Calculus 1 Lecture 4.3: Area Under a Curve, Limit Approach, Riemann Sums
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@Reformed4good6 жыл бұрын
I can't believe this dude teaches at a community college. I am quite sure they do not pay him what he is worth. He has changed my semester, and most assuredly my Calculus final grade. Thank you.
@J.B243 жыл бұрын
My Calc 2 teacher used him for the online lectures for the class. It was an online class. My teacher stole PL's salary as far as I'm concerned. He did nothing, he just posted PL's lectures and told us to watch them.
@nuzhatazim81942 жыл бұрын
Nah they get paid 100k
@HimuraK12 жыл бұрын
@@nuzhatazim8194 Not enough
@MrJ6912 жыл бұрын
@Trance - 009 Sound System Dreamscape it is
@ThanhTriet6002 жыл бұрын
@@J.B24 That sounds like a total scam to pay for a class you could get for free. You should take it up with the dean.
@blackjack27708 жыл бұрын
It's so sad how many professors just fly right through all this material without organizing it into a way we can all understand it. I wish every professor was like you... you break it down and explain so flawlessly, even the worse people in math will get it with the way you teach. Then they give you these difficult exams with problems that the students have never seen or even gone over before.... and the professors have the audacity to say how easy that was. OF COURSE IT'S EASY FOR THEM! They're fucking math teachers! Thank you Leonard for everything, I've been watching your videos since day one and don't know where I would be without them. If only there were more people like you in this world.
@mainefan018 жыл бұрын
+Danya Valentin agreed
@Peter_19864 жыл бұрын
I hate when math teachers give simple problems during lectures and then suddenly give super-hard problems during the exams, like wtf is that all about? The proper strategy would obviously be to _start_ with simple example problems and then gradually work up to exam-level example problems during the lectures _before_ the exam. I intend to become a math teacher in the near future, and that's exactly what _I_ am gonna do.
@alenaalena93224 жыл бұрын
Danya Valentin I agree!
@darthboganis13564 жыл бұрын
Sigma Notation 1:30 > Properties, multiplication of a constant 3:20 > Properties, addition/subtraction 8:45 > Open form/closed form notation 10:00 > Example problem 17:00 Rectangular Method Proof, Reimann Sums 22:45 > the integral is limit/sigma notation combined 49:15 > Arbitrary points - endpoints [left, middle, right] 55:00 > Example Problem 1:05:00 Net Signed Area 1:23:00 > Example 1:27:00 > proof (graph) 1:46:00 > Example 2 1:48:00
@adamharoon60213 жыл бұрын
Thank you!
@emptyFull1232 жыл бұрын
ありがと🥰
@armaanbath7532 жыл бұрын
you are a LEGEND
@barkhadibraahim10238 ай бұрын
thnaks bro
@violethill44548 ай бұрын
about the formulas for the sigma summation, what if the k is not equal to 1? lets say its 2, are those formulas still applicable?
@TehBluPanda4 жыл бұрын
Perfect, now I can finally find the area of those massive biceps
@Sito14794 жыл бұрын
Those are 3 dimensional. You’re gonna have to find the volume.
@Czmlol4 жыл бұрын
@@Sito1479 Triple integrals to the rescue.
@Peter_19864 жыл бұрын
@@Sito1479 I think that Jose means the surface area of the biceps.
@maximilianbur25604 жыл бұрын
@@Peter_1986 integral will spit out infinity
@lindarubio52119 жыл бұрын
I think its hilarious the way he gets caught up on spelling words like choose but he is a genius in mathematics. All jokes aside this is the best math professor I have ever had. Thank you sooo much for posting your lectures Professor Leonard!!
@AndyU968 жыл бұрын
Shouldn't be very hilarious, one has to do with intelligence and logic, the other has to do with knowledge. I hope you get what i mean
@kallmekrissarchivetiktoks80127 жыл бұрын
Ameerhun1996 it's objectively funny tho
@Peter_19864 жыл бұрын
Well, that basically demonstrates that spelling skills don't really say anything about intelligence. A lot of people don't realise that simple fact.
@BallsonPHACE10 жыл бұрын
prof leonard, you're amazing. sitting at home watching youtube is now meaningful instruction time
@miahua91113 жыл бұрын
Fax
@radwizard8 жыл бұрын
Yes @21:45 the answer is indeed 440, for us people at home.
@jameswilson43288 жыл бұрын
Riemann Sums start at 23:00
@typingaddict13197 жыл бұрын
mvp
@evanpeluso81895 жыл бұрын
my man
@syrenka65 жыл бұрын
thank you
@learnwithsalim12284 жыл бұрын
god bless you
@sarazebardast1082 жыл бұрын
This man posted sth 7 years ago and I'm finding it so helpful now, world turns they say?
@EYMmusic6 жыл бұрын
Thank you so much! I finally understand WHY i'm applying certain things. Beforehand, I was just memorizing and doing problems from pattern recognition without truly understand why I was doing it. I have a much deeper understanding now. THANK YOU. You're students are lucky to have you, and so are we. God bless everyone xx
@joshmick2 жыл бұрын
I raise my hand when he asks if I understand. I forget that I'm not actually in his class. I'm on my couch eating ice cream.
@MrCanadianplayer7 жыл бұрын
If I told you my math teacher did this lecture in 20 minutes and I couldn't understand anything.. well it happened.. Prof. Leonard.. I guess I'll be switching over to your Cal 2 class from now on!
@adityaekbote84983 жыл бұрын
me too
@edsteadham4085 Жыл бұрын
I teach this stuff and I can say without reservation this is the best calculus teacher on planet earth. I wish he would bottle his methodology and sell it.
@majokthuchlueth30484 жыл бұрын
When anyone gets an incredible Prof you feel like you are the one and only student who gets to understand Math! I can’t thank you enough Professor Leonard ❤️💕 your assistant would always be appreciate
@SteamPunkLV6 жыл бұрын
whenever you look at a blackboard, just imagine how much information has been written on that board, just how many things have been taught and understood on that board. imagine all the ink and all the calculus that has been written on it
@Tuanski8 жыл бұрын
So much math .. and muscles
@rchetype70297 жыл бұрын
A big guy, for you.
@univerex-80615 жыл бұрын
Nice Bane reference.
@charkeah3785 Жыл бұрын
This the only pro in the universe may you be blessed with more years to teach even unborn
@NS-zi1xv Жыл бұрын
We need to make a shrine for this man, he's out here changing lives.
@coledenver47644 жыл бұрын
When the kid at the very end said "because i hate myself", I got a noise complaint in the library. hahaha
@nattcattt7 жыл бұрын
This was fantastic. I missed my prof's lecture on this material because I was out sick and I probably learned more from this than I would have had I come to class. Very simple to follow and makes the material seem easy :)
@agh17504 жыл бұрын
if anyone's wondering why the sum from 1 to n is n/2(n+1) its because if you add the first and the last terms it equals n plus one, and when you add the second term to the second last term it's still n+1 because the amount gained from the first term to the second term is equal to the amount lost from the last term to the second last term. That is the hidden symmetry of the problem, the question then is of how many "n+1" terms you add up, and the answer is simple, since you're dividing your interval into pairs, you're adding "n+1" n/2 times so the total is the product of n/2(n+1)
@anonymoususer43562 жыл бұрын
Thank your Prof. Leonard, Excellent lecture. Best math professor i've ever had.
@sabel98414 жыл бұрын
my professor tried to teach us this in such a short amount of time and I spent WEEKS in a confused fog. this video cleared up my confusion and I feel confident for my final now! thank you so much professor :)
@sellakc Жыл бұрын
You have saved my butt! 😂 I can’t tell you how much I appreciated these incredible Calculus videos! I’m in an engineering program at a major university and the teachers are nowhere even near your excellent teaching style! You are getting these concepts through my 55 year old brain 😂
@FlorianHartfelder8 жыл бұрын
Leonard, you save lives. Thank you.
@yasminegarcia57089 жыл бұрын
many have worshipped your teaching, but i have to congratulate you! not every teacher can teach in the same manner that you do. ALOT ,if not all, of advisors from engineering told me to get out of that major however, they gave me a chance to pass calc 1 and youve made it EASY for me to understand. i thank you beyond measures!
@NguyenHaNhutLong7 жыл бұрын
You're the best teacher! You're my motivation to study math again! I'm currently taking an online math course at my university, but I never watch my professor's lecture. I go here on youtube and watch you! Thank you so much!
@jassimjaved3309 Жыл бұрын
Thank you Mr. Leonard! These are the best lectures of calculus I have seen and I wish I knew about them when I was studying calculus. I am watching them to finally know what calculus is all about! Thank you!
@princetgorson23436 жыл бұрын
If any difficulty in the class room I recommend KZbin, I can also learn from KZbin. Thanks for your tutorial.
@carsmiles40359 ай бұрын
The greatest teacher ever alive!
@user-op2qu6py1z3 ай бұрын
🙏🙏 Prof. cordial thanks for your benevolent help. After 21 yrs. of my numeric phobia on College math, really you implanted in my brain z joys and love of calculus so, i have got z real life resilience wisdom!
@1stplaceinvestments11 ай бұрын
I take this at University of Southern Mississippi in Hattiesburg, MS under Dr. Schroeder. He rushes through a couple of problems per class, usually and has never gone into any kind of depth. BY FAR, PROFESSOR LEANORD IS WHY I AM UNDERSTANDING ANYTHING IN THIS COURSE. Professor Leanord, if I did not have to pay for school right now, I would try and hook you up. I am looking forward to being able to contribute to your Patreon account. Thank You Professor Leanord!!! If I can EVER be mentioned in your category for anything that has to do with teaching, I would be honored. As students, we MUST demand and put pressure on Universities to teach in this manner!!!!!
@kevin-gg8ir5 ай бұрын
Yes!..The (Why?) Part! Love it Sir!
@cubajuanlolcubajuanlol85319 ай бұрын
I want to thank you Professor Leonard. Without you I would not have make this far in collage. You are amazing Professor! Thank you so much!
@user-xd4vv6uw3z Жыл бұрын
I would just like to say thanks for all of the videos you posted !
@vaibhavsethi49464 ай бұрын
I study at ubc and this man made me pass my midterms just with 1 day watching his videos. I wish I had a professor like you at my uni :)
@abdulsattarlutfi16653 жыл бұрын
Professor Leonard you are the best ever, thank you so much for sharing classes with us
@adrianloh69193 жыл бұрын
If i have 2nd chance to attend a class again, I won’t pack my backpack too fast, i would sit down enjoy to listen what lecturers talked at vey very end....
@sparkleyes10192 жыл бұрын
hardest calc 1 vid on this playlist
@asem8901 Жыл бұрын
Best show ever and this was my favorite episode
@user-kw2xs5rs2f Жыл бұрын
THESE LECTURES ARE SO GOOD! I FINALLY UNDERSTAND RIEMANN SUMS, THANKS PROF!
@surojpaul142 жыл бұрын
my utmost respect to professor 👏
@returntozero21128 жыл бұрын
Wish I found these videos at the start of the semester. Would have helped tremendously. Keep up the good work Prof Leonard.
@joeexotic60157 жыл бұрын
Prof.Leonard, i think you are one of the best math teacher I've ever met, which is that you can elaborate those Calculus ideas very straightforward and most importantly clear, I think you deserve smarter students to teach, and by the way I can definitely see the burning read flame in your eye that implies you are impatient with those kids.
@rabiataj70848 жыл бұрын
Actually you really help me in my semester exams GOD bless you and all the teachers like you. thankyou thankyou so much. Great job sir.:)
@cubbyhoo3 жыл бұрын
I was laughing so much at the way Leonard sighs and says "Remeber we just talked about bread?" @27:19
@senpai60182 жыл бұрын
Thanks sir. adamsın.
@thepsychocybe70784 жыл бұрын
damn this guy got his last bit of lunch money taken from him in gradeschool and got jacked.
@mn-yv2ur7 жыл бұрын
Professor Leonard, thank you so much. I am speechless. you are amazing. I watch all your videos. you've helped me a lot with your clear lecture. I wish I was your student.
@andimahendrinah70786 жыл бұрын
prof. you the highest of all math lecturers a saw, they teach us a complicated topic within 30 minutes thinking maybe that its a revision. I don't get anything from class but your teaching is raising me up coz I was falling. keep it that way pro may the Lord shower you with a lot of blessings. one more thing prof you are not selfish because anyone can watch your videos. keep that way!!!!!!!!!!!!!!!!!!!!!!!!
@marceladominguez55768 жыл бұрын
this video is saving me in calc 2 right now, bless your soul!!!
@benjaminombeni7885 жыл бұрын
Me too lol
@dankahraman3548 жыл бұрын
Dr.Leonard, I am downloading your Calculus 3 courses as they are becoming available. Any plans for Linear Algebra or other topics? Your courses are very well organized and the practical examples are great. Loved the curve sketching using f'(x) and f"(x). Concavity, maxima and minima. Finished lessons 4.1 & 4.2 in Calculus 1 today.
@abdullahmohammad56137 жыл бұрын
I had a roman professor ( Christian Enache) and you worth a million Enaches👏
@yasiraydn53186 жыл бұрын
Mindblown at 49:38 when i realized dx comes from deltax. Cool.
@sifiso50554 жыл бұрын
🤭
@DigaDupSuck3 жыл бұрын
yep! dy/dx = delta y/delta x = slope
@hoangpham44683 жыл бұрын
Good teacher, during in university I never had instructor like him
@kumaranurag6479 жыл бұрын
Best Teacher for CALCULUS till now
@joeboutros91368 ай бұрын
Bro saves all of us for our math classes and then gets an insane pump in afterwards. LEGEND
@yanaluvs3 жыл бұрын
Since I was having a problem at 6:48, we can replace the 1 with j^0 and then do the summation which would have been 1^0 + 2^0 + 3^0 + 4^0 + 5^0= 5 :D, this man is really gonna carry my entire two years of high school on his back like that
@RealEverythingComputersАй бұрын
Thanks! Best math teacher ever!
@interesting32512 жыл бұрын
I have been watching your videos sir. I watched all your previous videos. I am about to watch this video(still didn’t watch) but I know that I will understand this topic perfectly .
@MrCanadianplayer7 жыл бұрын
Sorry just to add on to my last comment.. WOW! I totally understood the topic! Thanks so much man! I really appreciate you putting this up!
@musakhumalo399126 күн бұрын
I don't regret the 2 hours !!!! Yessir💥💯Thanks sir!
@daybyday38403 жыл бұрын
I do not get how the kid got lost at 50:12 he is the best teacher ever!
@user-bu8mg7uq3s3 жыл бұрын
i wish you were at my school
@mr.faisal17083 жыл бұрын
YOU ARE A 'LEGEND'.
@bcproject4906 Жыл бұрын
why do the k^3 become ^2 on 2:06:13
@ericsills64842 жыл бұрын
"You were right; I just didn't hear you." "Then how do you know I was right?" "Welcome to academic probation!" :-D
@christopherwilkins17722 жыл бұрын
"I choo choo choose you" to be my professor. I'm learning so much from these lectures, wish you could upload some worksheets for each video. Not that I don't have enough work to do as it is...
@diegorodrigues7469 жыл бұрын
It's funny to see the students losing focus over time. Now i have an better understanding of the difficult of teaching math. Thanks a lot for this!
@mohammedkhirhatem36625 жыл бұрын
You Are The Legend ... Thank You Prof ...
@nihatdonmezov83543 жыл бұрын
thank you so much
@arjit11176 жыл бұрын
I think he should have all of the world population as his subscribers
@TheBigMeme672 жыл бұрын
"so far so good?" *cries inside*
@gtaganas6 жыл бұрын
I just got out of my chem review for my finals and getting so upset how my teacher (can't respect him enough to say professor) and how he practically says that greek organization system is an excuse, but seeing that you're in D.Chi, makes me respect you SO MUCH MORE!!!! (I'm in a local greek org mself) I wasted so much of my time focusing on chem that it made my Calculus grade suffer and now I'm setting for a C in calculus, but now learning from your class, I think I'm going to retake calculus and get the A grade. =)
@nicocapa1235 жыл бұрын
49:46 Mind == Blown
@oneofyk5 жыл бұрын
thank you so much professor leonard. i understand now
@richardblkmann32985 жыл бұрын
Not all heroes wear capes.. Although Professor Leonard looks like he might after class. Thanks for everything sir. I had my first experience with a really terrible teacher this semester (used to teach at your college actually. Pretty sure he had to have been fired) The majority of the class dropped or is failing. I have an A thanks to your videos. Looking forward to your videos for Calc 2.
@tb27483 жыл бұрын
Where can you find proof for the sum from k=1 to n of k^2 = (n(n+1)(2n+1))/(6)? It doesn't seem intuitive how someone came up with that
@benjaminombeni7885 жыл бұрын
Thank you superman.
@majic8ball3374 жыл бұрын
As a time-saving comment: put the playback speed to 1.25x to save about 20-25(?) minutes. Now you can watch more of his videos today!
@mortadhaborgi69215 жыл бұрын
Thank you so much for the explanation .great from Tunisia
@rainbowburritoguy3 жыл бұрын
GOAT
@jtwoms811916 күн бұрын
el GOAT de matematicas 🐐
@davidperrii7 жыл бұрын
His students are soooo lucky I'd probably be distracted in that class tbh like......WOW!!!! Professor Leonard oh my gosh 😂
@yamdeeyoumar4 жыл бұрын
Net signed area and summations.
@sahithgondi18609 ай бұрын
he does it again. my goat 🙌
@JamesAndTheGiantPeach9 жыл бұрын
Could you please add time links for the sections?
@arthurlimoncelli33393 жыл бұрын
You make calculus easy!!!!
@DevelopmentPill20023 жыл бұрын
This was taught beautifully
@tutingrubena15843 жыл бұрын
I really hope you also has a Geometry full length videos 😢
@mikeestrada24968 жыл бұрын
you're a great human being..
@zolekatafadzwantombela4023 жыл бұрын
Thank you Dr Leonard
@shanisharma1007 жыл бұрын
hello sir your online classes are very useful for me,, great work,,sir,,
@cakr58933 жыл бұрын
29:48 that was she said :D thanks for lessons Leo you are the best
@souzou10008 жыл бұрын
love ur videos...simple ...glad u r on youtube...u sure see my math prof the worst ever!!! keep up the good work...and def will see ur videos for next sem too :)
@Dave-op4jh2 жыл бұрын
At 43:00 f(x) times delta x signifies height f(x) times base delta x Just in case if anyone wonders why professor is saying base times height while the writing on the board seems the other way round Thanks
@ImtiazAleem5 жыл бұрын
Best Teacher Ever.
@zitingwang13522 жыл бұрын
A sigma male teaching sigma notation
@sdparsons4 жыл бұрын
No self doubt required at 14:00 - sum of 1-100 definitely is 5050 and it definitely was (perhaps apocryphally) the story of young Gauss! One of my fave stories (that makes me feel dumb, hah)