He is the first math professor I have ever seen who genuinely cares about the students. This is obvious from his habit of constantly checking that the students follow all of his steps - you _only_ act that way when you actually _want_ to teach people something.
I just want you to know that I sincerely appreciate you posting these lectures online. I love mathematics, it is just hard to see the concepts at times. You introduce and teach the topics in such a detailed way that I literally doubled my test scores after watching your videos. You have made such a difference, thank you. Thank you so much. -Kylie
I want to thank you profesor leonard. I received my final grade on Calculus 1 and it was an A. I remember going to the counselor considering repeating the class, but I stayed and persevered watching your videos. I took class with one of the worst reviewed professors at my college and I am infinitely grateful that I found your channel. Now let’s conquer Calculus 2.
I aspire to master calculus and someday teach it as well as this guy does, this man is brilliant. It's one thing to know how to do something, but to explain it in a manner that someone who is just starting out can grasp is an art! neither too much or too little detail, that is the key.
I just found your channel. I sat down and took notes while you talked like I would do in lecture. Difference is that you're significantly better at explaining than the math professors at one of the top Canadian universities that I go to.
@@magichorse18 uofa is ranked at number 4 overall officially and ranked number 1 for artificial intelligence in Canada, what are you even talking about? - And for mathematics, they are also among the top ranking for their research in algebra/ number theory. - Many reputable professors, like Don Page (who did his graduate work under Hawking) currently do research there - They are one of the few canadian universities that are partnered with large organizations like Google, CSIS and IBM. - They are also the only Canadian university with a division solely designed to study nanotech as well
@@llawliet2310 ok so i just checked the rankings and i was wrong! uofa is not too far off from being one of canadas top schools. www.timeshighereducation.com/student/best-universities/best-universities-canada I would consider the top 3, maybe top 4 to be our best. So like uoft, ubc, mcgill, and maybe mac. but uofa is def not as far off as i thought itd be!
You are the best Maths teacher that I have ever had. I am saying this because of your way of teaching. Most of the teachers especially professors are absolutely arrogant that they do not care whether their student have learned or not. You are a EXACT BIG BOSS...
I am taking calc 1 in the summer, my teacher sucks at teaching it because he just puts up powerpoints, without your videos i wouldve failed 2 of my tests by now. Thank you
The beer can comments at ~1:13 made me laugh out loud. I love your sense of humor, Professor. Not only do you make math easy to understand, but you also make it fun as well. Endless thanks to you for taking the time to make this great resource available to everyone!
I completely ignore my calculus professor during class so that I learn things the right way, with professor Leonard, right off the bat. This man is the best and he deserves better lighting in that classroom.
That's what i am saying best prof all time no bs HEEEE IS GREAT wish i knew him when i started calculus. But we live and we learn I am going to watch him for calc 2!
I just want to say thank you for this video! I am from Australia and actually have 3 hour assessment today all on optimisation and functions in general with restricted domains. This is really helpful and gave me a very clear, and increased understanding. Thank you so much!
I might as well just skip math class and watch your videos instead, because I literally don't understand anything with my current math teacher, but I can easily follow your lectures 99.99% of the time. So just thanks for that man and keep doing what you do
I"m taking an online calc class at a community college and I was getting so frustrated with this section in the book. It looked like gibberish. I've watched a lot of these videos but this one takes the cake. You make it easy to get a first-class education without having to pay big bucks for a school with professors that don't teach with half this amount of detail. Thank you so much for everything professor Leonard!
33:23 You could factor using AC method using -36x and -10x into (4(3x^2-36x-10x+120))=0. Also at 1:28:54 you could cross multiply since you have 2 ratios (left side is 4πr/1).
My Calc 1 class in college is stuck online bc COVID-19 has closed campus. Our professor has directed us to you and I have to say... You are awesome in your teaching and easy proccess to help understand the concepts. Shoutout from myself and my class at University of Northwestern, St. Paul. Thank you for the awesome lectures, keep it up Prof.
Professor Leonard, all the videos are much appreciated! They have helped me tremendously especially with Integrals. I definitely plan on watching your videos next semester for Calc 2. I respect the little things you do while teaching, for example, on this video from 44:12 - 44:24. Besides your math skills...Your off the cuff drawing skills are on point. Take Care.
I greatly appreciate your work here. You have a significant talent for teaching! Better than all of my professors combined. I can learn more from 30 minutes of your videos than I would with 5 hours of class time. Thanks a lot !!!
1:11:22 the equation is not correct for checking x=0 because if x=0 then there will be no ocean pipe, thus the cost is gonna drop to half at the (x^2+25)^1/2 part(we need to divide this with 2 in this scenario). The actual minimum cost should be (8+5)/2=6,5 dollars. Correct me if I am wrong please.
Thank you so much. I am watching your calculus one to get ready for my summer classes and they are awesome. Defiantly going to watch calculus two and three lessons along with my next courses.
For the second problem, anybody who has problem understanding it my suggestion would be, to take a piece of paper and cut the four sides and make a paper box. And maybe calculate whether you can fit more stuff in it that way or by guessing.
I've said it before and I'll say it again without your videos I would not be able to pass my Calculus class. The problem with the pipeline is almost exactly like a group discussion we're having (it's an online class with zero lecturing so you're basically teaching yourself) and the professor's comments on our posts are not helping.
The opportunity for a really corny "one if by land, two if by sea" joke was missed here. Other than that, this is perfect and I love it. Thank you, Professor!!
When x is 0, the total distance via the land is 5 + 8 = 13, and the cost is $0.5, so in total, it should be 13*0.5 = 6.5, but if we place x as 0 to the formula, we're getting $9. it doesn't make sense.
+Grigor Simityan x is the distance along the shore therefore the max is 8 (the case where you go 5 km inland and 8 km over) and the min is 0, the case where the length of pipe is = to the hypotenuse you're referring to and the pipe laid on land is 0
we are not allowed calculators for these calculations in our class. its not fair T_T. Btw Professor Leonard, thank you for all these videos, they are really useful. I turn off Adblock when I'm on your channel :)
Professor, at 54:53 why can't the maximum be 13 instead of 8 since the maximum distance we are looking at and trying to minimize is the 5km+8km distance? Thank you
In the beginning I was like fuck yeah, finally a framework on how to think in order to get word problems like these into numbers and variables, and then how to reduce your formula to one variable. After watching the whole video, it has all been reduced back to wizardry for me.
![How to Solve ANY Optimization Problem [Calc 1]](/img/n.gif)
You're the first math professor I've ever seen who actually apologized for skipping a step in a problem. I wish all profs were like that!
He is the first math professor I have ever seen who genuinely cares about the students.
This is obvious from his habit of constantly checking that the students follow all of his steps - you _only_ act that way when you actually _want_ to teach people something.
@@Peter_1986 Yes..the only pain i get when i watch his video is not discovering him earlier
Now if he would apologise for singing....just kidding!
Agreed!
I just want you to know that I sincerely appreciate you posting these lectures online. I love mathematics, it is just hard to see the concepts at times. You introduce and teach the topics in such a detailed way that I literally doubled my test scores after watching your videos. You have made such a difference, thank you. Thank you so much.
-Kylie
Nice
Double of 0 is still 0 honey
@@joe123-s9p LOL that’s a great one
I am just addicted to your style of teaching. Everything is clear, understandable and interesting. I wish I can jump from Uganda to your class
I want to thank you profesor leonard. I received my final grade on Calculus 1 and it was an A. I remember going to the counselor considering repeating the class, but I stayed and persevered watching your videos. I took class with one of the worst reviewed professors at my college and I am infinitely grateful that I found your channel. Now let’s conquer Calculus 2.
How'd it go?
@@Bilbus7 He dropped out after taking calc 2
I aspire to master calculus and someday teach it as well as this guy does, this man is brilliant. It's one thing to know how to do something, but to explain it in a manner that someone who is just starting out can grasp is an art! neither too much or too little detail, that is the key.
I wish you good luck :)
Yoo
Almost 2024 now. just out of curiosity, wanted to ask wether u mastered calc or not.
I just found your channel. I sat down and took notes while you talked like I would do in lecture. Difference is that you're significantly better at explaining than the math professors at one of the top Canadian universities that I go to.
UW or UofT?
UW is like mid tier. Tops include of UoftT McGill, UofA, UBC, and Queens. UW is known for their pure mathematics programs at the graduate level.
@@llawliet2310 bruh uofa could never even be close to being "top tier"
@@magichorse18 uofa is ranked at number 4 overall officially and ranked number 1 for artificial intelligence in Canada, what are you even talking about?
- And for mathematics, they are also among the top ranking for their research in algebra/ number theory.
- Many reputable professors, like Don Page (who did his graduate work under Hawking) currently do research there
- They are one of the few canadian universities that are partnered with large organizations like Google, CSIS and IBM.
- They are also the only Canadian university with a division solely designed to study nanotech as well
@@llawliet2310 ok so i just checked the rankings and i was wrong! uofa is not too far off from being one of canadas top schools. www.timeshighereducation.com/student/best-universities/best-universities-canada
I would consider the top 3, maybe top 4 to be our best. So like uoft, ubc, mcgill, and maybe mac. but uofa is def not as far off as i thought itd be!
You are the best Maths teacher that I have ever had. I am saying this because of your way of teaching. Most of the teachers especially professors are absolutely arrogant that they do not care whether their student have learned or not. You are a EXACT BIG BOSS...
Wonderful to be able to learn maths in my sixties. Great lectures Professor Leo.
are you dead yet?
Hope you are still alive and doing well.
He is the only reason i am passing calculus... Thanks so much!
+Noah Buck Same here
lolz
I'm still failing by a little bit.. but him and nancypi are the only reasons why it's only a little bit and not completely failing lol.
I am taking calc 1 in the summer, my teacher sucks at teaching it because he just puts up powerpoints, without your videos i wouldve failed 2 of my tests by now. Thank you
Ive watched so much of this series that I really wanna know what the classroom looks like behind the camera haha
Same here lol, we’re invested now
Thank you Jesus. Video from 5 years ago still helps me today!
make that 6 lol.
Thank you Leonard.
This teacher is hilarious and knows his stuff. You can really tell when someone loves what they do and when someone hates it.
when he apologizes for not explicitly showing the steps
''.'''
The beer can comments at ~1:13 made me laugh out loud. I love your sense of humor, Professor. Not only do you make math easy to understand, but you also make it fun as well. Endless thanks to you for taking the time to make this great resource available to everyone!
I completely ignore my calculus professor during class so that I learn things the right way, with professor Leonard, right off the bat. This man is the best and he deserves better lighting in that classroom.
That's what i am saying best prof all time no bs HEEEE IS GREAT wish i knew him when i started calculus. But we live and we learn I am going to watch him for calc 2!
I just want to say thank you for this video! I am from Australia and actually have 3 hour assessment today all on optimisation and functions in general with restricted domains. This is really helpful and gave me a very clear, and increased understanding. Thank you so much!
I might as well just skip math class and watch your videos instead, because I literally don't understand anything with my current math teacher, but I can
easily follow your lectures 99.99% of the time. So just thanks for that man and keep doing what you do
Facts
I"m taking an online calc class at a community college and I was getting so frustrated with this section in the book. It looked like gibberish. I've watched a lot of these videos but this one takes the cake. You make it easy to get a first-class education without having to pay big bucks for a school with professors that don't teach with half this amount of detail. Thank you so much for everything professor Leonard!
33:23 You could factor using AC method using -36x and -10x into (4(3x^2-36x-10x+120))=0. Also at 1:28:54 you could cross multiply since you have 2 ratios (left side is 4πr/1).
I feel like I leave a comment on every single one of his videos, but this man is responsible for me passing calculus.
just started my college calc 1 and have been struggling but your videos have made me actually understand whats going on
1:09:51 how doesssssss heeee dooooooooooo thattttttttttttttttt OOOoOoOOOooOoO
Get out weeb
"Doctor Strange aint got shit on me"
Ohh the magic of video
oh nothing he just going hyperbolic
A prof who is v humble explain v slowly to a point of understanding with simple english
Professor You are the best math teacher I ever came across
Sir, you are beyond amazing. I wish I was one of your students. With your clear and strict explanation, my math marks would reach the stars.
🙏
My Calc 1 class in college is stuck online bc COVID-19 has closed campus. Our professor has directed us to you and I have to say... You are awesome in your teaching and easy proccess to help understand the concepts. Shoutout from myself and my class at University of Northwestern, St. Paul. Thank you for the awesome lectures, keep it up Prof.
ua-cam.com/video/XPCgGT9BlrQ/v-deo.html 💐💐💐💐💐💐
Professor Leonard, all the videos are much appreciated! They have helped me tremendously especially with Integrals. I definitely plan on watching your videos next semester for Calc 2. I respect the little things you do while teaching, for example, on this video from 44:12 - 44:24. Besides your math skills...Your off the cuff drawing skills are on point. Take Care.
I greatly appreciate your work here. You have a significant talent for teaching! Better than all of my professors combined. I can learn more from 30 minutes of your videos than I would with 5 hours of class time. Thanks a lot !!!
You are the only reason why I'm being able to learn calculus
I'm in AP Calcluas and this helped me with my homework so damn much
No one like you in this world professor, you are the champion.
Not all heroes wear capes. Thank you for being a great teacher.
The cardboard box problem came up in my homework 2 days after I watched this video. Was extremely helpful to come back to, thank you 🙏
You just enlightened my soul.... those last 5 minutes answered all my questions thank you!
for that last example, the second derivative should be 4pi+4000/r^3
I AGREE. Jerry E. Shepherd
watch until the end. he corrected it.
Thank you for uploading this! It really helps clear up some of the past problems I have had with Applied Optimization
One of the best teachers ever thanks for helping me to pass....
I use my varsity just to get the transcript, he is the reason why i love mathematics, keep posting we will subscribe
Professor, your lectures are amazing! It is saving me for my final that I have tomorrow, thank you
Man, that S" = 4pi - 6000/r^3 at 1:32:48 threw me off for a good while until I realized it was a mistake.
sir , A BIG Thanks From EGYPT
This is so helpful, thank you for making these. Also 100% can't help but raise my raise my hand whenever you ask if your class gets it
1:18:00 The textbook didn't show where the formula came from. This is why I supplement the reading with your classes. Thank you!
ua-cam.com/video/XPCgGT9BlrQ/v-deo.html 👍💐💐💐
1:11:22 the equation is not correct for checking x=0 because if x=0 then there will be no ocean pipe, thus the cost is gonna drop to half at the (x^2+25)^1/2 part(we need to divide this with 2 in this scenario). The actual minimum cost should be (8+5)/2=6,5 dollars. Correct me if I am wrong please.
Taking Calc 1 in the summer semester was one stupid idea. But thanks to you it is going well (:
It's :) not (:
+Nicolino Will omg really who cares its a smiley he can write it how he wants
will you mind someone with a dock as a profile pic?
Yeah currently taking a 5-week calculus 1 summer class and after that a 5-week calculus 2 summer class. Pretty intensive... I don’t recommend it.
@@SantiagoRK96 I have calc 1, calc 2 and calc 3 in the same semester 😑😑😑😑😑
dude you rock this is life changing after having such a bad lecturing professor
Thank you so much for your video's! Greetings from the Netherlands, Petra
This video concludes my prep for mid semester exam.
Thankyou
Thank you so much. I am watching your calculus one to get ready for my summer classes and they are awesome. Defiantly going to watch calculus two and three lessons along with my next courses.
Thank you for posting these videos, I have been struggling in math and after watching this I feel like I have a better understanding of it :)
For the second problem, anybody who has problem understanding it my suggestion would be, to take a piece of paper and cut the four sides and make a paper box. And maybe calculate whether you can fit more stuff in it that way or by guessing.
I am tired of watching your lectures professor Leonard.
Thanks for your work.
Amazing lecture. Definitely going to subscribe. Everything is so clear, and you make it fun to learn. Thanks!
professor leonard, you sir are simply amazing at how you teach!!
ua-cam.com/video/XPCgGT9BlrQ/v-deo.html 💐👍💐
He makes math so much more enjoyable.
I passed my Calculus course with an A (:
Great video! It was very well explained and i felt after watching that video i could confidently approach any optimization problem.
7 years later after this video was posted, and im using it rn
thx :)
felt
I've said it before and I'll say it again without your videos I would not be able to pass my Calculus class. The problem with the pipeline is almost exactly like a group discussion we're having (it's an online class with zero lecturing so you're basically teaching yourself) and the professor's comments on our posts are not helping.
Awesome video, thanks for the help 🙏
what a great math professor:)
In the last part , derivative of -2000r^-2 is 4000/r^3 not 6000
you're the best!!!!!!! you help me every now and again........thank you very much
YES! I was hoping you'd sing the quadratic formula song. Ah, brings a tear to my eye. It's like I've been in your class the entire time!
FINALLY, BLESS YOU?! THESE VIDEOS SAVED ME 🙌 SO BLESS YOU SIR
You are just awesome . Looking forward for more videos from you
at 38:35 answer is actually 19600/27, not 726. But I'm sure you already know that :-)
ua-cam.com/video/XPCgGT9BlrQ/v-deo.html 💐💐💐💐💐👍
The opportunity for a really corny "one if by land, two if by sea" joke was missed here.
Other than that, this is perfect and I love it. Thank you, Professor!!
When x is 0, the total distance via the land is 5 + 8 = 13, and the cost is $0.5, so in total, it should be 13*0.5 = 6.5, but if we place x as 0 to the formula, we're getting $9. it doesn't make sense.
ua-cam.com/video/XPCgGT9BlrQ/v-deo.html 👍💐💐💐💐💐
bu yorumu arıyorum 1 saattir x 0 olunca artık deniz yolunu hic kullanmamıs oluyoruz dolayısıyla fiyat düsüyor
This was such a helpful and informational video! Thank you!
I wish you were my teacher
Best teacher ever
all volume questions end up just being the limit towards becoming a sphere!
I get 4000/x^3 as the 2nd part of the 2nd derivative. Can you please explain how you get to 6000/x^3?
It was just a small error, I checked with a derivative calculator; it is 4000/x^3.
32:10 😹 That's why I come here to learn
Awesome! I wish u were my math teacher!
OMG IT FINALLY ALL MAKES SENSE! Thank you so much!
These lectures are so helpful! ❤️
Hello, for the question at 1:10:00 why is the max 8 (the base). Shouldn't the max be the hypotenuse. So 8^2+5+2=rad89
+Grigor Simityan x is the distance along the shore therefore the max is 8 (the case where you go 5 km inland and 8 km over) and the min is 0, the case where the length of pipe is = to the hypotenuse you're referring to and the pipe laid on land is 0
we are not allowed calculators for these calculations in our class. its not fair T_T.
Btw Professor Leonard, thank you for all these videos, they are really useful. I turn off Adblock when I'm on your channel :)
He is such a good teacher damn.
What is said what the second derivative gives you in the final example at 1:32:45 ?
your a badass professor Leonard.
This is soooo good, great job!
Such a lifesaver. Thanks!
have you done 3.9 on differentials?
+Vianka Vianey Watch Calculus 3 Lesson 13.4. The Intro is about Differentials from Calculus 1
+Professor Leonard thank you 😍😘
Prof. You are the best
Anyone get the final answer for the second example with the volume of the box? After plugging in 10/3 is the answer 217 7/9 in^3 for the volume?
ua-cam.com/video/XPCgGT9BlrQ/v-deo.html 👍💐💐💐💐
Thanks I had the otter version of this type of problem but was able to complete it
thank you so much for your help again.
Do you have a video on Newton's method professor?
good work
This was really fun! Thank you very much! x)
I will definitely refer to your videos once I am taking calc 2 this video is so helpful
Thank you sir thanks🙏🙏🙏🙏🙏🙏🙏🙏🌹🌹🌹🌹
Dude. Prof. Leonard grew up on a dairy? He really is Clark Kent!
Being ripped and smart, that's what I wanna be. Teach me how to get ripped.
Professor, at 54:53 why can't the maximum be 13 instead of 8 since the maximum distance we are looking at and trying to minimize is the 5km+8km distance? Thank you
I also thouht that if the pipe goes just on the land distance must be equal 13km. then cost should be 13x0.5=6.5$
In the beginning I was like fuck yeah, finally a framework on how to think in order to get word problems like these into numbers and variables, and then how to reduce your formula to one variable. After watching the whole video, it has all been reduced back to wizardry for me.