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 !
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.
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.
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
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 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
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.
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.
@@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???
@@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
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.
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!
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
@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)
@@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.
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!
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.
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.
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.
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.
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!
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.
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.🤓
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!
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!
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.
Great stuff. I really want to become mathematically literate but for a while have found higher level math to be inaccessible. Hope this series will elucidate the subject. Thanks for everything you do.
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.
@@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.
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.
@@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)
@@shubhankardasgupta4777 Just watch PewDiePie's book reviews--he doesn't try to hide the fact that RU-vid videos are not the best use of our time. That honesty and self-awareness is redeeming (a little anyway).
To encourage everyone to take calculus, i go to the best university in Canada. I had failing grades on all of my calculus test the first time i tried it. I dropped out and I took introduction to mathematical proof (which is even harder) and i got really good with algebra and i just got really good at understanding mathematical problems. I passed Calculus with an A grade the second time i tried. This is not to brag, i really want to show how one can improve if they put the effort and interests in the subject. It's a really enjoyable section of mathematics from my opinion.
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.
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.
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!
This is the most engaging history of calculus video I've found on RU-vid. Thank you for a brief, quality video that's perfect for sharing with my high school class!
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.
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.
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.
@@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.
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)
@@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
@@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
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
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!
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!
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 🙏🙏
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.
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!
Calculus is magical because from then on, you don't have to accept "because I say so" from any math teacher/professor ever again because from that point on, you can actually understand most of the proofs for anything you are likely to learn in class.
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.
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.
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
i absolutely love calculus, i took a reay fast multivariable course last summer (4 days a week, 3 hrs a day, probably 5 weeks total) it was absolutely wild, but i kinda feel like i need to look through the book again before differential equations
I can't believe I thought calculus was hard but after a couple of days learning and watching videos on RU-vid 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.
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 ru-vid.com
+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.
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...
An excellent dissertation.I was taught the polygon area of a circle a slightly different way, that included the "outer" polygon and the inner polygon. The result indicated that as 'n' the number of polygon acute equilateral triangles both inside and outside increased, there was an asymptotic convergence to a single value. Each 'Equilateral' Triangle needed to be split in half to form two 'Right angle Triangles'. Then we could use Pythagoras. The difference between the inner and outer 'right angle triangles was that the 'Radius' alternated between defining either the 'hypotenuse' or the 'base' For example, draw the square 'inside' and 'outside' a circle. The inner area being the radius, is a small square equal to a quarter of the the diameter square, and likewise the larger square. which will have area D^2 where the inner square has the area 0,5*D^2 Thus with the average of a circle of Diameter 2 units, we get areas of 4 & 2. a so our approximate derivation of Pi is '3'. Next we can try the "Octagons" The Inner Octagon and the Outer Octagon. ... I will leave Professor Dave's Students to figure out that 'Average' and less approximate derivation of Pi.
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
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!
Calculus etymologically is from the Ancient Greek word ΧΑΛΙΞ (( Chalix ) = small stone - pebble ) which was used by the Ancient Greeks to calculate. The Ancient Greek word is still in use for kidney stones ( Calyx Calculus ) in medicine. Many small pebbles were used for hundreds of years to calculate. The word Χάλιξ - Chalix in Latin became Calyx and in plural Calculi. Later on the Calculi gave the word Calculator, Calculation in English. So, literally, calculating means counting pebbles ( add, subtract, multiply, divide )
@@mastershooter64 the same result if you key in your calculator 5 /0 ...but this was never a calculation at the ancient times since the number 0 added as a number in mathematics, thousands of years later, at around 1600 AD, number 0 did not exist at the ancient times....besides the fact that even the word ZERO is also descendant from Greek.
@@mastershooter64 The word ZERO is from ancient Greek word Zephyrus ( the west wind ) From wikipedia : The Italian mathematician Fibonacci (c. 1170-1250), who grew up in North Africa and is credited with introducing the decimal system to Europe, used the term zephyrum. This became zefiro in Italian, and was then contracted to zero in Venetian. The Italian word zefiro was already in existence (meaning "west wind" from Latin and Greek zephyrus) and may have influenced the spelling when transcribing Arabic ṣifr. The gentlest of the winds, Zephyrus is known as the fructifying wind, the messenger of spring. Zephyrus, sometimes known in English as just Zephyr (Ζέφυρος, Zéphyros), in Latin Favonius, is the Greek god of the west wind.
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 !!
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.
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
Professor, Based on what you said about the Greeks not grasping the concept of limits, I am under the impression that you have not heard about the "Method", a book written by Archimedes. I think the book was held by the Romans after they defeated the Greeks before Christ. Then, in the 800s, a priest erased the text from the papirus and wrote over religious text. Around 1900, someone discovered that there were marks or impression in the background of the pages. However, the technology to reproduce the erased text was not available at the time. In 1993, a millionaire purchased the book for more than 3 million dollars and donated it to a museum for examination. Well, the latest technology allowed to recover most of the writting made by Archimedes and what I learned about the content gave me goosebumps. Archimedes had developed the infinite calculus theory more than 200 years before Christ. Then the world had to wait more than 1500 years for Issak Newton to reinvent the wheel. Infinite calculus is the basis of engineering and progress. If you think about it, progress was delayed about 2000 years due to religion and a crazy priest.
According to the information we have today about what the Greeks before Christ determined, the Greeks came up with the foundation for the concept of Calculus, but didn't complete it to the degree that Newton and Leibnitz had. Whether they had completed it or not, was information we had lost over the years. We don't know what was in that original text, so it is all speculation as to whether the ancient Greeks did complete Calculus to the degree we know it today. I would think that they very likely could've completed the body of knowledge that we call Calculus today, and I find it hard to believe that they would come up with Zeno's paradox, and then never finish its implications to the point of practical application. They certainly knew how to produce n-gons to calculate pi, so Riemann sums seem like a logical extension of this knowledge.
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.
One of the hardest parts of math or learning in general is the ability to to store all these Information into ones brain and not forget about it later on. I guess we could say: Memory is the enemy against the effort of learning.
The calculus book by Silvestre Lacroix, 1802 (Charles Babbage was one of the 1816 English edition translaters) is worth reading IMO for anyone who has already learned calculus and likes it. Free on Google play books.
@@ProfessorDaveExplains yeah that's why u replied my comment . Just search on Wikipedia about madhava's work on calculus . There is simply historians said that European Jesuits came to India and translated Indian knowledge and brought that knowledge back to Europe . From where this knowledge spread . There are many discoveries that was done in India but Indian don't get credit for them cuz ur BS European racism . Heliocentrism was known to India , gravity too before Newton and atom theory that's why most of the quantum physicist always quotes vedanta . I'm not here to debate u about but it's just this the people don't give credit to us for our discoveries .
Calculus was formalized when Newton and Leibniz showed that differentiation and integration are inverse operations. They did not "copy" this insight. This does not negate the work of others that came before.
@@ProfessorDaveExplains but can u tell me how they both found calculus at the same time in the same year . Well we can see that there's no interaction between Newton and leibniz one was in Britain and other in Germany . And also the leibniz also plagiarism to Newton as he said Newton copied his work . And there is also one statement of Newton that he can look far by only standing on the shoulders of giants and there are possibilities of these so called giants were from Kerala school of mathematics. As these Indian mathematician were the to give infinitesimals series and other results related to calculus . Indeed Newton and leibniz were Great but if you are telling people about the history of calculus then you must add Indian mathematicians in this video too .
Yes, sometimes great minds reach similar conclusions nearly simultaneously. It's not that hard to understand. Newton did make accusations, but they can't be confirmed. Also, none of this has anything to do with what you said. Yes, all scientists and mathematicians work with the knowledge we already have. That's obvious. The concepts of calculus date back to the ancient Greeks. So what? No, this video is not the history of calculus. It's an introduction to teaching calculus. There is an ounce of historical perspective, that's all.
