you know he is a teacher true to his nature because he posts full length lectures on each subjects covered in calculus 1, 2 etc without doing the pay this much a month to get access to premium lectures bullshit. he is truly a rare diamond, arguably better than khan academy because he's just so much more thorough. Long live Leonard, the true heros don't need a cape
0:00 The Volume of a Disk 30:45 Volume of a Disk w/ Respect to Y 32:42 Ex 1 39:00 Solid of Revolution (various shapes) 47:00 Volume of Solids of Revolution 1:00:00 Ex 2 1:08:37 Derive the Volume of a Sphere 1:22:29 Washer Method 1:33:45 Ex 3 1:46:20 Washer Method where cross section is perpendicular to Y-Axis. 1:49:53 Ex 4 (DiskMethod w/ cross Section Perpendicular to Y-Axis) 2:00:14 Ex 4 but revolved about the X-Axis 2:03:50 Ex 5 Disk Method Around X-Axis 2:13:40 Ex 6 Washer Method Around Y-Axis 2:24:34 Ex 7 Washer Method, Solid Revolved around Y = constant (not Y-Axis)
I've been watching your videos since senior year of high school. Now I'm in college and last week I took a Calc 2 midterm exam. I ended up getting a 96%. Thank you so much, Professor. You are truly awesome.
For shells the rectangles are PARALLEL to the axis of rotation For disk and washers the rectangles are PERPENDICULAR to the axis of rotation Just a hint I used for my students when I taught mathematics for 33 years
I was failing calculus 2 until I found your videos, now my test scores are higher every time. I just want to thank you Professor Leonard for taking the time to make these videos. They're so helpful and you're doing a really good thing. Keep it up, proud of you.
It goes without saying how impressive you are as a teacher but your ability to draw appropriate 3D images to illustrate the functions is also very notable. Thanks for sharing these amazing talents and removing the struggle we would have without them in understanding such an obscure and enigmatic subject for us beginners.
Hey prof leonard, I know it's likely you will never see this, but your explanation of disk/washer is superior in every way to almost ALL math profs I have had the pleasure of working with. Your strongest asset is that you are willing to work through a problem to the end even if "we are supposed to know this stuff" Profs who only do a problem half way and then stop becuase "the rest is things you should know" is the biggest problem in mathematic academia, students need refreshers on this material and sometimes it's good to see a problem worked through to the end. Not to mention many students may understand a new concept but falter in execution because the older material was glossed over. Your lectures basically replaced my math prof lectures. And you follow the calc books to a T so the lectures come in order as they do in Uni. Thank you from the bottom of my heart.
Taking calculus 2 now and you are absolutely saving my life. Thank you for all the work you have done Professor Leonard. I think I can speak for many when I say that you are truly a fantastic teacher. I hope life has given you all that you have wished for because you truly deserve it.
Can you be my math teacher? Like forever until I graduate :) Update: This was four years ago! Well in 2019 I graduated with my BS in Mathematics. Thanks to Professor Leonard he helped me in my first year calc classes and Statistics. Thank You!
+Greg Santana Professor Leonard saved me in the Calculus 1 class and now, he is rescuing me in Calculus 2. Amazing lectures. I wish Sierra College had hired him to teach math at my college.
You are such genius professor . i am taking Calculus II now, my professor is really good at Math, but she is rushing after time . That is why, you rock it. Your explanations are so clear. I understand better like i'm the class with you , again thank you very much for sharing your knowledges in the public.
I've been struggling with the concept of washers and disks for so long and I didn't think I'd ever get it. Once again, you've shown me that math is possible. Thank you so much!
Thank god I found you, our classes only have 1 hr 30 min lectures 2 days a week and the teacher straight goes to examples and I'm always lost because i have no understanding of the concepts or how he gets things This video made things clearer for me how volume and the equation works Even if I might not pass at least now I understand things
I seen many you tubers create a Patreon Account so they can keep their channel alive, if you had one, I would gladly donate my unit 5 college class tuition because you are my proffesor this semester.
Firstly, you teach on a simplified way which we never expect in our lecture class. And the interesting thing what I admire your is that "your drawing is just amazing!!". Thank You very much for making this world simpler in Mathematical manner.
Jumping into calculus (online at that) after 10 years off since my last math class, I have to say that it would be near impossible to do well - or even pass - without videos from people like yourself and a few others. I sincerely appreciate your lectures and even the corny jokes. You remind me of one of my favorite math teachers from HS. Keep doing what you're doing, you're awesome!
I have been following your lessons for the last 3 years. You are simply the very best. Your lessons are so clear and so easy to understand even for anyone who has no prior knowledge of Calculus! Thank you so much for being such an awesome teacher!
i follow this lectures from france because it's obvious that this teacher loves his job and math becomes clear with this man ! thanks for your generosity
I'm really counting on these videos for my midterm exam tomorrow. I've learned so much by watching the videos I've watched thus far. You are an amazing teacher and you make calculus sort of...FUN. Thank you, sir.
Thank you so much for such a CLEAR and THOROUGH explanation on rotating about non-axis lines... was literally banging my head against the wall until I watched this video!
Am I the only one who is answering to his questions and raises hand when he say it? Leonard, your videos make me feel like I'm in the classroom. Thank you for the perfect lessons!
I love the way you teach. It is extremely grounded and isn't some weird conceptual explanation for things that you're forced to accept and abide by, not actually knowing the reasons for why things are the way they are.
I’m currently tutoring a college student in Calc II. They’re reviewing this concept at the moment. Though I’ve worked with calculus for years, Professor Leonard’s method of teaching has been a great resource to stay fresh on these core subjects.
after all these years, that feeling when you get the idea and he says "rise your hand if you understand that" 🤚😊 what a wonderful professor i really appreciate your efforts every day. Thankyou very very much
Professor Leonard you rock! Thank you for providing these lectures to the public as your teaching skills and ability to convey a thorough understanding of these concepts is something that many can benefit from. This is greatly helping me better understand this part of my Calc II class and I'm not struggling as much on the homework problems now! Cheers!
"Isn't that neat? Well it is neat until you find out you can do this without calculus." 37:03 Thanks for all of your help, Professor Leonard. I've been panicking every time I step into class since we learned this lesson, and now everything is beginning to come together.
my teacher didn't even show us we could just plug in one of the values in the [a,b] to find which function is on top. she was telling us to draw every single function for every problem. I have a midterm coming up in calculus 2 and just found your videos. I think they are my only hope!
Great professor of Maths.. ever seen throughout my career.. I am enjoying the calculus even after graduating due to the great professor Leonard. Stay blessed.
I bombed the entire section of disk, shell and washer method and cylindrical shell method on my cal 2 final. I hated this entire topic with such a passion and I still do. I literally cannot get better at it no matter how hard I try… 🤦🏻♂️🤦🏻♂️🤦🏻♂️
I'm in a similar situation after my first major exam. Completely failed the solids of revolution part. I'm technically in engineering math, which is supposed to be above calc. 2, so that makes it even harder to keep up. Hope you're doing better; Godspeed!
I had a hard time understanding the 3D slices/disk intro around the 7 minute mark but then I realized that I already understood the concept of the 3D model from some Autodesk programs that we toy with in school. Thanks for the cool video! 10/10
wish my professor would just play ur lectures in class instead of actually lecturing. you explain it so well; literally born to teach. most student like myself need to understand the technique in order to apply it to other problems and you understand that and teach accordingly. thank you so much, you make math understandable and able to be done
You saved my life. My current Calc professor has terrible hand writing and talks really fast. He made this seem extremely hard, but you made it seem like basic addition! Thank you!
man if I had been introduced to this channel sooner I wouldn't have failed Calc 2 three times...you explain it in such a slow and dumb-dumb friendly way it's really easy to follow and understand!
I'm convinced PhD's don't actually have any more knowledge than people with masters degrees. Prof. Leanard is way better and more knowledgeable than all my PhD professors in math..
Thanks a million! We are learning this in Calc 2 right now and I was kind of lost... You really take the time to visualize the concepts for students and I think that is so important when introducing a new topic.
Thank you so much for the videos. I wish I knew about these back when I took calc 1. You teaching style is so clear and concise and i love how you work through problems instead of just showing the answer. I'm currently in my third week of calc 2 but I feel like I'll make it with these👍
took cal 1 this summer worst decision ever...doing 3 and 4 chapters in one week is beyond overwhelming....your lectures have literately saved me....like for real
i appreciate you sooo much, thank you so much for drawing it in 3 dimensions my professor lacked that and felt like some of the class was confused as to why it looked like a washer
I went through Calc III in college without understanding why the formulas for volumes of solids of revolutions worked. I tried doing wacky things at first like breaking them apart into pieces of different shapes, and my professor would just be like, "No, no, it's so easy this way..." Thank you for posting this... Better late than never lol.
thank you so much!!! I am currently taking cal 2 and I always come to watch your videos after attending class. Seriously, helps me understand the material. I wish you taught discrete math too hahaha
you know he is a teacher true to his nature because he posts full length lectures on each subjects covered in calculus 1, 2 etc without doing the pay this much a month to get access to premium lectures bullshit. he is truly a rare diamond, arguably better than khan academy because he's just so much more thorough. Long live Leonard, the true heros don't need a cape
true but now I'd like to donate lol
Arguable whether or not it's arguable. I think he's hands down way better than Khan Academy.
@@christopherobrien7629 same, this dude is carrying me through my classes right now and I feel like i have to thank him somehow lol.
@@christopherobrien7629he has patreon I think
Must you compare?
0:00 The Volume of a Disk
30:45 Volume of a Disk w/ Respect to Y
32:42 Ex 1
39:00 Solid of Revolution (various shapes)
47:00 Volume of Solids of Revolution
1:00:00 Ex 2
1:08:37 Derive the Volume of a Sphere
1:22:29 Washer Method
1:33:45 Ex 3
1:46:20 Washer Method where cross section is perpendicular to Y-Axis.
1:49:53 Ex 4 (DiskMethod w/ cross Section Perpendicular to Y-Axis)
2:00:14 Ex 4 but revolved about the X-Axis
2:03:50 Ex 5 Disk Method Around X-Axis
2:13:40 Ex 6 Washer Method Around Y-Axis
2:24:34 Ex 7 Washer Method, Solid Revolved around Y = constant (not Y-Axis)
Legend
Thank you so much
👏
God bless you.
Thank you!
Got 95% as my final grade of Calclus 1 because of that man.
nice dude
Me too!
შენი წყალი გადმოგვსხმოდეს!
I've been watching your videos since senior year of high school. Now I'm in college and last week I took a Calc 2 midterm exam. I ended up getting a 96%. Thank you so much, Professor. You are truly awesome.
Sweet!! Good job
For shells the rectangles are PARALLEL to the axis of rotation
For disk and washers the rectangles are PERPENDICULAR to the axis of rotation
Just a hint I used for my students when I taught mathematics for 33 years
thank you!
Can you elaborate I didn’t understand what your meant
Very useful
Thank you!!!
Correct!
I was failing calculus 2 until I found your videos, now my test scores are higher every time. I just want to thank you Professor Leonard for taking the time to make these videos. They're so helpful and you're doing a really good thing. Keep it up, proud of you.
You pass ?
@@Robot_Chimpdude the comment was 7y ago ofc he pass😭😭😭😭😭😭
@@nadih9059 don't mean he passed brother
@@Robot_Chimp i mean if he failed
I guess he studied it again and again in those 7y..btw my calc 2 final exam this Monday wish me luuuckkkk
did you pass?
@@nadih9059
It goes without saying how impressive you are as a teacher but your ability to draw appropriate 3D images to illustrate the functions is also very notable. Thanks for sharing these amazing talents and removing the struggle we would have without them in understanding such an obscure and enigmatic subject for us beginners.
Hey prof leonard, I know it's likely you will never see this, but your explanation of disk/washer is superior in every way to almost ALL math profs I have had the pleasure of working with.
Your strongest asset is that you are willing to work through a problem to the end even if "we are supposed to know this stuff"
Profs who only do a problem half way and then stop becuase "the rest is things you should know" is the biggest problem in mathematic academia, students need refreshers on this material and sometimes it's good to see a problem worked through to the end. Not to mention many students may understand a new concept but falter in execution because the older material was glossed over.
Your lectures basically replaced my math prof lectures. And you follow the calc books to a T so the lectures come in order as they do in Uni.
Thank you from the bottom of my heart.
Taking calculus 2 now and you are absolutely saving my life. Thank you for all the work you have done Professor Leonard. I think I can speak for many when I say that you are truly a fantastic teacher. I hope life has given you all that you have wished for because you truly deserve it.
Can you be my math teacher? Like forever until I graduate :)
Update: This was four years ago! Well in 2019 I graduated with my BS in Mathematics. Thanks to Professor Leonard he helped me in my first year calc classes and Statistics. Thank You!
+Greg Santana Professor Leonard saved me in the Calculus 1 class and now, he is rescuing me in Calculus 2. Amazing lectures. I wish Sierra College had hired him to teach math at my college.
You gonna take forever to graduate?
I wish he taught math beyond differential equations, like techniques on how to do proofs, computer science math, etc.
i have started bs math in 2021 hopefully after 4 year i also can come back and say the same.......
hi, where can i find the linear algebra classes? i can't seem to find any
You are such genius professor . i am taking Calculus II now, my professor is really good at Math, but she is rushing after time . That is why, you rock it. Your explanations are so clear. I understand better like i'm the class with you , again thank you very much for sharing your knowledges in the public.
I've been struggling with the concept of washers and disks for so long and I didn't think I'd ever get it. Once again, you've shown me that math is possible. Thank you so much!
Ikr I thought I was never going to understand it until I watched this video. Thank you prof
Thank god I found you, our classes only have 1 hr 30 min lectures 2 days a week and the teacher straight goes to examples and I'm always lost because i have no understanding of the concepts or how he gets things
This video made things clearer for me how volume and the equation works
Even if I might not pass at least now I understand things
I seen many you tubers create a Patreon Account so they can keep their channel alive, if you had one, I would gladly donate my unit 5 college class tuition because you are my proffesor this semester.
javier d amen brother!!
javier d he actually has a patreon in his channel description, I think
Best 2 hours and 47 minutes of my life! : o )
Firstly, you teach on a simplified way which we never expect in our lecture class.
And the interesting thing what I admire your is that "your drawing is just amazing!!".
Thank You very much for making this world simpler in Mathematical manner.
رحمة الله والديك
+منيح الفيديو؟
Since my school moved to remote classes, you became my new math teacher. Your videos are the best. I truly appreciate you!
Jumping into calculus (online at that) after 10 years off since my last math class, I have to say that it would be near impossible to do well - or even pass - without videos from people like yourself and a few others. I sincerely appreciate your lectures and even the corny jokes. You remind me of one of my favorite math teachers from HS. Keep doing what you're doing, you're awesome!
I have been following your lessons for the last 3 years. You are simply the very best. Your lessons are so clear and so easy to understand even for anyone who has no prior knowledge of Calculus! Thank you so much for being such an awesome teacher!
i follow this lectures from france because it's obvious that this teacher loves his job and math becomes clear with this man ! thanks for your generosity
You are a great Professor.I have learned a lot, and your explanation is the best!
I'm really counting on these videos for my midterm exam tomorrow. I've learned so much by watching the videos I've watched thus far. You are an amazing teacher and you make calculus sort of...FUN. Thank you, sir.
Same tmw my midterm exam
Oh good luck! My final exam is next week :) Watching these all over again
got 100% from my final grade thanks to this man
Thank you so much for such a CLEAR and THOROUGH explanation on rotating about non-axis lines... was literally banging my head against the wall until I watched this video!
Am I the only one who is answering to his questions and raises hand when he say it? Leonard, your videos make me feel like I'm in the classroom. Thank you for the perfect lessons!
i say bless you when someone sneezes. bet i am not alone.
I love the way you teach. It is extremely grounded and isn't some weird conceptual explanation for things that you're forced to accept and abide by, not actually knowing the reasons for why things are the way they are.
I have a Calc 2 final tomorrow. Thank you for doing gods work.
Good luck! I have mine in 3 days :O
how did you do?
I'm learning this in calc 1
@@jesussaquin6266 who asked?
@@williamhcarlton Why you have to be that rude ?
Best Calculus channel on youtube, hands down
Professor Leonard is the best Calculus professor that I have seen. His teaching skills are tremendous.
I’m currently tutoring a college student in Calc II. They’re reviewing this concept at the moment. Though I’ve worked with calculus for years, Professor Leonard’s method of teaching has been a great resource to stay fresh on these core subjects.
I almost never comment on how helpful a video is, but for this I'll make an exception. By far the best calculus videos I've ever seen! Thanks so much!
No problem!
This is starting to get incredibly interesting. Can't wait to see what calc 2 and 3 bring.
You are an absolute legend, I would not understand this concept without your help. Thank you so much!
I got A+ in calculus 1 thanks for your videos, my doctor was horrible I didn’t get even 1% of the subject from him. THANK U SO MUCH
Came for the disk method. Stayed for the proof of the volume of a sphere.
Omg Do I wanna know what sphere you were looking at? Lmfao
lol hahahaha
Wow. You did it again. Another video which makes me love Maths even more ;D
i'm with you :D
after all these years, that feeling when you get the idea and he says "rise your hand if you understand that" 🤚😊 what a wonderful professor i really appreciate your efforts every day. Thankyou very very much
U r amazing sir , such a clear concept I'm learning , I'm feelings good now having this channel of mathematics
You are saving my Calculus 2 understanding, and my grade. Thank you for these videos.
Just so incredible explanation at a great pace. Love you Professor!!
I'm in calculus 2 right now learning disk/washer method. Was pretty lost but this video clarified so much for me. Thank you Leonard!
I’m doing it in my 8th grade c1 class.
You're videos have rescued my semester. Thank you!
Professor Leonard you rock! Thank you for providing these lectures to the public as your teaching skills and ability to convey a thorough understanding of these concepts is something that many can benefit from. This is greatly helping me better understand this part of my Calc II class and I'm not struggling as much on the homework problems now! Cheers!
Omg thank you so much, sir 🙏🏻🙏🏻🙏🏻
I had a doubt regarding that function part. Glad I watched your excellent explanation 🌟😁
I've never failed any calculus exam because of this man 😍😎 Sir, I'm grateful
"Isn't that neat? Well it is neat until you find out you can do this without calculus." 37:03
Thanks for all of your help, Professor Leonard. I've been panicking every time I step into class since we learned this lesson, and now everything is beginning to come together.
my teacher didn't even show us we could just plug in one of the values in the [a,b] to find which function is on top. she was telling us to draw every single function for every problem. I have a midterm coming up in calculus 2 and just found your videos. I think they are my only hope!
Great professor of Maths.. ever seen throughout my career.. I am enjoying the calculus even after graduating due to the great professor Leonard. Stay blessed.
I bombed the entire section of disk, shell and washer method and cylindrical shell method on my cal 2 final. I hated this entire topic with such a passion and I still do. I literally cannot get better at it no matter how hard I try… 🤦🏻♂️🤦🏻♂️🤦🏻♂️
Skill Issue
I'm in a similar situation after my first major exam. Completely failed the solids of revolution part. I'm technically in engineering math, which is supposed to be above calc. 2, so that makes it even harder to keep up. Hope you're doing better; Godspeed!
Thank you once again for these videos. Really grateful to be able to raise my hand in joy when you ask," How many people understood this?!"
I have huge respect for this professor, he is remarkable and enthusiastic!
Didn't hear a single word you said- spent 2 hours 47 minutes staring at those biceps
I had a hard time understanding the 3D slices/disk intro around the 7 minute mark but then I realized that I already understood the concept of the 3D model from some Autodesk programs that we toy with in school. Thanks for the cool video! 10/10
wish my professor would just play ur lectures in class instead of actually lecturing. you explain it so well; literally born to teach. most student like myself need to understand the technique in order to apply it to other problems and you understand that and teach accordingly. thank you so much, you make math understandable and able to be done
got 92 on my calc midterm when the class average was 47. thanks to you sir
The best calc prof hands down
You saved my life. My current Calc professor has terrible hand writing and talks really fast. He made this seem extremely hard, but you made it seem like basic addition! Thank you!
I always wondered why Half Life 3 never came out, now I see its because Gordon Freeman decided to teach math instead.
jajajajajajajaja :D
Jokes on you HL3 did come out lol
@@borbling half life alyx =/= half life 3, it's a prequel to hl2.
This is what exactly I am looking for. I truly didn't know what area and volume meant. But now I know. Thanks so much!
man if I had been introduced to this channel sooner I wouldn't have failed Calc 2 three times...you explain it in such a slow and dumb-dumb friendly way it's really easy to follow and understand!
You are a savior, sir. Thanks a ton
I click on the ads' links and watch them till the end just so that you can get credit for that. Thanks for your great job!!
Your method of teaching is intoxicating. Well done sir, you're awesome.
Thank you so much! Probably your videos help to many students to pass their exams and tests. I wish you were my professor!
Wishing you success in all your ways and always ! Your classes are like therapy to me. Lol
the most adorable math teacher that you can ever find - cute , funny , handsome and most importantly doing his job in the best way can ever be done!
Thank you so much Professor Leonard. I passed a calculus I exam because of your videos.
I'm convinced PhD's don't actually have any more knowledge than people with masters degrees. Prof. Leanard is way better and more knowledgeable than all my PhD professors in math..
l really hope this guy gets a million subscribers soon.You are just awesome prof Leonard.
Listen professor, I want you to know that you are a life-saver.
just want thank you for making my calculus class understandable. have a blessed day Professor Leonard.
Everything becomes easy with Leonard. I love math because of his wonderful and fun ways to make me understand. Thanks a lot 💞
Best teacher ever❤❤❤❤
Now i love and understand math because of you
Thank you very much for every lecture❤❤❤❤❤
AMAZINGGGGG NOW I UNDERSTAND U R THE BEST DUDE
Thank you prof may God bless you. you are making math clear and understandable
Great Professor! Particularly, I love your pictorial explanation. Thank you, Professor Leonard.
You know he is a good teacher when you can pause and do the question you self
I was in grade 8 when this video was created. Now I'm in 2nd year of university watching this to get me thru engineering
great prof hard to focus sometimes, because of your physical stature.
You mean his muscles are disturbing you?
dkblade27 more like distracting and turning her on.
Did you just assume someone's gender?
*triggered*
her name is Rachel.... 👀 try not to be so triggered. not worth it lol .
Evan Rodgers lmfao u ugly
Thank you. Your formula for the revolving about a line helped immensely. My professor didn't even give us the formula.
thank you, this video really helped for my calculus exam!
3 videos to start calc 2,so excited!!!
You are an incredible teacher man, my teacher just does every example in the book verbatim and doesnt seem to understand what hes doing.
OMG Thank You! I'm a Calculus BC student and this helped so much!
Thanks a million! We are learning this in Calc 2 right now and I was kind of lost... You really take the time to visualize the concepts for students and I think that is so important when introducing a new topic.
Thanks again Professor Leonard! I appreciate all your videos
keep up the good work I am studying in Italy and they make it as complicated as possible u surely saved my semester
Thank you so much for the videos. I wish I knew about these back when I took calc 1. You teaching style is so clear and concise and i love how you work through problems instead of just showing the answer. I'm currently in my third week of calc 2 but I feel like I'll make it with these👍
took cal 1 this summer worst decision ever...doing 3 and 4 chapters in one week is beyond overwhelming....your lectures have literately saved me....like for real
i appreciate you sooo much, thank you so much for drawing it in 3 dimensions my professor lacked that and felt like some of the class was confused as to why it looked like a washer
Oh, you're such a good professor. Thank you so much for helping me understand Calculus I and II. ^^
You are the best teacher ever!!!
This video is so precious... Thank you Prof. you are the best...
I went through Calc III in college without understanding why the formulas for volumes of solids of revolutions worked. I tried doing wacky things at first like breaking them apart into pieces of different shapes, and my professor would just be like, "No, no, it's so easy this way..."
Thank you for posting this... Better late than never lol.
Thanks for this video. I was having a hard time grasping this, but now I've got it.
thank you so much!!! I am currently taking cal 2 and I always come to watch your videos after attending class. Seriously, helps me understand the material. I wish you taught discrete math too hahaha
This is really great. Those students are really lucky
This is awesome, I wish he also taught economics, he explains really well.
This guy is a god-given gift for the math world
He is my favorite teacher ❤