Introduction to Calculus: The Greeks, Newton, and Leibniz

You've been dreading this for a long time, but there's no getting around it! Once we wrap up algebra and trigonometry, it's time to start learning calculus. Don't worry, it's not as bad as you've heard! We just have to learn a couple of new operations and algorithms, but we've done that so many times before! Before we dive into all that, let's learn a little bit about what calculus is and why it came about.
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Пікірлер: 1 000

  • @progyandas9650
    @progyandas96502 жыл бұрын

    Back in school in India , teachers straightaway jump to equations without giving us anything about why we are studying calculus , partly because they had to finish the humongous syllabus somehow and also partly because they just didn't want to. Mathematics isn't my area anymore but it might need it during research in political economy so thanks for this !

  • @sgt.boris4713

    @sgt.boris4713

    2 жыл бұрын

    Indian school sucks

  • @thetrickster9885

    @thetrickster9885

    2 жыл бұрын

    I am in high school in india, next year calculus courses will start, so I am just overviewing a year before, talk about efficiency. My teachers teach good but I don't trust them.

  • @pvp9423

    @pvp9423

    2 жыл бұрын

    Same experience for almost all. Not sure whether teachers knows it or not

  • @josejimenaz

    @josejimenaz

    2 жыл бұрын

    I know even in America they teach math rote memorization and monotous examples so boring n discouraging

  • @thelosttomato4020

    @thelosttomato4020

    2 жыл бұрын

    @buzz magister Please do

  • @callmedeno
    @callmedeno5 жыл бұрын

    I love that you actually provide the context. My brain just cannot be receptive to something until I know the hows the why's and the wherefores so it's much appreciated.

  • @skymoore3177

    @skymoore3177

    5 жыл бұрын

    Same here! If i don't understand the purpose or the groundwork of something it's nearly impossible for me to seriously grasp its nature.

  • @katelynneriehl4386

    @katelynneriehl4386

    5 жыл бұрын

    So true. Agree with you both 100%

  • @adenpower249

    @adenpower249

    5 жыл бұрын

    Whys and wherefores are the same thing

  • @hugoboy971

    @hugoboy971

    4 жыл бұрын

    Omg i thought i was alone! I would just end up not listening to the discussion if i dont know the hows and whys because my brain just cant stop finding answers about it

  • @yahyawasim1994

    @yahyawasim1994

    4 жыл бұрын

    Freaking same man. Couldn't have said it better myself.

  • @2Oldcoots
    @2Oldcoots5 жыл бұрын

    If Richard Feynman was "The Great Explainer" professor, you are his closest associate! Thank You for such a cogent video sir.

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    Any comparison to him is indeed a great compliment! Thanks kindly!

  • @richardfeynman9341

    @richardfeynman9341

    4 жыл бұрын

    @@ProfessorDaveExplains You're welcome.

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    3 жыл бұрын

    Joey I'm sensing a touch of jealousy from this and other comments of yours. You should bring it up with your therapist.

  • @kidzbop38isstraightfire92

    @kidzbop38isstraightfire92

    3 жыл бұрын

    @@ProfessorDaveExplains well now I just want to see Joey's comment

  • @abhinavbodybuilderanonymous

    @abhinavbodybuilderanonymous

    2 жыл бұрын

    @@kidzbop38isstraightfire92 🤣🤣🤣

  • @aman__gaur
    @aman__gaur3 жыл бұрын

    I'm a sophomore student in India and I was introduced to calculus while preparing for a competitive exam in my high school. I never understood how infinite series can generate a finite answer. I got it now. Mathematics is much more beautiful and is much more applicable in real life than what creativity killer institutes in India teach. Thank you so much, Prof Dave :)

  • @cabbage5114

    @cabbage5114

    2 жыл бұрын

    How did it the exam go? Some tips? I'm a 2023 JEE aspirant.

  • @alameen2496

    @alameen2496

    2 жыл бұрын

    @@cabbage5114 u sucks , this is the problem with india and its students only thing they need to byheart some mess omit it on exams and lead a wealthy life. He was pointing the brilliance he stricked on his studies and u still asking him about the freeking exams. U need to change For indian students like me ,quote this "TAKE EXAMS FOR YOUR FUTURE STUDIES & DONT TAKE STUDIES FOR YOUR FUTURE EXAMS " only the smartest one will even understand this

  • @user-nf1iz8bm6n

    @user-nf1iz8bm6n

    Ай бұрын

    ​@@cabbage5114how did yours go mate

  • @Primitarian
    @Primitarian3 жыл бұрын

    The math teacher who taught me calculus in high school could have save a lot of trouble if had he just shown me this video.

  • @NuisanceMan
    @NuisanceMan5 жыл бұрын

    Calculus is conceptually quite cool. Operationally, it's a one big, messy algebra problem after another.

  • @KaizorianEmpire

    @KaizorianEmpire

    5 жыл бұрын

    want to know something funny? i never formally studied calculus. In fact in high school i didn't get pass a C and i stopped studying maths at 15 before we were introduced to it. Now here is the funny thing. I did chemistry degree at university and i did so many of these problems and i suppose i just taught myself to intuitively understand it. It's only today that i realize all the kinets rates problems in chemistry were all complex calculus problems loool

  • @24kGoldenRocket

    @24kGoldenRocket

    4 жыл бұрын

    @HenryDavidT You write, "Of course, the good thing is, if we do know something quite well, getting an "A" or a job relating to it also is a by-product." NOT in the United States of America. Now you can know Science and Mathematics like the back of your hand. BUT WITHOUT THAT DEGREE your knowledge is USELESS in obtaining employment. You are idealistic and young. I am old, pragmatic and realistic. Just because I know that *xy = ∫ydx + ∫xdy* (Integration by parts) or if *w = f(x, y)* then *∆w = [∂w(x, y)/∂x]∆x + [∂w(x, y)/∂y]∆y* (Error Equation) and I very well know how to use these concepts... does not mean that I will be employable. In the United States of America it depends upon having that damned piece of paper, YOUR RACE, and, WHO YOU KNOW. GET REAL. (Don't you just love that H1-B Visa Program id you happen to be white and American? NOT)

  • @eminusipi

    @eminusipi

    4 жыл бұрын

    In Calculus you have to know your limits!

  • @tushurawat6001

    @tushurawat6001

    4 жыл бұрын

    i am in sixth grade and i love math i have done everything else and now i am starting calculus

  • @eminusipi

    @eminusipi

    4 жыл бұрын

    @@tushurawat6001 Good for you! If you have a solid foundation in algebra and trigonometry you'll enjoy it. After elementary calculus there is so much more. Since you are in sixth grade, calculus may be different from what you think it is at least in scope. Good luck and I'm sure you'll do well.

  • @schifoso
    @schifoso6 жыл бұрын

    It's amazing that Archimedes, using exhaustion and inscribed triangles and rectangles, nearly came up with integral calculus 2000 years before Newton and Lebnitz. Really looking forward to this part of your math series.

  • @kostas919

    @kostas919

    5 жыл бұрын

    @maria kerrid Sumerians didn't even have proofs for what they did Maths was a computational tool for them

  • @wbx9126

    @wbx9126

    5 жыл бұрын

    he wasn't even close. it's one thing to use method of exhaustion and something entirely different in conceiving the concept of limit and infinitesimal.

  • @Tethloach1

    @Tethloach1

    5 жыл бұрын

    A lot of things in history were destroyed so who really knows what they discovered and lost.

  • @Tethloach1

    @Tethloach1

    5 жыл бұрын

    @@kostas919 Math is a set of rules and logic, an alien would not agree with all of our rules like 4/0 = ??? 7/0 =??? 1/0??? the fact that you can't divide by zero means that the rules break down. undefined is that a real answer???

  • @kostas919

    @kostas919

    5 жыл бұрын

    @@Tethloach1 an intelligent alien would agree with us not because he would have the same system with us but because dividing by zero doesn't make sense . It's like 1/0=x that means that x*0=1 which is not true.Also, have a cake and try to cut into in zero pieces does that make sense to you? It's not a problem on the system it just can't happen

  • @davidcoleman4800
    @davidcoleman48005 жыл бұрын

    You are the teacher every high school student of calculus should have had. I subscribed because I can use the reminders, explained so well, to keep such a useful discipline fresh in my mind.

  • @nellAx19
    @nellAx196 жыл бұрын

    I’ve already taken 3 different calculus based classes within the past year in college and I’m still gonna watch this playlist. You explain things very well, keep it up!

  • @rosepierce9382
    @rosepierce9382 Жыл бұрын

    Wow, I had been searching for hours for a video that introduces the essence of calculus without going too much into the details. Most videos did a poor job of explaining the ideas without getting bogged down in the details and causing much confusion, but Professor Dave here gave us such an interesting account that makes me want to finish watching the whole playlist tonight! You have earned my like, sir. You truly have a gift for teaching and introducing new concepts cogently. Keep up the good work!

  • @intheshell35ify
    @intheshell35ify5 жыл бұрын

    Professor Dave, you are a comforting voice in a dark, dark abyss.

  • @Steffystr8mobbin

    @Steffystr8mobbin

    4 жыл бұрын

    Neutron star?

  • @shem7146

    @shem7146

    3 жыл бұрын

    @@Steffystr8mobbin school

  • @pinchermartyn3959
    @pinchermartyn39595 жыл бұрын

    Where were you in my youth? You are teaching the WHY which is so important!!! And all else follows. And the history!!! Facinating subject when taught well. Thank you for your generosity and service doing this. Awesome work!!! Many, many thanks.

  • @soupisready619
    @soupisready6194 жыл бұрын

    This is great, i am half way through Gilbert Strangs MIT course on calculus, and this is exactly what he is talking about. It is so great to learn all this stuff a second time right now, wish i had known this or were interested in it when i was in high school.

  • @maximiliancarey9047
    @maximiliancarey90472 жыл бұрын

    Professor Dave, you have a true talent for teaching. I went into this video truly terrified of mathematics and learning in general. I left this video, actually excited for calculus (especially now that I know what it is used for). Having a father who used to be a chemistry professor, I can recognize a love for learning when I see it. Congratulations and I honestly wish you the best. Thank you.

  • @paulchoudhury2573
    @paulchoudhury25734 жыл бұрын

    Excellent explanation of the background and motivation. Will have my son watch this as he's starting Calculus now.

  • @hl778
    @hl7782 жыл бұрын

    I really enjoy the fact that every time I watch your videos, whether it's the 1st or just about 100th time. I somehow manage to pick up something new, and understand a concept a little bit better. I love getting smarter, and I appreciate you helping me accomplish that!

  • @jimba6486
    @jimba64866 жыл бұрын

    This was a great video to get firmly grounded on the mindset of calculus

  • @m0narkh
    @m0narkh4 жыл бұрын

    I have actually pondered on some of this concept before, the finite result of infinite. I never thought that I was creating a basic understanding of calculus before I actually got to learning it, pretty cool if ya ask me. Great video!

  • @beedubb2653
    @beedubb26534 жыл бұрын

    Always found it more helpful to get the background like this with mathematical subjects before pressing further. It was just a way for me to maybe understand better how things might be connected, or how the practical applications might work. I think it sometimes help me better understand things when getting the big picture first, then breaking that down into the details.Thanks for posting.

  • @kidzbop38isstraightfire92
    @kidzbop38isstraightfire923 жыл бұрын

    If I was a math teacher, I would just show videos like these every day...the explanations are better than anything I could come up with

  • @turbobrain1342
    @turbobrain13425 жыл бұрын

    In college, I wanted to be an applied mathematician. I excelled at learning the new techniques and methods to solve problems. In grad school, I got tripped up by Abstract Algebra and Topologies and such. I floundered. Good luck on your new series.

  • @meab12

    @meab12

    2 жыл бұрын

    And? Tell us more? You cant just leave us hanging like that...

  • @AndrewMarcell
    @AndrewMarcell5 жыл бұрын

    This is the most engaging history of calculus video I've found on KZread. Thank you for a brief, quality video that's perfect for sharing with my high school class!

  • @NazriB

    @NazriB

    2 жыл бұрын

    Lies again? Gay Of LA

  • @mitkomilev4690
    @mitkomilev46902 жыл бұрын

    Professor Dave is the best! I love how he explains everything. I already knew about calculus's concepts before wathing this video and I still loved it. Thank you, Professor Dave!

  • @TiberiusStorm
    @TiberiusStorm3 жыл бұрын

    This is the simplest and best explanation I've seen thus far. Thank you!

  • @AmbatiManoj2327
    @AmbatiManoj23275 жыл бұрын

    Videos like this make education less horror...., Thank you,

  • @SuperKnowledgeSponge

    @SuperKnowledgeSponge

    4 жыл бұрын

    you mean less horrific. 😂

  • @jayfreeman3004
    @jayfreeman30044 жыл бұрын

    This is fabulous.i needed a calculus credit in university in order to enroll in a law school course ( intellectual property). I was never good at math and got completely intimidated by math.i could not understand it .This video has brilliantly bridged that understanding gap. For those of you who are intimidated by math, this series of videos is heaven sent.You might even surprise yourself and get good at it. It's a great place to start to dig in.🤓

  • @aeroraheem
    @aeroraheem Жыл бұрын

    The title of the video should be "First Video that everyone needs to see before learning Calculus". Thanks, Prof. Dave for sharing. I was the last bencher in my secondary school but my teacher Mr. Bhanu (Gowthan Jr. College, Hyderabad, India), got me to sit on the first bench (which motivated me) and started a differentiation class. That day he said, only those who finishes the differentiation problem will go out of my class, and I was the first one to move out. That motivation remains special for me, forever and the topic remains useful for me even now. BTW, I am an aerospace engineer and need a lot of calculus to understand flow physics. Many times in my life, I have been trying to conquer this topic fully and In sha Allah will continue to do so. Thanks again, Professor for sharing the topic.

  • @muntazeerreja9458
    @muntazeerreja94585 жыл бұрын

    Thank you. Thank you. Thank you. Thank you for what you are doing. Keep up the good work.

  • @geolover5958
    @geolover59583 жыл бұрын

    Your way of teaching mathematics is great.all maths teachers should follow these ways.

  • @cesarmiranda2205
    @cesarmiranda22054 жыл бұрын

    I do love Calculus, and your vídeo is outstanding. You were able to show the real soul of the MATH...

  • @sikyfushvanti3605
    @sikyfushvanti36053 жыл бұрын

    professor dave i have been following you fir a very ling time. Yoyr method of teaching is so simple. I hope you continue like this. Have learned alot from you

  • @ericheine2414
    @ericheine24145 жыл бұрын

    I got through it in college. Then I didn't use it and I forgot it. So this is a nice review. We needed it for p-chemistry. Hopefully this will help my memory. Thank you.

  • @joseph-ow1hf
    @joseph-ow1hf5 жыл бұрын

    Once I realized calculus is actually a language......it made it fun. It is the language of Newtonian physics.

  • @hanf4415

    @hanf4415

    5 жыл бұрын

    Yea, okay! So what does it have to do with early childhood education majors?

  • @lautheimpaler4686

    @lautheimpaler4686

    5 жыл бұрын

    @@thewizzard3150 That's like saying Charlie Chaplin was replaced by Diego Maradona 40 years ago.

  • @nationalstudyacademykim5030

    @nationalstudyacademykim5030

    4 жыл бұрын

    Excuse me but may I ask you a question? What is more important? Mathematics or language?

  • @anirudhsreeram4015

    @anirudhsreeram4015

    4 жыл бұрын

    @@thewizzard3150 Please explain what you are saying. If you're just perpetrating politics in science, then STOP. Classical Mechanics is a ridiculously accurate time-saver for earth-bound problems, like firing artillery and building bridges. If we used relativity for everything, the world would be a mess.

  • @cornelgherasim5684

    @cornelgherasim5684

    4 жыл бұрын

    @@nationalstudyacademykim5030 , the language of mathematics? 🤔

  • @palindrome1959
    @palindrome19592 жыл бұрын

    Beautiful explanation Dave, absolutely beautiful. My Maths and Physics Professors would be proud. Keep it coming!!! David

  • @shajisankar7930
    @shajisankar79303 ай бұрын

    This channel was what I was precisely looking for starting from the very basics to rlly complicated things I love itt

  • @tusshardhakate12
    @tusshardhakate124 жыл бұрын

    Wow, can't clearly understand more than that, amazing u finally made my curiosity an end, struggle d almost 10 years to get essence of calculas, keep going n thanks once again great work

  • @HopDavid
    @HopDavid5 жыл бұрын

    I'm happy to see you acknowledge Fermat as well as the ancient Greeks. Also in the mix are Isaac Barrow, Descartes, Cavalieri, Gregory and others. Mathematicians in Fermat's generation laid the foundations of calculus in the generation before Newton and Leibniz. Developing calculus was the collaborative effort of many people over many years. It annoys me when people credit a single person for inventing calculus.

  • @skiloist
    @skiloist2 жыл бұрын

    Thank you for this History video. I have a BsEET and when I took my Differential Calculus, I felt like I was just going with a flow I had no idea where it was going. Just seeing your "intro" video to Calculus just made some really muddy water VERY clear! Amazing how the brain works.

  • @blessingsjoelssen2499
    @blessingsjoelssen24992 жыл бұрын

    hello everyone, its 2022 here in SA... im so glad iwill no longer flunk math since i discovered this channel... nice to meet you professor Dave, now i know what the Y and A and all the silly letters... its so clear to me... thank you so much my good Sir !!! keep well and thanks again

  • @rencosbjd
    @rencosbjd5 жыл бұрын

    I had trouble learning math all throughout school. I think it is because I have something called dyscalculia, and would often fail tests because I tend to jumble numbers. I have recently become interested in mathematics, and would like to learn from the ground up at my own pace as a hobby. Thanks for this video!

  • @ajmalmuhammad5365
    @ajmalmuhammad53654 жыл бұрын

    Well explained Really superb the way you made it easy Thank you for this video..

  • @OwenMcKinley
    @OwenMcKinley2 жыл бұрын

    This should be required viewing material for all incoming calculus students and enthusiasts. Perfect way to introduce the subject!!!

  • @sharonchetia54
    @sharonchetia543 жыл бұрын

    Thank you for explaining this in such a simple and interesting way

  • @davidsweeney111
    @davidsweeney1116 жыл бұрын

    this is great, calculus is one of my favourite subjects!

  • @HAL-nt6vy

    @HAL-nt6vy

    5 жыл бұрын

    We can approach infinity by subscribing to PewDiePie!

  • @shubhankardasgupta4777

    @shubhankardasgupta4777

    5 жыл бұрын

    @@HAL-nt6vy Then I should apply Newton's third law of motion to actually give him subscribers in negative or to zero... :P I'm not a T-Series fan but neither that Swedish meatball fan(Pewdiepie)

  • @HAL-nt6vy

    @HAL-nt6vy

    5 жыл бұрын

    @@shubhankardasgupta4777 Just watch PewDiePie's book reviews--he doesn't try to hide the fact that KZread videos are not the best use of our time. That honesty and self-awareness is redeeming (a little anyway).

  • @HAL-nt6vy

    @HAL-nt6vy

    5 жыл бұрын

    @BLAIR M Schirmer What's to explain? Plenty of good calculus books available.

  • @eduardo703

    @eduardo703

    5 жыл бұрын

    David can you share some exercise!!?

  • @tushurawat6001
    @tushurawat60014 жыл бұрын

    I am in sixth grade ... and you made me actually understand calculus! Very interesting... makes math better than it was! I love math and now you make me adore it.

  • @Jose-oy1ow

    @Jose-oy1ow

    4 жыл бұрын

    And here I am in 12th grade struggling in calculus 😂

  • @tushurawat6001

    @tushurawat6001

    4 жыл бұрын

    @@Jose-oy1ow these wideos can make you better at calculus

  • @someonewholikesspace4646
    @someonewholikesspace46463 жыл бұрын

    My interest in math went from 8/10 to 100/10 thanks to this series! Can't wait until I can study calculus when I'm in high school!

  • @batangstem8452
    @batangstem84522 жыл бұрын

    i struggle a lot in understanding the idea of calculus but this video helps me understand it way better. Thank you sir for your great explaination

  • @Nemoguzapomnit
    @Nemoguzapomnit5 жыл бұрын

    Wow that video is so nice and neat! Thx for diving me into the story of calculus. Was rly interesting

  • @airplayrule

    @airplayrule

    5 жыл бұрын

    Actually, all significant knowledge, including math, originated with the Vedas. Nearly all significant maths was already known and taught long ago in the Vedas. It was called Ganit. For example, the concept of zero was originally called Shunya, or zero void. The symbol of zero and the decimal system was described in the Vedas (for example Atharva-Veda 5.15, 1-11) and also described is how the number increases by 10 by writing zero in front of it. The first usage of Pi also came from Vedic teachings. A (e.g. Rig-Veda 1.105.17) formula to find the area of a circle is mentioned showing that the Rishis knew of pi, approximating it to be equal to 22/7. The word Bijaganitam means “the other mathematics” and was given to math like, for example, what we call algebraic forms of computation. Eventually another notation that people called “Indian numerals” evolved from the Brahmi numerals and assumed common use. But under the dictatorship of Mohammad in the 7th/8th centuries, Arabs invaded and conquered the land from India, across northern Africa, to Spain & the math eventually spread in the world. For more info on this topic, check the main vid on kzread.info

  • @alyssachan6312
    @alyssachan63124 жыл бұрын

    Thanks for making this video cause I really didn’t like doing my calculus hw

  • @ccuny1
    @ccuny13 жыл бұрын

    I was familiar with the Leibniz-Newton fisticuffs but this wider historical perspective is really helpful. Thanks a lot.

  • @suruchisolanki3603
    @suruchisolanki36033 жыл бұрын

    This is the best video of calculus i've seen on youtube , makes easy to understand .Also thank you Prof . Dave ;)

  • @meandmybobbygee1812
    @meandmybobbygee18125 жыл бұрын

    Me: you have algebra homework, an essay, three languages to practice and a dog to walk. Me to me: but we should learn calculus.

  • @twiki1559
    @twiki15595 жыл бұрын

    Best explanation ever for the neophyte,

  • @alphasuperior100
    @alphasuperior1004 жыл бұрын

    I can't believe I thought calculus was hard but after a couple of days learning and watching videos on KZread I realized that I was so good at it that my teacher asked me what grade I wanted in Class. I even use to do Calculus in my head.

  • @rahulg.c4861
    @rahulg.c4861 Жыл бұрын

    I’m studying engineering after having long gap of stydying, calculus is something which I completely new topic to me. I’m quite looking forward to go deep into this and crack it. Vedios like this are very helpful to understand it’s background. Thank you.

  • @primajump
    @primajump4 жыл бұрын

    One of the best short and sweet introduction to calculus. Very nice job.

  • @trex5863
    @trex58633 жыл бұрын

    I am of 14 years old but just before going to bed got a mood to learn calculus 😃. The explanation was amazing professor Dave ❤️❤️ , best wishes from me 🙏🙏

  • @devanshisharma2447
    @devanshisharma24474 жыл бұрын

    calculus is the reason i adore math as a subject. thankyou for this!!

  • @littlebitmoreksp
    @littlebitmoreksp3 ай бұрын

    I can tell this is the exact kind of course I'm going to need to smooth over the inefficiencies in my current calculus education. Everything is explained so complicatedly using terminology I don't understand and proof notation I can't wrap my head around, and there's some severe difference between what I know and the baseline information I need to know to understand calculus formally. This, I feel, is the bridge that will cross this gap of inefficiency. Thank you, Professor Dave!

  • @karareiser9278
    @karareiser92785 жыл бұрын

    “involves things that are infinitely small or are infinitely close together” “we can do something infinitely many times and get a finite result”

  • @dabulls1g

    @dabulls1g

    5 жыл бұрын

    its called convergence!

  • @rokyericksonroks

    @rokyericksonroks

    5 жыл бұрын

    So we can equate infinite to a finite sum? Seems to be illogical. Took 200 years until Cauchy finally gave us a definition of a limit. Newton himself never bought into this “doesn’t exist” stuff.

  • @lautheimpaler4686

    @lautheimpaler4686

    5 жыл бұрын

    @@rokyericksonroks it's not. I can give you examples.

  • @dabulls1g

    @dabulls1g

    5 жыл бұрын

    Roky Erickson rocks yes, if it converges to a finite value that value is known as the sum of the series.

  • @beri4138

    @beri4138

    2 жыл бұрын

    Why are you quoting that? Are you suggesting it's incorrect? I see no problem with it.

  • @waterbuffalo4225
    @waterbuffalo42256 жыл бұрын

    Hey Professor Dave, thank you for this video. Do you have any tips on how I can look at symbols and apply them? I feel lost and robotic when I’m examining equations

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    6 жыл бұрын

    oh just repetition! and of course understanding what the symbols mean on a fundamental level. don't worry we will explain all the symbols very thoroughly!

  • @newtonianclub2530
    @newtonianclub25303 жыл бұрын

    Yeah! We've got yours videos as granted but I knew yours spectacular endeavour for many hours to create such incredible text. I'm really really thanking you for your contribution to multitude of students ☺☺☺

  • @timtravasos2742
    @timtravasos27425 жыл бұрын

    Great explanation. Look forward to more.

  • @hayliewu9604
    @hayliewu96046 жыл бұрын

    omg finally!! thank you sir!!!

  • @willk7184
    @willk71845 жыл бұрын

    I give this an A. Would have been an A+ if it included a simple definition of where the words "differential" and "integral" come from. Perhaps that info is forthcoming in the next video!

  • @ProfessorDaveExplains

    @ProfessorDaveExplains

    5 жыл бұрын

    It's a 35-part series, check it out!

  • @willk7184

    @willk7184

    5 жыл бұрын

    Will do! Looking forward to actually understanding what I used to be doing when I studied calculus years ago. @@ProfessorDaveExplains

  • @Vikermajit
    @Vikermajit8 ай бұрын

    Thanks for an awesome intro. to calculus, Prof. Dave.

  • @christopherarchuleta3669
    @christopherarchuleta3669 Жыл бұрын

    Calculus was one of the hardest things I've leaned (I hate math), but I did end up getting the hang of the basics. More importantly, I understand why it's important and where I'd expect it to be used even though I don't use it directly.

  • @ahappyimago
    @ahappyimago6 жыл бұрын

    You are a good man, Dave. Keep it up.

  • @toorisentou
    @toorisentou2 жыл бұрын

    Really. This genaration's Indian education system is really messed up, and these videos and tutorials are really helping me out. They put huge load and stress in the 11th grade which they don't prepare us from before so most of the students who performed quite well before and in 10th grades face a huge bottleneck at this point. Thanks Dave sir!

  • @aidell.178
    @aidell.178 Жыл бұрын

    Thank you so much! I’ve no idea I could be this OBSESSED with math before I met you…

  • @music4you372
    @music4you3724 жыл бұрын

    Just from the first 2 mins I learned how to do pie properly. Finally I've gotten good at it. Thank u i wish u were my maths teacher.

  • @abhay3448
    @abhay34486 жыл бұрын

    all set for calculus!!!

  • @kripashankarshukla4073
    @kripashankarshukla40736 жыл бұрын

    Your channel should be the most subscribed channel on youtube !!

  • @litlabproductions2043

    @litlabproductions2043

    5 жыл бұрын

    Stem doesn't even make up 20% of majors, people aren't willing to do the work! Love the channel, keep it up! xD

  • @pnachtwey
    @pnachtwey3 жыл бұрын

    +1000 for mentioning the history. I have always wondered what problem the mathematicians were trying to solve. This example is obvious but like Dave says, it gets harder.

  • @annacichy780
    @annacichy78011 ай бұрын

    I feel so sad knowing that I never had a teacher like professor Dave. My science teachers were horrible and I remember how frustrated I was when I couldn't understand the material. I had huge gaps in the program due to my mental health and house situation. I was raised in alcoholic household full of abuse. I couldn't focus and I believed I am not smart enough to understand. Years later I overcame depression, PTSD, PTSS and here I am, 35 year old, learning mathematics and physics. I am doing it for myself as that was my dream since I was 7 years old. I won't be a scientist anymore, but I am grateful I can learn it for my hobby. Thank you professor Dave.

  • @delaware137
    @delaware1375 жыл бұрын

    How to calculate derivatives and anti-derivatives should be taught in algebra and trigonometry classes. The calculations of calculus are not that hard, it's understanding the proofs and practical applications that require deeper insight and this would be made a lot easier if students already have some working knowledge of the subject.

  • @iflashlantern4292

    @iflashlantern4292

    5 жыл бұрын

    This sounds interesting. So the foundation of calculus (limits, derivatives, integrals) would be taught in Algebra 2 or Pre-Calc (or Algebra 3, depending on your school)? Would that mean that there would still be a calc class where it’s just applying those concepts, like in the related rates section of a calc textbook? It sounds like a good plan, but many times algebra classes don’t even cover trigonometry completely, so I don’t see where they would make time for calc topics.

  • @delaware137

    @delaware137

    5 жыл бұрын

    @@iflashlantern4292 Obviously this would be for students of higher aptitude, but I don't think it would take much time to teach. Students are taught the concept of slope in the first few weeks of Algebra I with y = mx + b ; essentially they are taught how to calculate the derivative of a linear equation from day one, so they get the concept of slope. When polynomials are taught it wouldn't be hard to introduce the power rule with some instruction on how to find local maxima and minima. To me this makes more sense than having them memorize things like the axis of symmetry for a quadratic equation is -b/2a, as many text require. In Algebra II the chain rule could be introduced as well as the product and quotient rules. In Trigonometry it wouldn't take much time to teach (without proof) the derivatives of sine, cosine, tan, cot, sec, and csc. With this, calculus class would then have more time to spend on limits, the fundamental theorem of calculus, proofs for the rules, trigonometric substitution and more advanced applications such as related rates and volumes by disc vs shell, etc.

  • @endofjourney665

    @endofjourney665

    5 жыл бұрын

    In Ukraine and Russia we learn derivatives in 10th grade aka high-school. We use derivatives to find the extreme (?) points for a function on some chunk of the axis. We also get to know how to find a derivative or an integral for a function but we may not use it further (except for geometrical calculus)

  • @NailujG

    @NailujG

    5 жыл бұрын

    @@endofjourney665 Any student in any grade is able to take calculus if they have completed alg 1, geometry, alg 2 and precalc/trig. So yes a 10th grader in the US is able to take calculus as wellm

  • @NailujG

    @NailujG

    5 жыл бұрын

    @@delaware137 Thing is related rate, optimization,disc/washer method, can be taught in a short amount of time. But yea i understand its possible to indulge the students more on the topic

  • @philiphengchow6490
    @philiphengchow64905 жыл бұрын

    Although I have strong feelings desire much, I am very weak in catching up quick. I am so thankful prof.. If you or someone help me. Thanks.

  • @cameronestrada1430
    @cameronestrada1430 Жыл бұрын

    I'm a freshman in high school but I'm really interested in Calculus so I asked my Geometry teacher for a calc. AB textbook, but it was a little confusing, so this series helped.

  • @saskiavanhoutert3190
    @saskiavanhoutert31905 жыл бұрын

    Thanks for some formulas let´s experience more of them, thanks for explanation,kind regards

  • @984francis
    @984francis5 жыл бұрын

    Actually, in engineering, we do use Newtonian notation for derivatives in differential equations, it's simply a shorthand.

  • @carultch

    @carultch

    2 жыл бұрын

    I would guess that Leibnitz's notation became the most popular, out of typographical necessity when the technology of typing was the most primitive. The same reason a lot of letters from old English got scrapped in favor of digraphs, like the letter thorn that is now represented with a th. Leibnitz's notation just needs letters and the slash, while Newton's notation needs the ability to overlay dots above letters. Leibnitz's notation also has the advantage of capturing the meaning of the derivative and integral within it. Newton's notation has the advantage of being space-efficient, and time-efficient to handwrite, which is why it is making a renaissance in modern times, and even being preferred for engineering and physics. Now that typing technology has improved, and we can overlay all kinds of marks on letters with modern computers.

  • @984francis

    @984francis

    2 жыл бұрын

    @@carultch Excellent points.

  • @itsdavidlo
    @itsdavidlo5 жыл бұрын

    This is why I majored in social science...

  • @markyounger1240
    @markyounger12404 жыл бұрын

    Best explanation I've seen.

  • @hejustleft
    @hejustleft4 жыл бұрын

    Loved the post Dave. Is it conceivable that there is a math that can show that PI , or any other irrational number can be resolved as a non-rational number/formula? 1st time i've seen your posts- subscribed. As I can't get to pose this elsewhere, I truly hope to get some kind answer/response from you. Thanks from an old man.

  • @ramratiram1152
    @ramratiram11526 жыл бұрын

    Awesome explanation sir..... This is the best tutorial.

  • @microguard
    @microguard5 жыл бұрын

    How is that schools are still on business? With so much quality informative videos like this one.. keep it up Proffesor !!

  • @giorgiomatessi976

    @giorgiomatessi976

    5 жыл бұрын

    Lol because of your comment... (spelling)

  • @microguard

    @microguard

    5 жыл бұрын

    @@giorgiomatessi976 maybe I also need grammar videos, LOL

  • @giorgiomatessi976

    @giorgiomatessi976

    5 жыл бұрын

    @@microguard lol no disrespect....

  • @dorianphilotheates3769

    @dorianphilotheates3769

    5 жыл бұрын

    microguard- Because, left to their own devices, most people will use the Internet to investigate the colour of their favourite ‘reality show’ celebrity’s undergarments...

  • @carultch

    @carultch

    Жыл бұрын

    @@microguard Because you don't pay to learn, you pay for your report card.

  • @ruvstof
    @ruvstof5 жыл бұрын

    As always, extremely clear.

  • @user-uh3ew1rj6u
    @user-uh3ew1rj6u3 ай бұрын

    You should be Prof. Savior, I am wondering how easily you teach the big concepts of math, hats off thanks a lot.

  • @rwharrington87
    @rwharrington874 жыл бұрын

    6:33 Haha - great choice of art.

  • @allaboutgk1100
    @allaboutgk11005 жыл бұрын

    Why am i watching this if i don't even know Calcul....................ations

  • @fouadnouioua7069
    @fouadnouioua70692 жыл бұрын

    Convincing answer to Zeno's paradoxe, thank you professor.

  • @kerrysammy3277
    @kerrysammy32774 жыл бұрын

    Thank you. Thank you very much. I was not much into learning by rote, without first understanding. When I went through high school ( British system), I got into A Levels. To read for physics, chemistry and zoology, ( for entry into university). We had to do a crash course in Add (higher) Maths. The teacher showed how to do the math without explaining the principle behind it as you have done. So I basically flunked it. I am now a retired senior high school science teacher, specialized in biology, who could have been more accomplished in my opinion if I understood differential and integral calculus.

  • @abhayjaiswal9836
    @abhayjaiswal98365 жыл бұрын

    If you have great knowledge of calculus you crack physics

  • @laprincesa9803
    @laprincesa98034 жыл бұрын

    I’m required to take Calculus for my major in college, I’m not scared of calc anymore lmao ppl made it seem like it’s horrible

  • @mohsinmohammed2022
    @mohsinmohammed20224 жыл бұрын

    Well done, thanks for your information.

  • @professionalbiologist7108
    @professionalbiologist71084 жыл бұрын

    My Math professors at college make calculus look like some boring old manual crap. You make this very fascinating and interesting.

  • @jimmybrice6360
    @jimmybrice63605 жыл бұрын

    you mentioned the ancient greeks. but no mention of the one who first founded calculus - some 2000 years before newton - archimedes, probably the brightest human to ever live if one looks at what archimedes did, compared to the information available, he was more beyond his time than anyone else. the ancient romans thought he was a sorcerer !!

  • @Slimm2240
    @Slimm22404 жыл бұрын

    According to quantum physics, you don't touch a wall but you feel the force of the wall pushing you back 🤷🏽‍♂️

  • @MostlyPennyCat
    @MostlyPennyCat4 жыл бұрын

    Having the understanding click in my mind. Where 1/s is the width of the slice and the infinitesimal (1/∞) is "as close to zero as is possible without being zero" gives you exactly the correct area under the curve. And it was correct and I understood it.

  • @sonitpullz
    @sonitpullz Жыл бұрын

    This content matches a lot with the james stewart textbook of calculus. Good to see professor's dave's incredible taste of math books

  • @andreisokolov8458
    @andreisokolov84586 жыл бұрын

    Thank you ; love from Russia 🇮🇳

  • @rento8572

    @rento8572

    5 жыл бұрын

    That doesn’t looks like the Russian flag 🇷🇺.

  • @jackyjackson7000

    @jackyjackson7000

    5 жыл бұрын

    Rento Hahahah exactly

  • @jackyjackson7000

    @jackyjackson7000

    5 жыл бұрын

    So u don’t know how does Russia’s flag looks like but u get calculus.. oh wow good for u!!

  • @adhiyanthaprabhujeyashanka2091

    @adhiyanthaprabhujeyashanka2091

    3 жыл бұрын

    That's indian flag 😂🤣