Calculus 1 Lecture 4.3: Area Under a Curve, Limit Approach, Riemann Sums

Calculus 1 Lecture 4.3: Area Under a Curve, Limit Approach, Riemann Sums

[@Reformed4good]

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.B24]

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.

[@nuzhatazim8194]

Nah they get paid 100k

[@HimuraK1]

@@nuzhatazim8194 Not enough

[@MrJ691]

@Trance - 009 Sound System Dreamscape it is

[@ThanhTriet600]

@@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.

[@blackjack2770]

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.

[@mainefan01]

+Danya Valentin agreed

[@Peter_1986]

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.

[@alenaalena9322]

Danya Valentin I agree!

[@darthboganis1356]

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

[@adamharoon6021]

Thank you!

[@emptyFull123]

ありがと🥰

[@armaanbath753]

you are a LEGEND

[@barkhadibraahim1023]

thnaks bro

[@violethill4454]

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?

[@TehBluPanda]

Perfect, now I can finally find the area of those massive biceps

[@Sito1479]

Those are 3 dimensional. You’re gonna have to find the volume.

[@Czmlol]

@@Sito1479 Triple integrals to the rescue.

[@Peter_1986]

@@Sito1479 I think that Jose means the surface area of the biceps.

[@maximilianbur2560]

@@Peter_1986 integral will spit out infinity

[@lindarubio5211]

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!!

[@AndyU96]

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

[@kallmekrissarchivetiktoks8012]

Ameerhun1996 it's objectively funny tho

[@Peter_1986]

Well, that basically demonstrates that spelling skills don't really say anything about intelligence. A lot of people don't realise that simple fact.

[@BallsonPHACE]

prof leonard, you're amazing. sitting at home watching youtube is now meaningful instruction time

[@miahua9111]

Fax

[@radwizard]

Yes @21:45 the answer is indeed 440, for us people at home.

[@jameswilson4328]

Riemann Sums start at 23:00

[@typingaddict1319]

mvp

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my man

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thank you

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god bless you

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This man posted sth 7 years ago and I'm finding it so helpful now, world turns they say?

[@EYMmusic]

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

[@joshmick]

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.

[@MrCanadianplayer]

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!

[@adityaekbote8498]

me too

[@edsteadham4085]

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.

[@majokthuchlueth3048]

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

[@SteamPunkLV]

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

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So much math .. and muscles

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A big guy, for you.

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Nice Bane reference.

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This the only pro in the universe may you be blessed with more years to teach even unborn

[@NS-zi1xv]

We need to make a shrine for this man, he's out here changing lives.

[@coledenver4764]

When the kid at the very end said "because i hate myself", I got a noise complaint in the library. hahaha

[@nattcattt]

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 :)

[@agh1750]

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)

[@anonymoususer4356]

Thank your Prof. Leonard, Excellent lecture. Best math professor i've ever had.

[@sabel9841]

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]

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Leonard, you save lives. Thank you.

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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!

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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!

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If any difficulty in the class room I recommend KZbin, I can also learn from KZbin. Thanks for your tutorial.

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The greatest teacher ever alive!

[@user-op2qu6py1z]

🙏🙏 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!

[@1stplaceinvestments]

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-gg8ir]

Yes!..The (Why?) Part! Love it Sir!

[@cubajuanlolcubajuanlol8531]

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]

I would just like to say thanks for all of the videos you posted !

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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 :)

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Professor Leonard you are the best ever, thank you so much for sharing classes with us

[@adrianloh6919]

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....

[@sparkleyes1019]

hardest calc 1 vid on this playlist

[@asem8901]

Best show ever and this was my favorite episode

[@user-kw2xs5rs2f]

THESE LECTURES ARE SO GOOD! I FINALLY UNDERSTAND RIEMANN SUMS, THANKS PROF!

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my utmost respect to professor 👏

[@returntozero2112]

Wish I found these videos at the start of the semester. Would have helped tremendously. Keep up the good work Prof Leonard.

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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.

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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.:)

[@cubbyhoo]

I was laughing so much at the way Leonard sighs and says "Remeber we just talked about bread?" @27:19

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Thanks sir. adamsın.

[@thepsychocybe7078]

damn this guy got his last bit of lunch money taken from him in gradeschool and got jacked.

[@mn-yv2ur]

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.

[@andimahendrinah7078]

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!!!!!!!!!!!!!!!!!!!!!!!!

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this video is saving me in calc 2 right now, bless your soul!!!

[@benjaminombeni788]

Me too lol

[@dankahraman354]

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.

[@abdullahmohammad5613]

I had a roman professor ( Christian Enache) and you worth a million Enaches👏

[@yasiraydn5318]

Mindblown at 49:38 when i realized dx comes from deltax. Cool.

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🤭

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yep! dy/dx = delta y/delta x = slope

[@hoangpham4468]

Good teacher, during in university I never had instructor like him

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Best Teacher for CALCULUS till now

[@joeboutros9136]

Bro saves all of us for our math classes and then gets an insane pump in afterwards. LEGEND

[@yanaluvs]

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

[@RealEverythingComputers]

Thanks! Best math teacher ever!

[@interesting3251]

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 .

[@MrCanadianplayer]

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!

[@musakhumalo3991]

I don't regret the 2 hours !!!! Yessir💥💯Thanks sir!

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I do not get how the kid got lost at 50:12 he is the best teacher ever!

[@user-bu8mg7uq3s]

i wish you were at my school

[@mr.faisal1708]

YOU ARE A 'LEGEND'.

[@bcproject4906]

why do the k^3 become ^2 on 2:06:13

[@ericsills6484]

"You were right; I just didn't hear you." "Then how do you know I was right?" "Welcome to academic probation!" :-D

[@christopherwilkins1772]

"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...

[@diegorodrigues746]

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!

[@mohammedkhirhatem3662]

You Are The Legend ... Thank You Prof ...

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thank you so much

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I think he should have all of the world population as his subscribers

[@TheBigMeme67]

"so far so good?" *cries inside*

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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. =)

[@nicocapa123]

49:46 Mind == Blown

[@oneofyk]

thank you so much professor leonard. i understand now

[@richardblkmann3298]

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.

[@tb2748]

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

[@benjaminombeni788]

Thank you superman.

[@majic8ball337]

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!

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Thank you so much for the explanation .great from Tunisia

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GOAT

[@jtwoms8119]

el GOAT de matematicas 🐐

[@davidperrii]

His students are soooo lucky I'd probably be distracted in that class tbh like......WOW!!!! Professor Leonard oh my gosh 😂

[@yamdeeyoumar]

Net signed area and summations.

[@sahithgondi1860]

he does it again. my goat 🙌

[@JamesAndTheGiantPeach]

Could you please add time links for the sections?

[@arthurlimoncelli3339]

You make calculus easy!!!!

[@DevelopmentPill2002]

This was taught beautifully

[@tutingrubena1584]

I really hope you also has a Geometry full length videos 😢

[@mikeestrada2496]

you're a great human being..

[@zolekatafadzwantombela402]

Thank you Dr Leonard

[@shanisharma100]

hello sir your online classes are very useful for me,, great work,,sir,,

[@cakr5893]

29:48 that was she said :D thanks for lessons Leo you are the best

[@souzou1000]

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-op4jh]

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

[@ImtiazAleem]

Best Teacher Ever.

[@zitingwang1352]

A sigma male teaching sigma notation

[@sdparsons]

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)

[@codeiscool5552]

Best math teacher ever