This is such a strange lie... it's not possible to fail the first exam and end the class with a 97%. You'd have had to literally get 100% on everything else and the first test would have still had to have been only like 10% of your final grade.
Lol. He says "Stop me if I make a mistake", Like he ever makes mistakes. This guy is single handedly helping me pass my Calculus 2 for Engineers class in college right now. thank you so much.
He has made mistakes in several videos - he just usually catches them, or is corrected by one of the students. And this actually makes him more human, instead of those robot teachers who pretend like they never ever make mistakes.
0:00 Setup 14:40 Ex 1 21:40 Ex 2 38:50 Ex 3 42:00 Ex 4 51:50 Ex 5 1:00:19 Ex 6 (in terms of y AND x) - 1:07:45 What are you integrating w/respect to? The hard way. 1:27:23 The easy way
TIP: @36:00 It helps to separate the constants from the variables when you go to evaluate the integral. For the first term in the integral, begin by writing 1/2 x^2 instead of x^2/2. That way you can pull out the 1/2 and be left with evaluating 3^2 - (-2)^2 which is much easier. You get 9 - 4 which equals 5 and then you multiply by 1/2 to get 5/2. Every time you see a constant, get rid of it before plugging in your bounds to evaluate and you'll make the math a whole lot easier and save yourself from doing the same work over and over again. :)
Going to my calculus lectures i was only getting 60-70 on my quizzes, using your videos ive gone up to 90-95 on my quizzes! Thanks Professor Leonard, you're a life saver!
+Fine Fina This man is awesome . I wish we had a teacher like him , but some points i do not understand that which school is that . I'm studying in university but i do not know if you guys are from university or some other school types. Sorry if my english is not enuough by the way. I hope i wont disturb you and you will answer me
You should be getting some sort of teacher of the year award 🥇 your teaching methods are outstanding. Your students are lucky to have you. Thanks for taking your time to teach the rest of us
If there is anyone for the first time, I just want to tell you that Professor Leonard helped me to get A* in calculus easily. He has made things simpler for al of us. I am following his videos since 2016.
honestly i dont usually comment on videos but sincerely thank you!!! you are taking the time to make us fully understand concepts and don't rush it like professor in the Top 20 universities in the world, however they expect students to understand things on the fly and being a student in these type of universities, people just expect you to be smarter than everybody and do well on everything but honestly we struggle to understand like everybody and i feel that professors are not aiming to teach us anywhere more than a hunger game attitude of keeping an average and testing who can survive. Truthfully thank you
Dear Brofessor Leonard, I'm on summer break between Calc 1 and Calc 2 and I've been going through your lectures of both. It's wonderful that you never assume that your students know things. You've cleared up so many random areas of confusion about logarithms, exponent rules, trig/inverse-trig, properties of this or that thing, all while watching videos that weren't even covering that topic.
I would not have passed my CAL 1 final without you. I am so thankful you decided to make videos and post them on youtube. I love math, but lately I have been completely lost.
I am so grateful to you Professor Leonard! If there weren't your classes on UA-cam I wouldn't be able to understand the materials professors are teaching in our university. You are being extremely helpful even to some people in Armenia.
Jesus, I am so grateful for all your videos!! 🙏 So brilliantly explained! Don't stop teaching ♡ You are allowing us to painlessly understand, all these otherwise excruciatingly difficult classes.
He spends the exact amount of time as my professor, but the outcomes are absolutely different... so nicely explained, good pace not too slow nor too fast.
Oh my goodness...I am so glad I found this channel...I think you're going to be the reason I pass Calc 2. Thank you so much. You are my professor now lmao.
Love how you ask the class if they like racing before using it as an example. A lot of other teachers would be like this example is about knitting and I don't care if you like it or not 🤣
*TIP:* @36:00 It helps to separate the constants from the variables when you go to evaluate the integral. For the first term in the integral, begin by writing 1/2 x^2 instead of x^2/2. That way you can pull out the 1/2 and be left with evaluating 3^2 - (-2)^2 which is much easier. You get 9 - 4 which equals 5 and then you multiply by 1/2 to get 5/2. Every time you see a constant, get rid of it before plugging in your bounds to evaluate and you'll make the math a whole lot easier and save yourself from doing the same work over and over again. :)
i honestly dont understand a lot of the stuff my teacher talks about in class, but when i watch his videos everything makes complete sense. I would not be passing calc without you!
You've saved me yet again. You've helped me through community college when I was working full time and studying at night and you're helping me now that I've transferred to Stanford. Can you teach others to teach like you?
Ive watched all his videos so far for this playlist and not once has he lost me or confused me, this man has a true god-given gift for teaching. Thank you Professor Leonard
Thank you! You have the most amazing talents of making the very complicated subjects in calculus understandable. Your lectures help me peruse my dreams. Much love!
Thanks Professor Leo, I studied Statistic and Calculus 1 via Pro.Leo's lectures, and then I got A on these classes. Mr Leo, now I am taking Calculus 2 and I haven't not understood about work done, and the section "Application to physics and Engineering to find F and P and Moment. Pro Leo could you please post the lecture for these part in your channel. You are great Professor, and your lectures have helped me alots. Thanks so much
love your methods of teaching you really helped me out in calc2, kept me at an A average for the class. Now I'm just rewatching videos to study for my finals.hope everything goes well
Superman coming to rescue the world... well, at least he's helping me greatly at the moment. Professor Leonard always simplifies complicated topics and does it interactively. Thank you for teaching effectively!!
Thank you so much Professor Leonard. Everything makes so much more sense thanks to your lectures and its entirely free. You are doing a great service to every student in America.
Everything explained very well, not just rushed to go ahead. Thanks Professor. I never had a good teacher since my school time that's why my base is very poor. You are amazing.
Hi, professor Leonard, from Ensenada, México, thank you very much. Im a gramma but I wanted to stydy calculus and found it a little complicated some times, you have been of great help.
Thanks god bump into this. Have my midterm this week and have to many thing that i forgot. Thanks Professor Leonard. Best regards from Malaysia Student :)
i'd love to meet professor leonard at a red light and race with him hahaha what a nice guy. thanks for all, see ya on calculus 2 playlist. greetings from chile by an autodidact
I've been having a really rough time getting rebooted on calc because of stress, and this is very helpful for understanding from the ground up. Just need to get muuuch better at basic conversions and trig identities...
My Calc 2 teacher at the university of Akron is probably the worst math teacher I have ever had I sat through 20 minutes of this lecture and understood more from this video than 2 hours in my actual lecture.
if i am not wrong, he was explaining the Rolle’s Theorem when he said when f is continuous over the closed intervals [a,b] and differentiate over open intervals (a,b), then there must exist a number c when f’(k)=0.
Maybe I missed something. In the last example, the one with the sideways parabola, why is the area calculated the Total area and not the area above the x-axis minus that below? Or is it?
Legit was failing my first exam.... this man brought me up 70% on exams. I ended my CALC 2 class with a 97%. Love this man so much lol.
Nice, well done!
that's not possible so ur lying
@@lcv8525Unless the course doesn’t care much about test scores…unlikely.
its also possible for professors to drop the lowest test score. Some of them do that.@@lcv8525
This is such a strange lie... it's not possible to fail the first exam and end the class with a 97%. You'd have had to literally get 100% on everything else and the first test would have still had to have been only like 10% of your final grade.
Lol. He says "Stop me if I make a mistake", Like he ever makes mistakes. This guy is single handedly helping me pass my Calculus 2 for Engineers class in college right now. thank you so much.
same fam
He has made mistakes in several videos - he just usually catches them, or is corrected by one of the students.
And this actually makes him more human, instead of those robot teachers who pretend like they never ever make mistakes.
Hes not a god for god sake every human makes mistakes...?
Calculus for Engineers II class. Struggle-cuddling these videos rn while I try not to go rock back and forth in the corner of my room lmao
Yep, waaay better than my actual prof that just put a 5 min video explaining the whole chapter -_-
0:00 Setup
14:40 Ex 1
21:40 Ex 2
38:50 Ex 3
42:00 Ex 4
51:50 Ex 5
1:00:19 Ex 6 (in terms of y AND x)
- 1:07:45 What are you integrating w/respect to? The hard way.
1:27:23 The easy way
Thank you
Hero
*TIP:* In Calculus 3, these concepts will be extended to find the area between 3-D surfaces and 3-D objects.
TIP: @36:00 It helps to separate the constants from the variables when you go to evaluate the integral. For the first term in the integral, begin by writing 1/2 x^2 instead of x^2/2. That way you can pull out the 1/2 and be left with evaluating 3^2 - (-2)^2 which is much easier. You get 9 - 4 which equals 5 and then you multiply by 1/2 to get 5/2. Every time you see a constant, get rid of it before plugging in your bounds to evaluate and you'll make the math a whole lot easier and save yourself from doing the same work over and over again. :)
@@taekwondotime wow
Going to my calculus lectures i was only getting 60-70 on my quizzes, using your videos ive gone up to 90-95 on my quizzes! Thanks Professor Leonard, you're a life saver!
This is the best thing that has ever happened to youtube!!!!
I agree
Really true
I find myself raising my hand when I watch your videos. lol
+Fine Fina This man is awesome . I wish we had a teacher like him , but some points i do not understand that which school is that . I'm studying in university but i do not know if you guys are from university or some other school types. Sorry if my english is not enuough by the way. I hope i wont disturb you and you will answer me
Same :V
me too
Same here🙌
Same here
You should be getting some sort of teacher of the year award 🥇 your teaching methods are outstanding. Your students are lucky to have you. Thanks for taking your time to teach the rest of us
I DONT GO TO CLASS FOR CALC 1 OR CALC 2 & PASSED 97% BECAUSE OF YOU NEVER HAD TO GO TO CLASS THANK YOU NO ONE ELSE EXPLAINS IT LIKE YOU !!
If there is anyone for the first time, I just want to tell you that Professor Leonard helped me to get A* in calculus easily. He has made things simpler for al of us. I am following his videos since 2016.
Quarantine classes need you, I'm so glad I found your page!
honestly i dont usually comment on videos but sincerely thank you!!! you are taking the time to make us fully understand concepts and don't rush it like professor in the Top 20 universities in the world, however they expect students to understand things on the fly and being a student in these type of universities, people just expect you to be smarter than everybody and do well on everything but honestly we struggle to understand like everybody and i feel that professors are not aiming to teach us anywhere more than a hunger game attitude of keeping an average and testing who can survive. Truthfully thank you
i'm in UofT and prof is the worst.. tbh I would fail without youtube. online learning sucks
Perfect example of true teacher. Your way of teaching exceeded my expectations.
Because of you today, I was able to transfer from Merced College to Cal Tech, your videos absolutely helped me get transferred to caltech
At 14:10 you can hear someone saying really soft "it doesn't make sense" lmao i feel you bro
He said the opposite actually, "it makes sense"
Dear Brofessor Leonard,
I'm on summer break between Calc 1 and Calc 2 and I've been going through your lectures of both. It's wonderful that you never assume that your students know things. You've cleared up so many random areas of confusion about logarithms, exponent rules, trig/inverse-trig, properties of this or that thing, all while watching videos that weren't even covering that topic.
I would not have passed my CAL 1 final without you. I am so thankful you decided to make videos and post them on youtube. I love math, but lately I have been completely lost.
My professor is proficient in giving us assignments/tests/quizzes we are not prepared for.
Thank you for doing these videos
Nice voice, clear handwriting, pleasant demeanor, concise notes and lectures. I wish I could have Prof. Leonard for all of my math classes.
I am so grateful to you Professor Leonard! If there weren't your classes on UA-cam I wouldn't be able to understand the materials professors are teaching in our university. You are being extremely helpful even to some people in Armenia.
hi...i wanna talk to you
Jesus, I am so grateful for all your videos!! 🙏 So brilliantly explained! Don't stop teaching ♡ You are allowing us to painlessly understand, all these otherwise excruciatingly difficult classes.
He spends the exact amount of time as my professor, but the outcomes are absolutely different...
so nicely explained, good pace not too slow nor too fast.
Every professors should teach like you. Your teaching is simply amazing.
I did'nt know that I am capable of doing calc until I stumbled upon your videos. Thank You!
Oh my goodness...I am so glad I found this channel...I think you're going to be the reason I pass Calc 2. Thank you so much. You are my professor now lmao.
This is the most chad calc professor I have ever seen
I almost lost the semester if it weren't for your videos. They saved my life 😢
Love how you ask the class if they like racing before using it as an example. A lot of other teachers would be like this example is about knitting and I don't care if you like it or not 🤣
I just found this channel and holy smokes this guy is good. I love how he goes into detail and asks questions that other youtube channels don't
*TIP:* @36:00 It helps to separate the constants from the variables when you go to evaluate the integral. For the first term in the integral, begin by writing 1/2 x^2 instead of x^2/2. That way you can pull out the 1/2 and be left with evaluating 3^2 - (-2)^2 which is much easier. You get 9 - 4 which equals 5 and then you multiply by 1/2 to get 5/2. Every time you see a constant, get rid of it before plugging in your bounds to evaluate and you'll make the math a whole lot easier and save yourself from doing the same work over and over again. :)
my final is tomorrow and this helped me understand area between two curves so much better!
i honestly dont understand a lot of the stuff my teacher talks about in class, but when i watch his videos everything makes complete sense. I would not be passing calc without you!
I owe this man so much. If I could be any super hero I'd be Professor Leonard.
You've saved me yet again. You've helped me through community college when I was working full time and studying at night and you're helping me now that I've transferred to Stanford. Can you teach others to teach like you?
Ive watched all his videos so far for this playlist and not once has he lost me or confused me, this man has a true god-given gift for teaching. Thank you Professor Leonard
Thank you! You have the most amazing talents of making the very complicated subjects in calculus understandable. Your lectures help me peruse my dreams. Much love!
wow, youre a lot better than my college professor! Let's see if I can pass my final with your videos.
Did you pass !!?
did you?
Don't leave us hanging
Cmon, we want to know.
@@Windcutter_Flora lmao
Thanks Professor Leo, I studied Statistic and Calculus 1 via Pro.Leo's lectures, and then I got A on these classes.
Mr Leo, now I am taking Calculus 2 and I haven't not understood about work done, and the section "Application to physics and Engineering to find F and P and Moment. Pro Leo could you please post the lecture for these part in your channel. You are great Professor, and your lectures have helped me alots. Thanks so much
honestly i dont even waste time watching the lecture videos coz i know ill end up here. so i just come to you and you never disappoint.
big thank you
love your methods of teaching you really helped me out in calc2, kept me at an A average for the class. Now I'm just rewatching videos to study for my finals.hope everything goes well
Professor Leonard is amazing. What an awesome environment for learning. Great teaching!!!
You’re an excellent professor 👍! , your table helps me so much when doing these questions!
Wow ! Your discussion is more understandable than my professor. Thank you very much Sir! :)
Your charisma and way of teaching is perfect. Thank you so much!
Superman coming to rescue the world... well, at least he's helping me greatly at the moment. Professor Leonard always simplifies complicated topics and does it interactively. Thank you for teaching effectively!!
You help me got an A on my exam!!!! Thank you very much!!!!! I wish you could be my teacher at Long Beach City College.
A month into calculus 2 at my school and I still haven't even graduated Professor Leanards calc 1! His students must be crushing calc 2.
Thank you so much for helping students all around the world. It's been 6 yrs ago but I'm still watching them and your ideas feel so fresh
Thank you so much Professor Leonard. Everything makes so much more sense thanks to your lectures and its entirely free. You are doing a great service to every student in America.
Everything explained very well, not just rushed to go ahead. Thanks Professor.
I never had a good teacher since my school time that's why my base is very poor. You are amazing.
He just saved my life.WHERE THE HECK DOES HE TEACH ANYWAY?
+Aung Lin Brazzers.
+Aung Lin Merced College in California
+bell hill 😂😂😂😈😈😆😆😆😆😅😅
Now i guess it's North Idaho university
Hi, professor Leonard, from Ensenada, México, thank you very much. Im a gramma but I wanted to stydy calculus and found it a little complicated some times, you have been of great help.
I have been going in the lecture room for this calculus coming out empty but when I have watched this tutorial video i have known thanks professor
you explain concepts with such lucidity, its refreshing
you're a REAAAAALLY GOOD teacher
Any amount of thanks would't be enough...I appreciate all of the hard work that you have put in.
I love your classes without you I would be lost. A+ here I come.
Im studying environmental engineering
And im pretty much failing my calculus class
Cramming up your video before my finals in 10 days
i want this guy to be my cal professor lol great videos Mr. Leonard!
Thanks god bump into this. Have my midterm this week and have to many thing that i forgot. Thanks Professor Leonard. Best regards from Malaysia Student :)
Me: took precal roughly 6 years ago.
Prof: "Can you solve it?... I sure hope so"
Me: sweats.
i'd love to meet professor leonard at a red light and race with him hahaha what a nice guy. thanks for all, see ya on calculus 2 playlist. greetings from chile by an autodidact
proud to be a student of professor leonord
My teacher sounds like the love child of Squirdward and Sandy from the tv show Spongebob, you sir have been voted as my teacher from now on.
I don't understand my teachers lectures so here I am and now I feel like my brain is expanding
U R the Best 👌👌👌👌👌👌👌
Awesome job as always dude! Every single video is a banger🔥🔥🔥
0:46:00, IMO, if x^3-x is an odd function, the net signed area is 0, and total area is 1/2.
Professor Calc Kent! That's great! Mild Mannered Calc Kent to the rescue! Slippery Slope Me!!
I've been having a really rough time getting rebooted on calc because of stress, and this is very helpful for understanding from the ground up. Just need to get muuuch better at basic conversions and trig identities...
@10:50....this idea...damn I love math. I was literally smiling as he revealed this
Awesome explanation. Thank you!
This is the second lecture where he mentioned his car! I really want to know what he drives. He already mentioned twin turbos :)
Thank you Professor Leonard. Your videos are the best.
i really hate maths but after seeing your video i kinda get interested in it, i wish i had a cool lecturer like you in every module i do
Love your lectures...
thank you dr , the extra good news about your lessons is that you take examples from the same book I have in my cal2 course .
book name plz
Thank you, TY Ty Ty
My Calc 2 teacher at the university of Akron is probably the worst math teacher I have ever had I sat through 20 minutes of this lecture and understood more from this video than 2 hours in my actual lecture.
Life Saver
hey,you are very good in this. I'm astonished
may God bless professor leonard these tutorial are the best .thank you for your tutorial professor you the best and love you.
When instead of teaching, your professor just links this guy's video.
this is the most helpful video i've ever seen...Thanks professor 💖💖
you're a great teacher
This guy is so good at teaching
Thank you professor! You're one of the greats!
OMG , you cleared my concept ❤️
Love your videos!
Why am I not in his class room, learned this section way easier watching this than in my actual class
if i am not wrong, he was explaining the Rolle’s Theorem when he said when f is continuous over the closed intervals [a,b] and differentiate over open intervals (a,b), then there must exist a number c when f’(k)=0.
da goat
Awesome lecture!!!
Very well explained. Prof. you really made this simple
Still watching in 2019!
even in 2020
@@memoonajamil4213 2021 soon, ja!
excellent
Wow that car example is pretty neat!!!
Calculus final is in 3 days and you give me hope good sir
Great teacher
"Failure to preform... nobody likes that!"
Maybe I missed something. In the last example, the one with the sideways parabola, why is the area calculated the Total area and not the area above the x-axis minus that below? Or is it?