The skinny on how to set up trig sub 18:30 (good conceptual discussion) Examples 36:00 Another example 54:00 >> look for a square root in your problem If a definite integral problem, change your bounds to avoid having to change back into x terms, which requires revisiting the triangle Example 1:11:00 > trig identities 1:24:00 If it doesn't fit, change to sines and cosines 1:26:00 Consider the function as it stands now. What method works best? Look at all the techniques > In this case, don't use more identities... but appreciate that U-sub works here. Reminder for U:Sub: You want to turn the function into something on the integral table. picking cos as u would leave a sin behind, but differentiating sin would cancel out the cos i.e. replace it with du Final example 1:32:00 Process: Is it in the table? U-Substitution? IBP? Trig-Sub, does it have a square root? > if it doesn't fit 'something squared minus something squared, change that. In this example, complete the square [1:35:20]. This was the idea because the stuff under the square root resembles a quadratic/polynomial 1:40:30 substitute to get rid of 'x+1' 1:52:00 sec^4(x) is an even power >> use identities [1 + tan^2(x)] to cancel out sec^2 via derivative and substitution rules > note: half angle identities are power reduction formulas. > video for integral of cos^4(x): ua-cam.com/video/NSAwZNzjex4/v-deo.html Substituting back 1:56:00
Professor Leonard, you're a legend. I went back to college 10 years after i graduated high school. Before I discovered your channel, I was failed every math class that I had to take as a computer science student. Now that I've discovered your channel and learned how to study properly, I'm actually understanding this stuff! It's amazing. Thank you so much for giving me the opportunity to learn the material and not feel like an idiot. The way you break down problems piece by piece and teach the algorithms of how to approach problems is something I've never seen before. You're a truly a top-tier professor. I appreciate all of the hard work that goes into making these videos and all of the videos you make outside of class.
I've had to drop out of calc 2 twice, and only now that we're forced to watch online lectures because of the pandemic, am I FINALLY UNDERSTANDING what nobody else could seem to make me wrap my head around. Love it love it love it.
I swear you're one of the most professional and experienced professors I can ever find to teach math. You simply love what you're doing and that's what makes you an excellent professor. Keep going big man 💪🏻
I love you. My math professor barely speaks English. I go to class and get an idea of what's going on then I come home and watch your lectures to actually grasp everything.
Cant believe I paid $1200 UC tuition for my 5 week online calc 2 class when I only use your videos to learn the material. THANK YOU for my first A+ in a STEM class, I seriously couldn't have done it without you. I subbed to your patreon, hopefully one day I can do more but I'm eternally grateful.
someone posted this comment that I think more people should see higher up: For those who just happened to watch this video (because they are struggling with trig substitution) and watched up to 12:36, the lecture he's talking about is Lecture 7.1 starting at 1:16:39
I have always had to learn the trig subs off by heart. Man, for the first time I really understand trig subs thanks to your method of UNDERSTANDING WHAT WE ARE DOING. A million thanks to you Professor Leonard, you are THE BEST.
You are truly an amazing professor. I wish my Calc 2 teacher taught as well and understandable as you. All she does is practice problems and no explanation of concepts, formulas, or theorems. You are my new Calc 2 professor, keep up the amazing teaching!!!!
Professor Leonard - You do magic with mathematical functions. I am watching this after 21 years of my senior school when we did integration calculus and things then had never been so interesting. I was really good with trigonometry but integration had become a nightmare for me. I appreciate that you tell students not to memorize but to understand the concepts. You have patience, you love the subject, and you add humor too, the batches of students studying under your guidance are really lucky. Keep up the fantastic work!! We should have more Math, Physics and Chemistry teachers like you ☺
Your professors don't suck, it's just that they don't know how to speak dumb. They went into teaching math because of how well they get it, not to mention how well they get it after they've gone way beyond undergrad with it. They don't know how to speak dumb and they take their knowledge of it for granted. I don't blame them, but this guy is just gifted at seeing it how we see it.
No wonder I'm failing calc 2. My teacher sucks at explaining stuff unlike this guy. Hopefully I can binge on these videos and catch up in time to pass!
Understanding how to set up your triangle is way better than memorizing which identity you should use. I was worried about my upcoming midterm at first, now I feel much more prepared.
WOW! The way you explain actually makes sense, I thought I'd never say that for any professor. I honestly am so glad I found this channel and just wanted to say thanks. I wish I could have stumbled upon this channel earlier but oh well, as long as I have it now:) Thanks Professor Leonard, you have a new subscriber.
Great introduction video! It's great that he tries to explain these substitutions using the most basic ideas and building from the ground up from them. It's amazing how much time this saves later on down the road when thoroughly explain these concepts at the beginning. So many other instructors treat this like memorization, and hand you formulas.
I have been pursuing a degree in Mathematics because I love Math. I get to Cal II and just feel lost and so frustrated, these videos are so amazing and have truly made me remember why I love the subject so much. Thank you so much!!! I hope to be a professor as amazing as you one day!!
Professor Leonard I can't express how much this has helped me figure out the different cases of triangles when using this method of trig sub. Thank you so much for everything, you are the best.
Professor Leonard, why u r so good in calculus I, II, III and in maths in General? and why their is no that good maths professors in most universities? U r so awesome and the best maths teacher I ever know. Actually I know one great maths professor in Ethiopia but not as great as you. your videos are great and so help full for all of my calcs and linearalgebra. yr method of teaching and problem solving skill makes the big concept so easier. any person who's taking advanced maths courses or trying to be an engineer use his youtube video as one important tool of yr maths success. I strongly encourage you to write your own calc book too. "U Z BEST"
This video is 9 years old and im taking the class now and after a year and half of not getting it , your explanacion made it make sense! Thank you so much
YOU ARE GODSENT 🙏🏾🙏🏾🙏🏾 thank you for helping us actually understand where the formulas come from and why to use them and explaining every step it helps a lot my algebra is a bit rusty
I watched this video 4 years ago, but I came back to talk about how useful this was. Professor Leonard is by far the best professor for anything Calc 2 and above. After Calc 2 organic chemistry tutor falls off
Man it is so nice to understand what is going on in Calc II, my teacher does not explain anything and it just goes right over my head. These videos have saved me
I am so thankful for these lectures! Breaking it down and starting simple like you do have saved my life. I was pulling my hair out trying to understand why these rules apply, and YOU HAVE MADE MY LIFE SO MUCH BETTER! 🙌
Professor Leonard you probably know how brilliant you are. I am in college third year and so far I have seen only couple teachers who explains clearly. I am taking calculus 2 but you are my teacher.
I really like how you go step by step on how to solve these problems, and make sure that we understand how we do each step. My professor likes to go through the material really fast, and often skip steps, leaving me confused on certain parts of the problem. These videos help me fully understand the concept and solving problems! Thank you Professor Leonard!
My professor posts 2 minute lecture videos for each Calc II lesson, then just links us to Professor Leonard. Can't even be mad at him for that, it's the best way to learn. Thanks P Leonard!
My dawg! These videos are saving me due to classes moving online because of Covid-19. Out of all the hours I've spent watching other videos trying to catch up in class these have helped WAY*** more. You are the Mr. Miyagi of Calculus
as a student, I always wanted to know why things happened the way they did, so thank you for explainig that! I now have a better understanding of which trig substitution to use, based on my original problem
I wish you had walk through step by step lectures like this for differential equations because your videos are the only reason how I made it past calculus 3 !
"Don't just fall into the pattern of looking at the formulas. I HATE THAT!" 57:43 Preach it! I love how righteous he gets about being a lazy math student. The strength o f Leonard's methods is that they never rely on memorization of formulas. Too many students fall into the trap of relying on memory instead of employing their understanding of concepts.
Thank you so much for these! They stick so well in the memory when you get where these formulas come from... And it gives you a strong fallback solution in case you forget them. Just draw the triangle and it hits you.
These videos are a god-sent. You have no idea how much of a hero you are to so many students!! I spent hours on practice problems for this stuff but once you explained it everything was so clear and I could EASILY do problems. You make me interested in calculus and math for the first time in years. You and your class are so sweet and funny which makes every video that much better!
Your awesome man!! You should teach teachers how to teach! You make it so conceptual instead of..."here is the formula, work out the problem!" Thanks for the video!
I wish he was my professor, my professor literally just does examples on the board super fast while facing the board and doesn't answer questions - I am so happy I found you!
Thank you sir for that video, i’m currently studying science in Quebec and this videos answered all the questions that I had for this chapter of my calculus course. We’re currently confined because of Covid-19 and it his hard to see our teacher since we can’t go to school. Your channel is the greatest thing that I found to help me succed in my integral class. And I shared your videos with my classmates so that everyone can see this. Thanks a lot for sharing the knowledge, this actually helps build a better world!
So many years ago, I took calculus class but my teacher didn't explain it well. I used to spent my whole day to figure out a simple question and formulas. I was so frustrated because i couldn't understand a single thing about calculus 1day before exam. I ended up getting F in my final exam and rejected by university. But now u rescue me, everything makes sense now. Thanks . U make calculus so interesting
So grateful for this video, thank you! You slowed down the process of setting up that pythagorean triangle in such a way that I am now able to easily integrate with trig. sub. where I was totally stuck before. Two very enthusiastic thumbs up!
It’s crazy to me how after I graduate I have to pay back loans for a teacher that doesn’t even care to teach well. Most Calculus professors are just graduate students forced to teach to do their research and grad work, and many of those don’t spend the time necessary to make sure student are getting the absolute most out of their classes. You really can judge how well a teacher is doing based on how many hours students spend re-learning the concept outside of class. Professor Leonard is one of the best calculus teachers I have ever seen, he intuitively breaks down the mechanics of concepts, engages the class routinely, and never skips 3 or 4 steps while teaching, making sure to cover every single logical step that takes place even if it’s simple 3rd grade arithmetic. We need to find a way to get our student loans to filter to people like Professor Leonard instead of our professors. Professors get the same pay regardless of how well they teach, but if their students are consistently resorting to relearning each concept on Khan Academy, Professor Leonard, or Paul’s Notes, then that money should be going to those people, not the school. If schools know they can get more money with better teachers, then that could be a step in the right direction. While I love Professor Leonard, the goal of education is to make sure Professor Leonard’s videos are not necessary.
you tech calculus perfectly, i love that you get your students engaged and make sure they know their stuuf and omg you actually explain how things work unlike most of my college profs ugh also... u look like a dad
Hi Prof. Leonard, I've been using your videos to review some trig sub and am doing the examples before you solve them. Thank you so much for all the videos you make, it's very comforting to have you guiding me through all this. Hope you're doing well, can't wait to see your new videos!
I watched this lecture and felt like I learnt a tonne. I give another UA-cam teacher a go on the same topic and the only reason I could follow along was because of this video. The other video was just a plug and chug formula video there’s no way you could learn and remember much from it. On the other hand professor Leonards lecture was unbelievable, a very good intro to the theory and why it works followed by fully worked solutions with explanation of each step, perfect way to learn 👍
Thank you so much for the playlist Mr. Leonard. I wish I discovered your channel before in my Cal 1. My teachers aren't teaching at all because of the online class. And it's like I got to experience the teaching style of another country coz I was just playing and understanding your videos. Thank you so much!!!
It's been a few years since I took calc 2. But this is the first time I feel like I fully understand this as a concept. I was able to get through the class perfectly fine just memorizing the formulas but after I completed the class I often found I had to keep looking up the substitutions every time I had to use this method again. I had a friend taking calculus at the same time that told me there was a better way where you can derive the formula's each time by starting with the right triangle. I always liked this approach and wanted to use it but I never fully understood it because I didn't know what to pick for my sides. I didn't realize that there was some ambiguity to it and you could draw two possible right triangles for each substitution. And nobody told me that the other substitutions that we never use, i.e. with cotangent, cosine and cosecant work.This explanation finally made it click for me. It's not that we have to draw the triangle in the way you draw them, you just pick the triangle that allows us to integrate something more convenient. For the first integral we could have just as easily integrated the csc^3 instead of sec^3 to get the answer, which I verified just now. But integrating secant is a little less cumbersome than integrating cosecant.
I just want to thank you a lot for having this channel, you are a brilliant professor, it's amazing how I understand everything crystal clear with your lessons. Thank you!!!!! +Professor Leonard
For those who just happened to watch this video (because they are struggling with trig substitution) and watched up to 12:36, the lecture he's talking about is Lecture 7.1 starting at 1:07:53.👍
Seriously thank you! my professor is extremely knowledgeable but you make things so much clearer somehow. i was getting frustrated working on my homework before i watched your lecture, so again thank you!
I totally owe you one if I pass my calculus 2 class! My lecturer can't teach as well as you do. You're a lifesaver! so grateful that i found your channel!
Thank you very much for this video, I was having such a hard time understanding trig sub and all of a sudden it's so clear! This was the first prof leonard video I watched and it earned you a subscription
OOOH MY GOD I don't know how to thank you Professor. My academic coach Stephen recommended this video to me. thanks to him, I feel better about trig sub now.
you should call your channel Calc Kent.
saving the world one differentiation at a time
I always thought the S looked like an integral symbol
I go to college to take calculus 2, but you are my teacher, Professor Leonard. Thank you so much
+mrburns805 same, I go to a highly reputable engineering college but guess what, I learn most of my mathematics and science from youtube which is kinda sad b/c college is expensive :(
+bell hill
You should have gone to a community and then transferred.
+bell hill exactly me i could not learn anything from college
SKYNET #2025 That's exactly what I am doing!
Yep I can’t even understand my teacher lol
I have been frustrated past tears by my Calc II class... my professor doesn't use class time to explain anything, and my classmates and I have been spending hours and hours outside of class trying to figure it out on our own. This video GIVES ME HOPE. I actually understand this!! Professor Leonard I hope you read these, because I am so thankful for this and your other videos. I wish my tuition was going towards your salary, not my professor's. Thank you!!!!
Cassie Johnson same tho
Professor Brandon Leonard teaches at North Idaho College in Coeur d'Alene, Idaho. Take your tuition dollars there. I'm sure that Professor Leonard would be thrilled to have you in his class.
@@jpdemont hey there! If i was you i would delete that comment of where he teaches, idk but im guessing if he doesnt have it on his profile or is public about it is because he doesnt want weird people following him around, shamefully the internet can carry scary people!
@@dianampm99 I'll compromise. If Professor Leonard asks me to delete the posting, I will, immediately and without reservation.
@@dianampm99 His sources are not even correct anyways, with a quick google search you can easily find his true college
What can I look for? 1:00
> Pythagorean theorem works. The function can be one side. [3:30]
The idea of trigonometric substitution 7:00
Example 11:00 - x = tan(theta), dx/dtheta = tan (theta) > dx = sec^2(theta) dtheta
integral of sec^3(x): ua-cam.com/video/6XlSP58u-is/v-deo.html
> convert the problem back into terms of x
The skinny on how to set up trig sub 18:30 (good conceptual discussion)
Examples 36:00
Another example 54:00 >> look for a square root in your problem
If a definite integral problem, change your bounds to avoid having to change back into x terms, which requires revisiting the triangle
Example 1:11:00
> trig identities 1:24:00 If it doesn't fit, change to sines and cosines
1:26:00 Consider the function as it stands now. What method works best? Look at all the techniques
> In this case, don't use more identities... but appreciate that U-sub works here. Reminder for U:Sub: You want to turn the function into something on the integral table. picking cos as u would leave a sin behind, but differentiating sin would cancel out the cos i.e. replace it with du
Final example 1:32:00
Process: Is it in the table? U-Substitution? IBP? Trig-Sub, does it have a square root?
> if it doesn't fit 'something squared minus something squared, change that. In this example, complete the square [1:35:20]. This was the idea because the stuff under the square root resembles a quadratic/polynomial
1:40:30 substitute to get rid of 'x+1'
1:52:00 sec^4(x) is an even power >> use identities [1 + tan^2(x)] to cancel out sec^2 via derivative and substitution rules
> note: half angle identities are power reduction formulas.
> video for integral of cos^4(x): ua-cam.com/video/NSAwZNzjex4/v-deo.html
Substituting back 1:56:00
ua-cam.com/video/y_XwQkchwrE/v-deo.html
Great work.
thank you so much❤
A hero
i love you
I got 100% on my test 1 & 2 and my calculus exam, because his videos. Now I am referring this to my sister's whom are doing calculus this year
Great job!!
Professor Leonard, you're a legend. I went back to college 10 years after i graduated high school. Before I discovered your channel, I was failed every math class that I had to take as a computer science student. Now that I've discovered your channel and learned how to study properly, I'm actually understanding this stuff! It's amazing. Thank you so much for giving me the opportunity to learn the material and not feel like an idiot. The way you break down problems piece by piece and teach the algorithms of how to approach problems is something I've never seen before. You're a truly a top-tier professor. I appreciate all of the hard work that goes into making these videos and all of the videos you make outside of class.
100% agree!
I've had to drop out of calc 2 twice, and only now that we're forced to watch online lectures because of the pandemic, am I FINALLY UNDERSTANDING what nobody else could seem to make me wrap my head around. Love it love it love it.
Best trig substitution lecture EVER!!! Thank you Professor Leonard!
I swear you're one of the most professional and experienced professors I can ever find to teach math. You simply love what you're doing and that's what makes you an excellent professor. Keep going big man 💪🏻
that looks just like his arm
I love you. My math professor barely speaks English. I go to class and get an idea of what's going on then I come home and watch your lectures to actually grasp everything.
Cant believe I paid $1200 UC tuition for my 5 week online calc 2 class when I only use your videos to learn the material. THANK YOU for my first A+ in a STEM class, I seriously couldn't have done it without you. I subbed to your patreon, hopefully one day I can do more but I'm eternally grateful.
Are you like a math professor now
someone posted this comment that I think more people should see higher up:
For those who just happened to watch this video (because they are struggling with trig substitution) and watched up to 12:36, the lecture he's talking about is Lecture 7.1 starting at 1:16:39
You've taught me more calculus in 3 videos than my professor has in 2 1/2 weeks of unit 2. Thank you so much! #mathgod
Where has this man been all my life?!! Not only is he saving me on my Calc2 class but he's so easy on the eyes!!!
ua-cam.com/video/y_XwQkchwrE/v-deo.html
😭😭 Real
All I could think during the whole lecture was how lucky these students must feel!
Some of the best calculus videos out there. Very thorough. Thank you.
This is the clearest explanation I have ever seen that delves into the WHY of constructing the triangle and choosing the substitution.
I have always had to learn the trig subs off by heart. Man, for the first time I really understand trig subs thanks to your method of UNDERSTANDING WHAT WE ARE DOING. A million thanks to you Professor Leonard, you are THE BEST.
You are truly an amazing professor. I wish my Calc 2 teacher taught as well and understandable as you. All she does is practice problems and no explanation of concepts, formulas, or theorems. You are my new Calc 2 professor, keep up the amazing teaching!!!!
holy fucken shit do not skip the first part of this lecture! that is the KEY the GOD! my professor didn't say it.
Professor Leonard - You do magic with mathematical functions. I am watching this after 21 years of my senior school when we did integration calculus and things then had never been so interesting. I was really good with trigonometry but integration had become a nightmare for me. I appreciate that you tell students not to memorize but to understand the concepts. You have patience, you love the subject, and you add humor too, the batches of students studying under your guidance are really lucky.
Keep up the fantastic work!! We should have more Math, Physics and Chemistry teachers like you ☺
how is it that this guy is so cool. hes way better than my prof teaching this.
I know right all my calc professors have sucked i've been using his lectures since beginning of calc 1 almost exclusively.
Your professors don't suck, it's just that they don't know how to speak dumb. They went into teaching math because of how well they get it, not to mention how well they get it after they've gone way beyond undergrad with it. They don't know how to speak dumb and they take their knowledge of it for granted. I don't blame them, but this guy is just gifted at seeing it how we see it.
No wonder I'm failing calc 2. My teacher sucks at explaining stuff unlike this guy. Hopefully I can binge on these videos and catch up in time to pass!
+aliphim I'm in the same boat, buddy. Let's destroy this shit!
How did it go for y'all?
@@nuetro1709 They ded.
we usher in the newest generation of believers @@DAT-OFFICIAL
aliphim same
Understanding how to set up your triangle is way better than memorizing which identity you should use. I was worried about my upcoming midterm at first, now I feel much more prepared.
WOW!
The way you explain actually makes sense, I thought I'd never say that for any professor.
I honestly am so glad I found this channel and just wanted to say thanks.
I wish I could have stumbled upon this channel earlier but oh well, as long as I have it now:)
Thanks Professor Leonard, you have a new subscriber.
ua-cam.com/video/y_XwQkchwrE/v-deo.html
This is some good stuff right here.
professor leonard, you are absolutely amazing. You make this seem so much easier and Im forever grateful
Great introduction video! It's great that he tries to explain these substitutions using the most basic ideas and building from the ground up from them. It's amazing how much time this saves later on down the road when thoroughly explain these concepts at the beginning. So many other instructors treat this like memorization, and hand you formulas.
I have been pursuing a degree in Mathematics because I love Math. I get to Cal II and just feel lost and so frustrated, these videos are so amazing and have truly made me remember why I love the subject so much. Thank you so much!!! I hope to be a professor as amazing as you one day!!
Cheers.
He makes Calculus 1 & Calculus 2 so much easier. Thanks Professor Leonard!
Professor Leonard I can't express how much this has helped me figure out the different cases of triangles when using this method of trig sub. Thank you so much for everything, you are the best.
Professor Leonard, why u r so good in calculus I, II, III and in maths in General? and why their is no that good maths professors in most universities? U r so awesome and the best maths teacher I ever know. Actually I know one great maths professor in Ethiopia but not as great as you. your videos are great and so help full for all of my calcs and linearalgebra. yr method of teaching and problem solving skill makes the big concept so easier. any person who's taking advanced maths courses or trying to be an engineer use his youtube video as one important tool of yr maths success. I strongly encourage you to write your own calc book too. "U Z BEST"
This video is 9 years old and im taking the class now and after a year and half of not getting it , your explanacion made it make sense! Thank you so much
i don't even pay attention in my classes anymore i always study from your videos haha
YOU ARE GODSENT 🙏🏾🙏🏾🙏🏾 thank you for helping us actually understand where the formulas come from and why to use them and explaining every step it helps a lot my algebra is a bit rusty
Let's all sign a petition to bring back Prof. Leonard!
He's working with Sal Khan to run for president in 2028
Love this guy. Wish he'd go on some podcast and tell his story.
I watched this video 4 years ago, but I came back to talk about how useful this was. Professor Leonard is by far the best professor for anything Calc 2 and above. After Calc 2 organic chemistry tutor falls off
Man it is so nice to understand what is going on in Calc II, my teacher does not explain anything and it just goes right over my head. These videos have saved me
I am so thankful for these lectures! Breaking it down and starting simple like you do have saved my life. I was pulling my hair out trying to understand why these rules apply, and YOU HAVE MADE MY LIFE SO MUCH BETTER! 🙌
Professor Leonard you probably know how brilliant you are. I am in college third year and so far I have seen only couple teachers who explains clearly. I am taking calculus 2 but you are my teacher.
You are such a good teacher! I like, enjoying and understand your explanation. THANK YOU PROFESSOR LEONARD!
I really like how you go step by step on how to solve these problems, and make sure that we understand how we do each step. My professor likes to go through the material really fast, and often skip steps, leaving me confused on certain parts of the problem. These videos help me fully understand the concept and solving problems! Thank you Professor Leonard!
I'm glad they are helping :)
@@ProfessorLeonard they are helping!
i have seen many of your videos and by far you are the best math teacher
My professor posts 2 minute lecture videos for each Calc II lesson, then just links us to Professor Leonard. Can't even be mad at him for that, it's the best way to learn. Thanks P Leonard!
My dawg! These videos are saving me due to classes moving online because of Covid-19. Out of all the hours I've spent watching other videos trying to catch up in class these have helped WAY*** more. You are the Mr. Miyagi of Calculus
Outstanding sir.Your methodology towards the students is up to the mark.
Like from Paistan⭐⭐
as a student, I always wanted to know why things happened the way they did, so thank you for explainig that! I now have a better understanding of which trig substitution to use, based on my original problem
I wish you had walk through step by step lectures like this for differential equations because your videos are the only reason how I made it past calculus 3 !
"Don't just fall into the pattern of looking at the formulas. I HATE THAT!" 57:43
Preach it! I love how righteous he gets about being a lazy math student. The strength o f Leonard's methods is that they never rely on memorization of formulas. Too many students fall into the trap of relying on memory instead of employing their understanding of concepts.
I'm so glad I found this video, thanks for the help. My calc 2 teacher makes absolutely no sense when she teaches.
thank you for starting from the most basic understanding of a problem, it really helps.
you are literally saving my calculus grade and you are v nice to look at so thank you for that
Professor Leonard is the truth, and he lifts unlike my scrawny Uconn professors
Thank you so much for these! They stick so well in the memory when you get where these formulas come from... And it gives you a strong fallback solution in case you forget them. Just draw the triangle and it hits you.
you are so patient with your student sir! how i love it!
These videos are a god-sent. You have no idea how much of a hero you are to so many students!! I spent hours on practice problems for this stuff but once you explained it everything was so clear and I could EASILY do problems. You make me interested in calculus and math for the first time in years. You and your class are so sweet and funny which makes every video that much better!
Your awesome man!! You should teach teachers how to teach! You make it so conceptual instead of..."here is the formula, work out the problem!" Thanks for the video!
You made me pass my finals and now I’m an engineer thanx to you ! Always keep you in my prayers my man 🙏
what did you end up doing with the degree? you making any money?
2019 still a hero
he's always a hero
Why couldn't my teacher be more like you! Thanks so much for the videos, will save my butt this semester.
Thank God for this man. Professors/textbooks don’t go in depth or are as clear as you.
You are such an amazing instructor, all of your videos are so easy to follow. Your students are extremely lucky
I wish he was my professor, my professor literally just does examples on the board super fast while facing the board and doesn't answer questions - I am so happy I found you!
Thank you sir for that video, i’m currently studying science in Quebec and this videos answered all the questions that I had for this chapter of my calculus course. We’re currently confined because of Covid-19 and it his hard to see our teacher since we can’t go to school. Your channel is the greatest thing that I found to help me succed in my integral class. And I shared your videos with my classmates so that everyone can see this. Thanks a lot for sharing the knowledge, this actually helps build a better world!
So many years ago, I took calculus class but my teacher didn't explain it well. I used to spent my whole day to figure out a simple question and formulas. I was so frustrated because i couldn't understand a single thing about calculus 1day before exam. I ended up getting F in my final exam and rejected by university. But now u rescue me, everything makes sense now. Thanks . U make calculus so interesting
So grateful for this video, thank you! You slowed down the process of setting up that pythagorean triangle in such a way that I am now able to easily integrate with trig. sub. where I was totally stuck before. Two very enthusiastic thumbs up!
You are saving my butt on my exam tomorrow, BLESS YOU PROFESSOR LEONARD!
It’s crazy to me how after I graduate I have to pay back loans for a teacher that doesn’t even care to teach well. Most Calculus professors are just graduate students forced to teach to do their research and grad work, and many of those don’t spend the time necessary to make sure student are getting the absolute most out of their classes. You really can judge how well a teacher is doing based on how many hours students spend re-learning the concept outside of class. Professor Leonard is one of the best calculus teachers I have ever seen, he intuitively breaks down the mechanics of concepts, engages the class routinely, and never skips 3 or 4 steps while teaching, making sure to cover every single logical step that takes place even if it’s simple 3rd grade arithmetic.
We need to find a way to get our student loans to filter to people like Professor Leonard instead of our professors. Professors get the same pay regardless of how well they teach, but if their students are consistently resorting to relearning each concept on Khan Academy, Professor Leonard, or Paul’s Notes, then that money should be going to those people, not the school. If schools know they can get more money with better teachers, then that could be a step in the right direction. While I love Professor Leonard, the goal of education is to make sure Professor Leonard’s videos are not necessary.
you tech calculus perfectly, i love that you get your students engaged and make sure they know their stuuf and omg you actually explain how things work unlike most of my college profs ugh also... u look like a dad
Thank you with awesome two years with your videos Professor Leonard, I pass Calculus 1,2,3 THANKS TO YOU!!! FREEEEEEE
Hi Prof. Leonard, I've been using your videos to review some trig sub and am doing the examples before you solve them. Thank you so much for all the videos you make, it's very comforting to have you guiding me through all this.
Hope you're doing well, can't wait to see your new videos!
I go to the best-ranked university in the African continent (UCT), yet watching your amazing lecture videos is far more helpful!
I watched this lecture and felt like I learnt a tonne. I give another UA-cam teacher a go on the same topic and the only reason I could follow along was because of this video. The other video was just a plug and chug formula video there’s no way you could learn and remember much from it. On the other hand professor Leonards lecture was unbelievable, a very good intro to the theory and why it works followed by fully worked solutions with explanation of each step, perfect way to learn 👍
Thank you so much for the playlist Mr. Leonard. I wish I discovered your channel before in my Cal 1. My teachers aren't teaching at all because of the online class. And it's like I got to experience the teaching style of another country coz I was just playing and understanding your videos. Thank you so much!!!
It's been a few years since I took calc 2. But this is the first time I feel like I fully understand this as a concept. I was able to get through the class perfectly fine just memorizing the formulas but after I completed the class I often found I had to keep looking up the substitutions every time I had to use this method again. I had a friend taking calculus at the same time that told me there was a better way where you can derive the formula's each time by starting with the right triangle. I always liked this approach and wanted to use it but I never fully understood it because I didn't know what to pick for my sides. I didn't realize that there was some ambiguity to it and you could draw two possible right triangles for each substitution. And nobody told me that the other substitutions that we never use, i.e. with cotangent, cosine and cosecant work.This explanation finally made it click for me. It's not that we have to draw the triangle in the way you draw them, you just pick the triangle that allows us to integrate something more convenient. For the first integral we could have just as easily integrated the csc^3 instead of sec^3 to get the answer, which I verified just now. But integrating secant is a little less cumbersome than integrating cosecant.
You're an awesome teacher. You explained much better then my Calculus II teacher did. I'll be recommending your videos to my classmates.
No one comes close to your "can do"attitude!
I really like these lectures because they explain the concept, something that is rare in my calculus classes, thank you.
I just want to thank you a lot for having this channel, you are a brilliant professor, it's amazing how I understand everything crystal clear with your lessons. Thank you!!!!!
+Professor Leonard
thank you very much you are very good teacher i hope to have a teacher like you
اشكرك انت استاذ رائع اتمنى ان اقابل استاذ عظيم مثلك
For those who just happened to watch this video (because they are struggling with trig substitution) and watched up to 12:36, the lecture he's talking about is Lecture 7.1 starting at 1:07:53.👍
ty BUT its at 7.1 1:16:39
Thank you!!!
You are the hero of students who have cruel math instructors
Thank you!!! Clearest explanation by far.
Dude, due to Covid my calc II class is online and it's brutal. Finding this channel is a game changer. Thank you
Thanks a lot I really understand the concept from you , keep going wait for calculus 3 👏🏻
Seriously thank you! my professor is extremely knowledgeable but you make things so much clearer somehow. i was getting frustrated working on my homework before i watched your lecture, so again thank you!
Thank you Professor, you have made what was daunting and confusing, in to engaging and understandable!
You have changed my life for the positive! Thank you for everything! :) Keep changing the world!
I totally owe you one if I pass my calculus 2 class! My lecturer can't teach as well as you do. You're a lifesaver! so grateful that i found your channel!
I wish I would have found your videos earlier in the semester of calc 2!
Thank you so much Proffesor Leonard, you have really helped me under this part of using identities🙏🙏 I had no idea about them
Thank you very much for this video, I was having such a hard time understanding trig sub and all of a sudden it's so clear! This was the first prof leonard video I watched and it earned you a subscription
OOOH MY GOD I don't know how to thank you Professor. My academic coach Stephen recommended this video to me. thanks to him, I feel better about trig sub now.
It's so amazing how he makes the students have fun while learning something as hard as this
Thank you, Professor Leonard. ...Love the conceptual approach, relaxed pace, and mini-summaries.
He is wonderful ,he gives this for free!!
God will bless you my math professor. I am very happy with this videos so much because they really solve my problems. my problems are settle
Lots Of love From China.Thank you Sir❤.Just because Of your teaching method I feel like my base is improving day by day.
Sir you are the REAL HERO! Thank you a lot. You are lifesaver!