I mean, better than the teacher I've never had. Calc is hard when the textbook is your only teacher, and then you got all your other classes thrown at you.
3:59 I love that you point this out. I've found that a big problem in learning is intimidation. A lot of the concepts are extremely simple and intuitive once you know the vocab. And anything can be broken into easier parts.
First time I am watching a video of yours. I have to say the quality is simply amazing. No silly background noise or music, no rush, no unnecessary crap. Just what people need in a smooth voice and language with a great quality video. Keep up the great job man!
this video actutally expaining what calculus, differentiation, integration IS and how it's basically slope and sum of curved functions is SO much clearer, less stressful, and is better for deeper understanding in a shorter amount of time than the confusing non-explanations in school class with stress homework, reading difficultly worded textbooks, spending so much time on an example that doesn't make sense to try to extract the core concept of calculus.
I’m in school and I’m learning calculus. We have never simply been given formulas to memorize but rather focus on understanding how the formulas are derived
I'm currently in 11th grade, my math teacher is simply the best teacher that has ever taught me, but unfortunately, since she had focused a lot on lessons before calculus like functions, and had spent a long time to teach it to us, we barely, and I mean barely, were able to finish the book right before the finals, so yes, she did breifly explain what calculus is, but still I couldn't understand from just two lessons, and today as I'm writing this, I'm actually having that exam about two hours later, and I don't know what to hope for, I'm actually pretty good at math, but pretty bad at memorizing, so calculus is gonna be a big pebble in my shoe!
When you're at calculus 1 the hardest thing is the algebra but once you get to cal 2 and other classes that have integration techniques you realize integrals can be a bish
Really? You need a good teacher and a good reference book. In my first year of calculus we had neither; anything above 40% was considered an A, and that was 40 years ago. Ironically that did not stop me. Over the years I too have come to the belief that calculus can be easy with the correct resources.
Taught myself a decent amount of calculus 1 and 2 during the fall. Really an amazing topic to dive into; incredibly useful. I think linear algebra is also as mind blowing, just in a different way.
@@bealu9459despite its name, linear algebra doesn’t have anything to do with graphing lines. it’s mainly about two things: vectors and matrices. Vectors are like a fancy way of storing coordinates. And matrices are a way of representing certain transformations you can do to those coordinates. linear algebra has a ton of fun applications, so I’d really recommend you learn more about it.
Your video popped up on my feed literally when I checked TH-cam after taking my integration test. All of you're saying is amazingly simple but true (which is something really hard to achieve) and made me love Calculus even more. Keep up the good work
The most interesting college course I have had so far, I got 15/20 on my first exam because I was lazy on that day, 20/20 on my last exam which include the whole theory the professor taught during the semester. I give credits to my calculus teacher, she was one of the best math professors I’ve had and she made sure she gave us real scenario problems to solve in order to truly learn and understand the theory.
This is by far the best! Video I've seen on the topic. You have no idea how much your explanation has helped me see the connection between what I'm learning and how it's applied. I'm beginning to realize why many see math as an art. A million thanks to you sir!
used it yesterday. the calculate the time something takes to cool down in temperature. if a glass of water is 21celsius and is going to cool to 20celsius in a 10 celsius room. the difference in temperature between the glass will change as the glass cools down. so its rate of change will be smaller. here we used integrals and differential equations
I'm a retired electrician and I wasn't really that good with math but I learned trigonometry in reverse by learning to bend conduit by using the 30, 45 , 60 degree offsets and 90 degree stub up . The UGLY book was helpful in learning trig ratios and 6 trig functions by remembering Oh Hell Another Hour of Andy. I find the unit circle a really good method for learning trig and I still have fun drawing it to visualize the beauty in the patterns and repetition as it changes from one quadrant to the other. It lifted my confidence a lot so now I dabble with light calculus and find projectile motion very interesting. At 64 yo I find algebra more difficult to grasp than trig but that's just me. Any way thanks for your video.
Nyquist taught us that the best way to derive the value of a curve was to take the value at the beginning of the sample and the value at the end of the sample and average them together to produce the best result. The finer the samples, the better the accuracy. The same holds for most/all of calculus too I think.
KE is the integral of momentum WITH RESPECT TO VELOCITY .... u gotta mention that and know that here, Mass does not varry........... Here’s my question if someone know, is there something like integral of KE with respect to Variable Mass, when velocity is constant ?
I am 61 years old retired Mechanical Engineer from Chennai India.,i am still learning calculus as I like and dislike both.sometime very interesting and othertime frustrating., Indian has the knack of learning without understanding the basics., that is our education is all about.never ever had pictorial during our days but now lot of changes as many people write GRE or SAT ., keep it up my boy.,
I haven't watched this yet, I certainly look forward to any and all of the content you post. I thought I'd never use Calculus, or Trigonometry (which is kind of REALLY important in many areas of calculus, wish I discovered that sooner) in high school because none of my teachers really knew how to apply it outside of teaching, or at least few gave real-world examples if they did. I took an interest in additive manufacturing, electronics, and robotics. Computer Science in general interests me personally, so AI in general of course, but that tends to use more linear algebra in my own personal experience. In 3D printing and robotics, a common "tuning" algorithm is PID feedback loop. A Proportional-Integral-Derivative control loop is used to "tune" Servo motors (brushless AC and DC multi-pole, multi-phase motors, not the cheap DC three word RC 'servos') as well as heaters, fluid pumps, fans, and a ridiculous amount of applications in many different industries. It is a relatively simple control algorithm that gets fantastic results after a few cycles and really improves efficiency and reduces error. Another use I've come across is how my 3D printer (running with a Duet 2 controller with dc42's fork of Reprapfirmware, an OSH and OSS project) auto calibrates itself using a "root mean square" algorithm after probing the print bed. Had I known how useful some of these concepts were in computer science and robotics, I would have paid MUCH better attention in high school. I was never exposed to it as a kid. Not only is your content educational and high-quality (as far as editing and scripting is concerned) but it is also [high-quality education]. Being 25 years old, I can assure you and anyone else that education, especially in America, is not always high-quality. That cannot go unnoticed, I find tremendous value in the content you post and only wish you uploaded content more frequently.
Yes this video motivated me as well to learn calculus. I'm too, a student of Computer Science. I've keen interest in programming. But without calculus, as far as I'm concerned of, my journey will end one day. I've to teach calculus myself. I don't care about the grade I got in maths. But really, our professors don't know how to teach maths. Thus, this channel is my inspiration.
Sourav Goswami Have you ever heard of Khan Academy? The Domain of Science's channel is not so much about specifics, although he does indeed give some fantastic examples and simplifies it to an easy to understand, far less intimidating, and potentially enjoyable subject. For him to legitimately teach some of these subjects would require much longer videos. He seems well-educated enough, I am unsure if he will take it that far. I am working, so perhaps this video is more in-depth, I don't know. Nevertheless, EdX, MiT Open-Courseware, and specifically Khan Academy should be more than enough for you for now. Really look at Khan Academy, I cannot stress that enough. You could legitimately replace school with the amount of education that is in there.
Kevin Delaney I love Khan Academy, and of course I see other TH-cam channels as well... Thank you for the suggestion you gave me... I will try to see more...
This video is sooo nostalgic for me, I first watched it in class 9, when calculus was not in our syllabus. This video made me learn a bit of calculus in my own. Thank you very much.
Its Wednesday my dudes Integration is by far the hardest part of calculus, and that is because its super mysterious. When do you use integration by parts, when do you use trig sub? Can you use both at the same time? These questions make integration harder than any other calculus topic.
The Gaming Army Generally you use integration by parts when there's a product of two functions that are not all polynomials. For example ln(x)*sin(x). If you're confused just ask yourself "what is the derivative counterpart to this method of integration?" For example the integration by parts above is derived from the product rule, so it must involve multiplication that cannot be solved by other rules
this gets me excited for university! lol will be a chemistry major and can kind of tell that calculus will be used a lot in something like kinetics or physical chemistry probably other things that i don't know of yet which is exciting to be honest!
Here I am in my mid-sixties and retired, and I always wanted to understand the use of calculus. I can't tell you how satisfying this is. Thank you very much.
I have the exact same reason as you as to why I chose physics as my career, cause it is so cool when you feel like a wizard with the the tools. But I think education system should start teaching calculus at earlier age than University to help them understand why physics is just amazing and why people should go for it, I think this is the reason for people not choosing scientific careers because they just thought it would be memorizing stuff but after they know this, they probably will make a better career choice than a SoundCloud rapper. In India, we start calculus at ages of 14. I think other countries should step up too if they are already not.
Its crazy because I thought I was so good at math in school, but as I got older I realized I did not understand it as much as I thought I did. I knew enough to get by and get great grades, but lacked the deeper understanding of why we are doing the calculations and how they apply to other things. I was failed in my education, but I will take it into my own hands now!
The plays of Shakespeare, the symphonies of Beethoven, the art of Renaissance Italy, these are the highest points of our culture, and calculus fits right in among them. Brilliant. Beautiful, Powerful. I often think, "Here I am struggling to understand calculus, and these guys freakin' invented it, using quill pens and candlelight."
Conservation laws are the reasons why we forge these equations. Conserved properties like momentum and energy allow prediction and their meaning is derived from that. "Super kinetic energy" might be valuable if it is conserved in a reaction. Emmy Noether showed that symmetry gives rise to conservation properties. So there would need to be a symmetry condition to make that so.
If you want to be a fighter pilot you have to know advanced calculus. The irony is that you will probably never use it unless your onboard computer goes down.
I took calculus in college, but before that, I had never taken pre-calculus. After talking with some people, they told me that pre-cal wasn't really necessarily a prerequisite for calculus, which I found odd. Anyways, it was an interesting class. I actually began to enjoy finding derivatives, but determining limits confused me a bit. It'd be so amazing to gain a mastery of calculus. I never continued with it past just the very basics, but maybe someday I will.
Thanks, and apologies I have had a deadline to hit on writing the next Prof Astro Cat book, which delayed my video production. But on the plus side I'll definitely have the next few videos out quicker, one more this month at least.
Yes but not as frequently because they take so long to make. I'm planning on making several videos like this in a row and then a map video every so often.
Another job was in a gun propellant factory, I was the only physicist under a lot of chemists. The chemists new some of the physical laws but not the details. For instance, the combustion speeds of propellant is expressed as v = beta * p^alpha as physicist it is obvious that this is the differential equation for an exponential v proportional to dp/dt = beta * p^alpha, I wondered why do these guns not explode but then learned, that this was the art of judging the size of the propellant grains so that the bullet has enough time to start to move. As most of the exponents are integers or brocken integers and alpha was close to one, so I told the chemists to put it to one, in addition this gave a very, very simple linear expression to calculate the first approximation for the propellant dimensions involving only the velocity and weight of the bullet, both known very precisely. I later read in a defence book, that actually alpha is equal to one above pressures of around 300 bars compared to 3000 to 7000 bars of peak pressure, so it was a good approximation.
Did you know that Calculus was invented in India centuries before Newton - in fact, most of what the modern West called Modern Mathematics 500 years ago was Ancient Indian Maths. Arithmetic is the Indian Decimal Place-Value Number System with Zero - which Cambridge profesor John Barrow wrote is the greatest intellectual invention ever made by humans. When this Indian system reached medieval Italy [Leonardo of Pisa translated Al Khwarizmi's Arab translations of Indian works], people paid to watch mathematicians do calculations such as 27 x 14 in their heads at fairs - prior to this system, doing long calculations was much more complicated and error-prone. Laplace wrote that we do not appreciate the genius of the Indian Number System as it is so simple, yet it was beyond the abilities of the greatest Greek mathematicians, Archimedes and Apollonius. Back in 1817, Henry Colebrooke showed that modern Algebra is derived from the ancient Indian Algebra (bijaganita). The Persian Al Khwarizmi who translated Indian Arithmetic into Arabic also translated Indian Astronomy texts which utilized the Indian bijaganita. Colebrooke pointed out that the Greeks inherited Babylonian Algebra and did not make much improvements on it. Late on in the Greek world (4th Century c.e.) Diophantus did develop algebra somwhat but the Indian Algebra was far more sophisticated and advanced than the work of Diophantus. Modern Trigonometry owes much to the work of Indian Aryabhatta known as the Aryabhatiya (499 c.e.)which also contained a heliocentric model of the solar system and was translated into Greek and Latin centuries before Copernicus. Of course Aristiarchus of Samos had proposed heliocentrism long before Aryabhatta - but note the mythology surrounding Copernicus. Even Calculus originated in India centuries before Newton and Leibniz - see theconversation.com/five-ways-ancient-india-changed-the-world-with-maths-84332
@cmiller8492 LOL -In your little mind perhaps. Just because you have not heard of it does not mean that no one else has. Eurocentric Westerners hide this stuff but educated people have heard of it! And you use the word 'meaning' as if only what is known to you is meaningful to others! The Iberian Voyages of Discovery used Indian Astronomy inherited from the Moors for navigation [Nothing important indeed to your racist mind]. Astronomical questions supposedly resolved first by the likes of Tycho Brahe etc. had already been solved by Indian astronomers. The so called 'Fibonacci Series' [named after Leonardo Bonacci of Pisa] and other such maths, supposedly discovered in Europe was well known in Ancient India. In the 18th Century, French astronomer Bailly and Scot Playfair showed that the ancient Brahman Astronomy was just as good for practical purposes [predicting eclipses etc.] as the latest Western work of Cassini. As US mathematician Charles Seife stated in his 'Zero'; the mathematical Physics of Descartes and Newton would have been impossible without Indian Mathematics especially the Zero! The Westerners have peddled colonial myths that the rise of Science was due to Greek knowledge. In fact Colonial Westerners concocted their racist Classics and the myth of the Greek Miracle in Science and Philosophy falsely presenting Shamans such as Pythagoras, Empedocles and Parmenides and mystics such as Democritus and Heraclitus as if they were somehow 'scientists'. In fact most Greek Philosophy was no different from mystical Oriental Philosophies [Plato's philosophia meant Love of the Light of Cosmic Wisdom - or seeking Divine Illumination/Enlightenment] and, as numerous scholars have shown, all the elements of Miletian Monism were already well-established in Indian philosophy, Empedocles' '4 elements' were copied from older Indian versions which are actually more in tune with modern Physics than his etc. I myself have identified the physical correlate of what Plato called 'Sophia' - the Inner Light with the brainwaves of the Reticular Activating System - demonstrating the scientific basis of Ancient Yogic knowledge of Consciousness [www.sutapas.com ] In fact the Hindu Nyaya Logic surpassed all formal logic in the West until the work of George Boole in the 19th Century. Robert Oppenheimer wrote that ancient Indian logician Dignaga resolved logic problesm which stumped Frege and Russell in the 20th Century. Panini's ancient Sanskrit Grammar inspired the development of Linguistics in Europe. BTW - if you are British - you probably don't know that as late as the 1790s English experts pronounced Indian wootz steel to be the best in the world and the English copied its techniques. Note that the Brits looted $45 Trillion (£36 Trillion) from India and this loot financed the Industrial Revolution as well as much other Western development whilst killing tens of millions of Indians as they also looted India's foodgrains: www.express.co.uk/news/world/1059012/india-news-bombshell-how-british-empire-stole-36trillion-from-india-lied-spt www.aljazeera.com/indepth/opinion/britain-stole-45-trillion-india-181206124830851.html As H.H. Wilson wrote in 1853, the likes of Manchester could not have risen - not even with steam power - had the British not systematically destroyed the competition from Indian textiles which were both cheaper and superior in quality - this included breaking the fingers and cutting the thumbs off Indian weavers.
@cmiller8492 LOL Again - Great logical thinking from you there - that development is correlated with the use of Calculus! Oh- I bow to your 'genius' - and your deluded claims to argue with facts! Who except for you is claiming such absurd things! I was responding to your claim that Ancient Indians were not advanced - and showed you that, relative to Ancient and medieval Europeans, they were advanced. Note also that Hindu India was invaded by Muslims from 1200 c.e. and again by the Mughals in 1515 and this led to decline in Indian scientific achievements. But even in 1616 English Ambassador Thomas Roe described Delhi as the Treasury of the World - and the British takeover of India was motivated by the silver drain [much of the gold and silver looted by Europeans from the Americas ended up in India] due to India's world-dominant textiles industry, spices etc. So how comes France which was widely recognized as the world's leading scientific nation in the 18th Century - doing all the decimal/metric standardization and producing the greatest scientists of the era - did not industrialize as discussed in famous works such as Musson and Robinson's 'Science and Technology in the Industrial Revolution'. How comes Egypt was the 2nd most industrialized country in the 1830s - it was not a scientific nation? What about the fact that in the 1840s Paraguay became the first industrial and the richest nation in Latin America but, as this threatened Britain's exports, Britain funded an invasion by Brazil and Argentina which killed 5/6 of the Paraguayans, seized some of its territory and stopped further industrialization [see 'Open Veins of Latin America' by Eduardo Galeano]. It is Politics [not Calculus!!!!] that determines industrial development. The fact that Britain industrialized first had to do with numerous non-scientific factors such as lack of wood due to shipbuilding and the need for coal and numerous other historical accidents! If you bother to read the links I sent about how Britain stole $45 Trillion from India, you will also find that the Industrial Revolution depended upon the massive surplus capital that Britain attained from looting India [prior to this loot and the opium peddling to China, the Atlantic Slave Trade was Britain's biggest earner]. As also indicated, even after the Industrial Revolution started, in the 1790s English experts pronounced wootz steel the best in the world. The fact was that Britain undertook a policy of systematic deindustrialization and plantationization of India to turn it into a source of raw materials. The oldest seaworthy ship in the Royal Navy is HMS Trincomalee in Hartlepool - built by Indian shipbuilders in Bombay in 1817 - and built of hardwood teak so it was superior to British oak. British shipbuilders lobbied Parliament to prevent shipbuilding in India, just as with textile industrialization and other industries. It was only with the 1914-18 Great War in Europe that Britain eased some of its deliberate deindustrialization policies. BTW, I have lived in Britain since 1967 and it is amusing to see how Britain has declined over this period - without the loot from the empire. In the meantime India has risen economically and is currently about to overtake Britain in nominal GDP - and by 2030 will become the 3rd largest economy. By 2050 things will be returning to historical normalcy with India and China probably as the top two economies as they have been for millennia - with the newcomer the USA also a contender.
i remember when i was in high school, at first I wasn't truly convinced that a derivative can compute the slope of a curve at any point...so i tried to prove it by manually computing, first select any x-value (X1) then get corresponding y-value (Y1) by plugging x to the function and solve y. Now you have 1st point (X1,Y1). To get a nearest point (X2,Y2) to my (X1,Y1) just do the same process but with X2=X1+0.01, then compute the slope of these two points. It will be approximately equal to the value of derivative at that point (X1,Y1).
Could you make a video describing the order in which different fields of math are related and what ordered they should be studied? (Should I study linear before discrete, what should I brush up on before going into calc 2, etc)
Excellent presentation I come across on integration & differentiation. We learned at school but never were told why we do integration & differentiation. In school we had to just solve an equation involving integration (single, double or triple) and differentiation (full or partial). Both are very interesting specially when you try to convert these equations into linear system of equations and solve them by forming matrices and solving it using certain boundary equations. I hope you hv such vlogs at an advance level e.g. solving an electromechanical problem using finite element method,
Thank you so much for finally explaining to me what the actual thing was that we were supposed to be calculating . Had you been my first year calculus teacher my life would have been very different.
The Question should be,What is Calculus not good for? When you have the answer to that Question,you will then know,what is Calculus good for. The Alpha is the Omega.
How many of us could have ACTUALLY UNDERSTOOD calculus if the education system had bothered to teach us some of this. I'd have rathr not gotten so far in math and more thoroughly understood what we did. This is what we need. Thanks for the video!
I honestly think they should start teaching calculus a lot younger, and with a more conceptual basis to prepare students for the technical hard bits, so that most people should at least have a handle on it by the end of high school. Because the degree to which people (or, I guess, from my experience, Americans) don't understand calculus is a TRAVESTY, and so many things in every day life would be easier if people thought about them in calculus terms instead of arithmetic terms.
Why would they want to make people smart? Population os supposed to be a bunch of sheeps. Ot's why education sucks. Thanksfully, there is Internet where there is a lot of websites to learn everuthing like math and programming.
@@quantumsoul3495 Since you seem like a person who wants to learn and become better, it is thankfully not thanksfully and everything is with a y not u but i guess that one is just a typo.
I actually did it. In 12 weeks, I managed to learn Algebra 2 and fundamental Calculus [for the first time in my life]. It was HELL. Time to tackle Mathematical Modelling. FML.
I am just wondering, say there is an alien civilization just as advanced as us, what kind of mathematical concepts did they invent to describe the universe. Do you think their math would be similar to our math, but just with different symbols for representing numbers, addition, subtraction, multiplication, and division. Or, they have invented some new form of arithmetic and a different way of doing the same thing calculus does.
A lot of mathematics arise quite naturally from simple concepts, so I believe that aliens would have similar ideas behind their mathematics. Of course the way of representing those ideas could be very different. Also, a civilization could not be as advanced as us without knowing quite a lot of mathematics.
Great video, keep up the good work. I was not taught calculus at school, I did not know that it even resisted, but I have been fascinated even since I discovered it. A really brilliant explanation
Sadly, my mind does NOT "work that way", I have trouble learning calculus without applying to something real. You're right, the pathetic American school system doesn't have time to teach application of calculus, instead we get "just do the formula"...my mind need to connect it with something (the motion of stars). What's more sad, I'm MORE prone to use advance math on a daily basis than any of my classmate from high school due to the type of hobby I have (designing airplanes, foils and hulls). Today, I still don't get calculus and hoping someone can explain it in such a way that my mind can connect it with "getting things done" in my life.
It's not only american education the same happends in western Europe. Even more sad was that half of the students on my school stopped their physics study at an university (which costs alot and takes away 1 full year of potential studying) after realising it was alot of math, because highschool fails to give a view of what physics is really about. About your calculus problem I think that 3blue1brown has an awesome way of explaning it (you prob tried already since it get mentioned by everyone), but I also like the channel 'Michel van Biezen' this guy has alot of videos where he explains not specific calculus but he uses it alot and explains why he does that , this guy really helped me.
I'm currently a physics major and calculus becomes the algebra. What I mean by that is once you reach calculus, algebra should be second nature and it is one of the biggest reasons people fail calc. Well after calc, calculus becomes the new basic idea that you need for the rest of your math career! Calculus one through three are probably one of my favorite math classes thus far and I'm ready for more!
It brought back to me lovely memories of high school...It applies also to economy if you a cost function of x2 +3x +4 (just and example, the first derivative would be 2x +3 and the area between two points on the curve would be the total cost . Thank you for that memory
You didn’t explain how we know the integral of momentum with respect to velocity is Kinetic Energy. You explained how you got the equation, and I get that, but how do we know it’s for KE?
To show that in full generality would take a long series of videos. You can get some insight from an example problem, though. The most important feature of energy is that it's conserved (in many systems). If we start with an example system, say a weight of mass *m* on a spring of stiffness *k*. The motion of the simple system could be, with a particular starting condition, x=x0 cos[sqrt(k/m) t]. This described a simple oscillating motion, the frequency depending on the spring stiffness and mass. If you calculate the kinetic energy of this system [1/2 m (dx/dt)^2], you'll see that it varies with time. If you calculate the potential energy of the system [1/2 k x^2] you'll find that it also varies with time. The sum of the two, though, does not change with time. In other words, it is conserved. This fact (more or less) justifies calling these two quantities "energies." And, of course, you can verify that the derivative of kinetic energy with respect to the velocity (= dx/dt) is, indeed, *m v*. If you want a totally general answer to this question, you can study up on Lagrangian mechanics. Fair warning, though, this view of things is much more abstract, and also requires comfort with calculus.
you can deduct that using the original equation, the slope is dy/dx and integral, in the simplest term, is y * x (the area under) it's an established fact that Momentum * Velocity = Kinetic Energy so in the graph of Momentum vs Velocity, if you find the integral (y * x) you get the Kinetic energy it's not the exact explanation, but it serve well as a visualization
LegendofVII I dont know about you but I recommend learning calculus from now just in case. It wont hurt to learn besides you might change your mind about engineering
Il be honest with you. I am a dumbass at math but I am still going for engineering. I am in Calc 2 now and its hell. The amount of understanding needed is crazy. Calc 1 is not hard compared to calc 2. Dont be afraid and dont let anyone tell you, you cant do it. Who cares if you fail calc 5 times, at the end you will get your degree and you will be the winner. If you want to succeed, first dont worry about money, but still be considerable about it.
Calculus isn't hard. It's just taught horribly. Many just regurgitate what sone dry teacher or book told them. Relate it to real life, then everyone will love calculus.
Calculus is one of the highest achievements of human thought. That alone makes it a source of wonder. Those who understand it can appreciate the beauty that most are not able to know.
Im more surprised you learned calculus at uni. I was taught calculus when I was 16 (through to 18). That was still part of mandatory education. Now Im at the first year of uni in an engineering degree and we started with a very brief recap of calculus (1-2 classes) and then we did Analysis for the rest of the semester. In the second semester we had linear algebra. Also when we had physics at school we were always taught the derivations of the equations so we would understand them toroughly. Anyhow, great video
That is great! You went to a good school. The UK system is a little different and we do '6th form college' ages 16-18 where you do learn calculus, but only if you take mathematics. So I did learn calculus before University, but only the derivations at University.
My high school didn't require calc or physics so my first 2 years of engineering were a bitch. You then get into your junior year and all you did algebra with short cuts to skip the calculus lol.
I am fourteen years old and love math and physics with my life, but school is very slow so I've got to get books and study on my own. I just discovered this channel and I am completly in love. PD: If I have a mistake I'm sorry but I am spanish- speaking.
First Principle, ("first do no harm"), so if there's no derivivation of why this is a use-question of a particular observable cause-effect purpose, then this video is about the "how" technique in a 2D of 3D assumed coordination system that is the apparent "whatever" physical application seems relevant to "try".., and the original implied existence of what, how, when and why, an aspect of fitted location in a projected drawing of difference distribution is relevant.., is the why here-now-forever orientation of human participation? In the holistic awareness of Perspective, differentiations and integrations are equivalent processes that "approaches the limits" of calculation, but the real-time wave-package envelope-shaping in Singularity Perspective Pointing to Positioning is inherent in the e-Pi-i sync-duration Eternity-now in logarithmic circularity, equating the sync-duration resonance @.dt, formulation formatting. (It's unlimited and "Mathemagical"!)
I hated calculus in school, but i was decent in it, but in Engineering university i got see how its actually applied in real world and after working with different transformations, calculus feels normal math don’t even think about it.
Ha! You recommended 3Blue1Brown's channel! I have been subscribed to that channel for months! That's exactly where I learned more about machine learning after you made some of your videos. His videos on linear algebra are superb. You're right, that whole channel is phenomenal. Admittedly, I don't watch as much of his videos as I'd like to be able to. An electrical engineer, more of a hardware engineer, an ex hardware engineer for HP (one of the smartest men I've ever met before, actually taught me about Boolean algebra and how computer memory functioned and cry displays functioned) told me that if someone cannot explain something, anything, in a simple manner...it is because they do not fully understand it. That does not appear to be a problem for you so far:) Even if the video is scripted, it is the way in which you speak that confirms my suspicions about you. A very well done video about a complex subject. Mathematics, not unlike physics, can easily intimidate individuals who are less educated on the subject. You see some of the more complicated examples of this and it's easy to understand why. You do a very good job of kind of enticing or inviting people to take a closer look at the subject, "it's not that hard" I feel you calling out. And while I wouldn't say it's always easy, most of the calculus I've encountered so far isn't nearly as difficult as I anticipated. Very well done.
I never "got" maths until I discovered calculus, and now I'm hooked
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In one min and 53 seconds you explained calculus better than any teacher I ever had.
If you have more time .....watch Eddie woo's channel.
I mean, better than the teacher I've never had. Calc is hard when the textbook is your only teacher, and then you got all your other classes thrown at you.
They themselves don't know what will they explain you that's the problem with our system 😔😔😭😭
@Rudraksha Dwivedi It is your fault you were no able to learn grammar
@Rudraksha Dwivedi guess you're still typing in anger 1 year later then...
3:19 Never forget to +C
Peter Bergmann unless ur dealing w a definite integral
@@elenildodossantos8629 I see you're a fellow man of culture
the bane of my existence in calc one was forgetting the constant
My maths sir cut 1 marks for it last year😓
3:59 I love that you point this out. I've found that a big problem in learning is intimidation.
A lot of the concepts are extremely simple and intuitive once you know the vocab.
And anything can be broken into easier parts.
First time I am watching a video of yours. I have to say the quality is simply amazing. No silly background noise or music, no rush, no unnecessary crap. Just what people need in a smooth voice and language with a great quality video. Keep up the great job man!
this video actutally expaining what calculus, differentiation, integration IS and how it's basically slope and sum of curved functions is SO much clearer, less stressful, and is better for deeper understanding in a shorter amount of time than the confusing non-explanations in school class with stress homework, reading difficultly worded textbooks, spending so much time on an example that doesn't make sense to try to extract the core concept of calculus.
I’m in school and I’m learning calculus. We have never simply been given formulas to memorize but rather focus on understanding how the formulas are derived
that's actually really cool because in our school all we have to do is memorize and none of us know what calculus actually is
That's how schools are supposed to do (Which, unfortunately, doesn't do often)
I'm currently in 11th grade, my math teacher is simply the best teacher that has ever taught me, but unfortunately, since she had focused a lot on lessons before calculus like functions, and had spent a long time to teach it to us, we barely, and I mean barely, were able to finish the book right before the finals, so yes, she did breifly explain what calculus is, but still I couldn't understand from just two lessons, and today as I'm writing this, I'm actually having that exam about two hours later, and I don't know what to hope for, I'm actually pretty good at math, but pretty bad at memorizing, so calculus is gonna be a big pebble in my shoe!
@@3dsaulgoodmanhow did it go? I hope you did well
we are cramming the stuff o'er here -_-
Calculus, what is it good for?
Good for lowering my gpa...
at what rate tho?
He skipped class to know that.
well thats not good at all.
Software Man 0great
Absolutely nothing, sing it again! lol (
Calculus is easy to understand, but hard af to master.
Sushant Prasad preach
When you're at calculus 1 the hardest thing is the algebra but once you get to cal 2 and other classes that have integration techniques you realize integrals can be a bish
Either you are brilliant or you don't really know what calculus is.
Really? You need a good teacher and a good reference book. In my first year of calculus we had neither; anything above 40% was considered an A, and that was 40 years ago. Ironically that did not stop me. Over the years I too have come to the belief that calculus can be easy with the correct resources.
That's so true！！！！
we need more teachers and professors like u who know what they talking about
Taught myself a decent amount of calculus 1 and 2 during the fall. Really an amazing topic to dive into; incredibly useful. I think linear algebra is also as mind blowing, just in a different way.
after finding the slope(m) and the intercept(b) and graphing that is there more to linear algebra
@@bealu9459despite its name, linear algebra doesn’t have anything to do with graphing lines. it’s mainly about two things: vectors and matrices. Vectors are like a fancy way of storing coordinates. And matrices are a way of representing certain transformations you can do to those coordinates. linear algebra has a ton of fun applications, so I’d really recommend you learn more about it.
Your video popped up on my feed literally when I checked TH-cam after taking my integration test. All of you're saying is amazingly simple but true (which is something really hard to achieve) and made me love Calculus even more. Keep up the good work
The most interesting college course I have had so far, I got 15/20 on my first exam because I was lazy on that day, 20/20 on my last exam which include the whole theory the professor taught during the semester. I give credits to my calculus teacher, she was one of the best math professors I’ve had and she made sure she gave us real scenario problems to solve in order to truly learn and understand the theory.
Bro that first minute blew my mind. I need to start applying what I know in one area and apply it to other areas of my life
You are the epitome of Einsteins quote, “if you cannot explain it simply you do not know it well yourself” ❤❤
This is so fascinating to watch.
Really maths is beautiful.
This is by far the best! Video I've seen on the topic. You have no idea how much your explanation has helped me see the connection between what I'm learning and how it's applied. I'm beginning to realize why many see math as an art.
A million thanks to you sir!
In some natural science applications,Calculus can be used to quantify the rates of change in some natural processes.
used it yesterday. the calculate the time something takes to cool down in temperature. if a glass of water is 21celsius and is going to cool to 20celsius in a 10 celsius room. the difference in temperature between the glass will change as the glass cools down. so its rate of change will be smaller. here we used integrals and differential equations
Calculus is hard.
Real Analysis : Hold my Beer
Topology : Hold my Mathematics
Enosh Subba REAL ANALYSIS😡😡
Enosh Subba why do millennials all follow stupid speech patterns like sheep?
@Another Random Cuber r/iamverysmart
π : am I joke to you?
Heavens to Murgatroyd Ok boomer
The math series from “how does it tick” also goes over the history mathematics - the story for math deserves some glamour too!
The love and appreciation Isaac Newton must've had for physics and mathematics is absolutely astonishing,what a brilliant dude.
I'm a retired electrician and I wasn't really that good with math but I learned trigonometry in reverse by learning to bend conduit by using the 30, 45 , 60 degree offsets and 90 degree stub up .
The UGLY book was helpful in learning trig ratios and 6 trig functions by remembering Oh Hell Another Hour of Andy.
I find the unit circle a really good method
for learning trig and
I still have fun drawing it
to visualize the beauty in the patterns and repetition as it changes from one quadrant to the other. It lifted my confidence a lot so now I dabble with light calculus and find projectile motion very interesting. At 64 yo
I find algebra more difficult to grasp than trig but that's just me.
Any way thanks for your video.
Wish I had this explanation from my teacher at school, so easy to understand now
Nyquist taught us that the best way to derive the value of a curve was to take the value at the beginning of the sample and the value at the end of the sample and average them together to produce the best result. The finer the samples, the better the accuracy. The same holds for most/all of calculus too I think.
I had no idea that KE was the integral of Momentum
DaStormBringa And force is the derivative of momentum.
Only in systems that the mass doesn't variates
You can literally found many physics equations that were derived from calculus.
KE is the integral of momentum WITH RESPECT TO VELOCITY .... u gotta mention that and know that here, Mass does not varry...........
Here’s my question if someone know, is there something like integral of KE with respect to Variable Mass, when velocity is constant ?
This video is highly significant for the learners learning Physics in a philosophical aspect. Thanks.
I also love 3blue1brown, and I can't wait to become a physics wizard like you!
fefe he’s great!
Physics Wizard more Like, Physics Scientist.
I am 61 years old retired Mechanical Engineer from Chennai India.,i am still learning calculus as I like and dislike both.sometime very interesting and othertime frustrating., Indian has the knack of learning without understanding the basics., that is our education is all about.never ever had pictorial during our days but now lot of changes as many people write GRE or SAT ., keep it up my boy.,
I haven't watched this yet, I certainly look forward to any and all of the content you post.
I thought I'd never use Calculus, or Trigonometry (which is kind of REALLY important in many areas of calculus, wish I discovered that sooner) in high school because none of my teachers really knew how to apply it outside of teaching, or at least few gave real-world examples if they did. I took an interest in additive manufacturing, electronics, and robotics. Computer Science in general interests me personally, so AI in general of course, but that tends to use more linear algebra in my own personal experience. In 3D printing and robotics, a common "tuning" algorithm is PID feedback loop. A Proportional-Integral-Derivative control loop is used to "tune" Servo motors (brushless AC and DC multi-pole, multi-phase motors, not the cheap DC three word RC 'servos') as well as heaters, fluid pumps, fans, and a ridiculous amount of applications in many different industries. It is a relatively simple control algorithm that gets fantastic results after a few cycles and really improves efficiency and reduces error.
Another use I've come across is how my 3D printer (running with a Duet 2 controller with dc42's fork of Reprapfirmware, an OSH and OSS project) auto calibrates itself using a "root mean square" algorithm after probing the print bed.
Had I known how useful some of these concepts were in computer science and robotics, I would have paid MUCH better attention in high school. I was never exposed to it as a kid.
Not only is your content educational and high-quality (as far as editing and scripting is concerned) but it is also [high-quality education]. Being 25 years old, I can assure you and anyone else that education, especially in America, is not always high-quality. That cannot go unnoticed, I find tremendous value in the content you post and only wish you uploaded content more frequently.
Thanks for that Kevin, much appreciated.
Holly crap it’s taken me longer to read this comment then the length of the video. LOL
Yes this video motivated me as well to learn calculus. I'm too, a student of Computer Science. I've keen interest in programming. But without calculus, as far as I'm concerned of, my journey will end one day. I've to teach calculus myself. I don't care about the grade I got in maths. But really, our professors don't know how to teach maths. Thus, this channel is my inspiration.
Sourav Goswami Have you ever heard of Khan Academy? The Domain of Science's channel is not so much about specifics, although he does indeed give some fantastic examples and simplifies it to an easy to understand, far less intimidating, and potentially enjoyable subject. For him to legitimately teach some of these subjects would require much longer videos. He seems well-educated enough, I am unsure if he will take it that far. I am working, so perhaps this video is more in-depth, I don't know.
Nevertheless, EdX, MiT Open-Courseware, and specifically Khan Academy should be more than enough for you for now. Really look at Khan Academy, I cannot stress that enough. You could legitimately replace school with the amount of education that is in there.
Kevin Delaney I love Khan Academy, and of course I see other TH-cam channels as well... Thank you for the suggestion you gave me... I will try to see more...
This video is sooo nostalgic for me, I first watched it in class 9, when calculus was not in our syllabus. This video made me learn a bit of calculus in my own. Thank you very much.
Sir please start a series for teaching integration and differentiation..
3blue1brown has a series
Its Wednesday my dudes preach
Check out Professor Leonard's Series it is amazing
Its Wednesday my dudes Integration is by far the hardest part of calculus, and that is because its super mysterious. When do you use integration by parts, when do you use trig sub? Can you use both at the same time? These questions make integration harder than any other calculus topic.
The Gaming Army Generally you use integration by parts when there's a product of two functions that are not all polynomials. For example ln(x)*sin(x). If you're confused just ask yourself "what is the derivative counterpart to this method of integration?" For example the integration by parts above is derived from the product rule, so it must involve multiplication that cannot be solved by other rules
Dude why did not i watch this 2 year ago . This kind of explanation u wont expect from ur high school teachers.
this gets me excited for university! lol will be a chemistry major and can kind of tell that calculus will be used a lot in something like kinetics or physical chemistry probably other things that i don't know of yet which is exciting to be honest!
I can't recall ever seeing the triangle method as an approach to demonstrate the derivative - I like it.
I took a year of calculus in college and a year of statistics. Over the next 40 years i rarely used calculus but did use statistics - life sciences.
As much as I hate *doing* calculus, I do greatly appreciate taking the time to understand it.
Here I am in my mid-sixties and retired, and I always wanted to understand the use of calculus. I can't tell you how satisfying this is. Thank you very much.
I have the exact same reason as you as to why I chose physics as my career, cause it is so cool when you feel like a wizard with the the tools. But I think education system should start teaching calculus at earlier age than University to help them understand why physics is just amazing and why people should go for it, I think this is the reason for people not choosing scientific careers because they just thought it would be memorizing stuff but after they know this, they probably will make a better career choice than a SoundCloud rapper. In India, we start calculus at ages of 14. I think other countries should step up too if they are already not.
Bad thing about calculus is that not everyone knows its application....
Its crazy because I thought I was so good at math in school, but as I got older I realized I did not understand it as much as I thought I did. I knew enough to get by and get great grades, but lacked the deeper understanding of why we are doing the calculations and how they apply to other things. I was failed in my education, but I will take it into my own hands now!
The plays of Shakespeare, the symphonies of Beethoven, the art of Renaissance Italy, these are the highest points of our culture, and calculus fits right in among them. Brilliant. Beautiful, Powerful. I often think, "Here I am struggling to understand calculus, and these guys freakin' invented it, using quill pens and candlelight."
Conservation laws are the reasons why we forge these equations. Conserved properties like momentum and energy allow prediction and their meaning is derived from that. "Super kinetic energy" might be valuable if it is conserved in a reaction. Emmy Noether showed that symmetry gives rise to conservation properties. So there would need to be a symmetry condition to make that so.
If you want to be a fighter pilot you have to know advanced calculus. The irony is that you will probably never use it
unless your onboard computer goes down.
QUINDI
RFFCGGGBHHGXZZFGFFDDOKK
So what? You do the calculus while you're flying and under enemy fire?
@@maurirodriguez8753 Your the reason why Trump built the wall.
@@michaelproctor8100 lmao you have no idea what youre talking about
Ha ha fenny fellow
I took calculus in college, but before that, I had never taken pre-calculus. After talking with some people, they told me that pre-cal wasn't really necessarily a prerequisite for calculus, which I found odd. Anyways, it was an interesting class. I actually began to enjoy finding derivatives, but determining limits confused me a bit. It'd be so amazing to gain a mastery of calculus. I never continued with it past just the very basics, but maybe someday I will.
Precalc is essentially a recap of Algebra two and trigonometry. When doing calculus on trig it is beneficial to understand how trig works.
Been waiting for ages for your videos.
Thanks, and apologies I have had a deadline to hit on writing the next Prof Astro Cat book, which delayed my video production. But on the plus side I'll definitely have the next few videos out quicker, one more this month at least.
And are you going to make also map video's?
Yes but not as frequently because they take so long to make. I'm planning on making several videos like this in a row and then a map video every so often.
It's worth the wait
Ninjas need calculus too. How will they explain it to their children. Magic?!! uuhumm I don’t think so...
Another job was in a gun propellant factory, I was the only physicist under a lot of chemists. The chemists new some of the physical laws but not the details. For instance, the combustion speeds of propellant is expressed as v = beta * p^alpha as physicist it is obvious that this is the differential equation for an exponential v proportional to dp/dt = beta * p^alpha, I wondered why do these guns not explode but then learned, that this was the art of judging the size of the propellant grains so that the bullet has enough time to start to move. As most of the exponents are integers or brocken integers and alpha was close to one, so I told the chemists to put it to one, in addition this gave a very, very simple linear expression to calculate the first approximation for the propellant dimensions involving only the velocity and weight of the bullet, both known very precisely. I later read in a defence book, that actually alpha is equal to one above pressures of around 300 bars compared to 3000 to 7000 bars of peak pressure, so it was a good approximation.
These are some of the best science and math videos on TH-cam. Great job, Dominic!
: “The secret of getting ahead is gettingstarted
like the way you explain, no hastiness and no hindering music. thanks for making it interesting.
Did you know that Calculus was invented in India centuries before Newton - in fact, most of what the modern West called Modern Mathematics 500 years ago was Ancient Indian Maths.
Arithmetic is the Indian Decimal Place-Value Number System with Zero - which Cambridge profesor John Barrow wrote is the greatest intellectual invention ever made by humans. When this Indian system reached medieval Italy [Leonardo of Pisa translated Al Khwarizmi's Arab translations of Indian works], people paid to watch mathematicians do calculations such as 27 x 14 in their heads at fairs - prior to this system, doing long calculations was much more complicated and error-prone. Laplace wrote that we do not appreciate the genius of the Indian Number System as it is so simple, yet it was beyond the abilities of the greatest Greek mathematicians, Archimedes and Apollonius.
Back in 1817, Henry Colebrooke showed that modern Algebra is derived from the ancient Indian Algebra (bijaganita). The Persian Al Khwarizmi who translated Indian Arithmetic into Arabic also translated Indian Astronomy texts which utilized the Indian bijaganita. Colebrooke pointed out that the Greeks inherited Babylonian Algebra and did not make much improvements on it. Late on in the Greek world (4th Century c.e.) Diophantus did develop algebra somwhat but the Indian Algebra was far more sophisticated and advanced than the work of Diophantus.
Modern Trigonometry owes much to the work of Indian Aryabhatta known as the Aryabhatiya (499 c.e.)which also contained a heliocentric model of the solar system and was translated into Greek and Latin centuries before Copernicus. Of course Aristiarchus of Samos had proposed heliocentrism long before Aryabhatta - but note the mythology surrounding Copernicus.
Even Calculus originated in India centuries before Newton and Leibniz - see
theconversation.com/five-ways-ancient-india-changed-the-world-with-maths-84332
@cmiller8492 LOL -In your little mind perhaps. Just because you have not heard of it does not mean that no one else has. Eurocentric Westerners hide this stuff but educated people have heard of it! And you use the word 'meaning' as if only what is known to you is meaningful to others! The Iberian Voyages of Discovery used Indian Astronomy inherited from the Moors for navigation [Nothing important indeed to your racist mind].
Astronomical questions supposedly resolved first by the likes of Tycho Brahe etc. had already been solved by Indian astronomers. The so called 'Fibonacci Series' [named after Leonardo Bonacci of Pisa] and other such maths, supposedly discovered in Europe was well known in Ancient India. In the 18th Century, French astronomer Bailly and Scot Playfair showed that the ancient Brahman Astronomy was just as good for practical purposes [predicting eclipses etc.] as the latest Western work of Cassini.
As US mathematician Charles Seife stated in his 'Zero'; the mathematical Physics of Descartes and Newton would have been impossible without Indian Mathematics especially the Zero! The Westerners have peddled colonial myths that the rise of Science was due to Greek knowledge. In fact Colonial Westerners concocted their racist Classics and the myth of the Greek Miracle in Science and Philosophy falsely presenting Shamans such as Pythagoras, Empedocles and Parmenides and mystics such as Democritus and Heraclitus as if they were somehow 'scientists'. In fact most Greek Philosophy was no different from mystical Oriental Philosophies [Plato's philosophia meant Love of the Light of Cosmic Wisdom - or seeking Divine Illumination/Enlightenment] and, as numerous scholars have shown, all the elements of Miletian Monism were already well-established in Indian philosophy, Empedocles' '4 elements' were copied from older Indian versions which are actually more in tune with modern Physics than his etc. I myself have identified the physical correlate of what Plato called 'Sophia' - the Inner Light with the brainwaves of the Reticular Activating System - demonstrating the scientific basis of Ancient Yogic knowledge of Consciousness [www.sutapas.com ]
In fact the Hindu Nyaya Logic surpassed all formal logic in the West until the work of George Boole in the 19th Century. Robert Oppenheimer wrote that ancient Indian logician Dignaga resolved logic problesm which stumped Frege and Russell in the 20th Century. Panini's ancient Sanskrit Grammar inspired the development of Linguistics in Europe.
BTW - if you are British - you probably don't know that as late as the 1790s English experts pronounced Indian wootz steel to be the best in the world and the English copied its techniques.
Note that the Brits looted $45 Trillion (£36 Trillion) from India and this loot financed the Industrial Revolution as well as much other Western development whilst killing tens of millions of Indians as they also looted India's foodgrains:
www.express.co.uk/news/world/1059012/india-news-bombshell-how-british-empire-stole-36trillion-from-india-lied-spt
www.aljazeera.com/indepth/opinion/britain-stole-45-trillion-india-181206124830851.html
As H.H. Wilson wrote in 1853, the likes of Manchester could not have risen - not even with steam power - had the British not systematically destroyed the competition from Indian textiles which were both cheaper and superior in quality - this included breaking the fingers and cutting the thumbs off Indian weavers.
@cmiller8492 LOL Again - Great logical thinking from you there - that development is correlated with the use of Calculus! Oh- I bow to your 'genius' - and your deluded claims to argue with facts! Who except for you is claiming such absurd things! I was responding to your claim that Ancient Indians were not advanced - and showed you that, relative to Ancient and medieval Europeans, they were advanced. Note also that Hindu India was invaded by Muslims from 1200 c.e. and again by the Mughals in 1515 and this led to decline in Indian scientific achievements. But even in 1616 English Ambassador Thomas Roe described Delhi as the Treasury of the World - and the British takeover of India was motivated by the silver drain [much of the gold and silver looted by Europeans from the Americas ended up in India] due to India's world-dominant textiles industry, spices etc.
So how comes France which was widely recognized as the world's leading scientific nation in the 18th Century - doing all the decimal/metric standardization and producing the greatest scientists of the era - did not industrialize as discussed in famous works such as Musson and Robinson's 'Science and Technology in the Industrial Revolution'. How comes Egypt was the 2nd most industrialized country in the 1830s - it was not a scientific nation? What about the fact that in the 1840s Paraguay became the first industrial and the richest nation in Latin America but, as this threatened Britain's exports, Britain funded an invasion by Brazil and Argentina which killed 5/6 of the Paraguayans, seized some of its territory and stopped further industrialization [see 'Open Veins of Latin America' by Eduardo Galeano]. It is Politics [not Calculus!!!!] that determines industrial development.
The fact that Britain industrialized first had to do with numerous non-scientific factors such as lack of wood due to shipbuilding and the need for coal and numerous other historical accidents!
If you bother to read the links I sent about how Britain stole $45 Trillion from India, you will also find that the Industrial Revolution depended upon the massive surplus capital that Britain attained from looting India [prior to this loot and the opium peddling to China, the Atlantic Slave Trade was Britain's biggest earner]. As also indicated, even after the Industrial Revolution started, in the 1790s English experts pronounced wootz steel the best in the world.
The fact was that Britain undertook a policy of systematic deindustrialization and plantationization of India to turn it into a source of raw materials. The oldest seaworthy ship in the Royal Navy is HMS Trincomalee in Hartlepool - built by Indian shipbuilders in Bombay in 1817 - and built of hardwood teak so it was superior to British oak. British shipbuilders lobbied Parliament to prevent shipbuilding in India, just as with textile industrialization and other industries. It was only with the 1914-18 Great War in Europe that Britain eased some of its deliberate deindustrialization policies.
BTW, I have lived in Britain since 1967 and it is amusing to see how Britain has declined over this period - without the loot from the empire. In the meantime India has risen economically and is currently about to overtake Britain in nominal GDP - and by 2030 will become the 3rd largest economy. By 2050 things will be returning to historical normalcy with India and China probably as the top two economies as they have been for millennia - with the newcomer the USA also a contender.
That sure makes you D so big now does it? Good for you.
@@Crimsonfireball I know right - winding up people like you makes 'me D' even bigger!
@@sutapasbhattacharya9471 Dont take other people accomplishment as your own tho. Your just a loser to me
Good video some youtubers won’t shut the hell up and get carried away but this is all exactly what you need to hear
A great video.
I finally see the use of calculus!
It brought out my interest for maths through physics
Not the normal type of video I watch but liked and subbed because I love that your spreading information keep it up man I respect all teachers
I NEVER UNDERSTOOD THE EQUATION FOR KENETIC ENERGY AND YOUR TELLING ME I DIDN'T UNDEESTNSD BECUSE NO ONE TAUGHT AS MOMENTUM IN GR 11
Ive done calculus at school. Easy to learn hard af to be good and get very confusing. But like coding, it take time to learn and you can master it.
"what is it good for?" literally everything
i remember when i was in high school, at first I wasn't truly convinced that a derivative can compute the slope of a curve at any point...so i tried to prove it by manually computing, first select any x-value (X1) then get corresponding y-value (Y1) by plugging x to the function and solve y. Now you have 1st point (X1,Y1). To get a nearest point (X2,Y2) to my (X1,Y1) just do the same process but with X2=X1+0.01, then compute the slope of these two points. It will be approximately equal to the value of derivative at that point (X1,Y1).
Could you make a video describing the order in which different fields of math are related and what ordered they should be studied? (Should I study linear before discrete, what should I brush up on before going into calc 2, etc)
Excellent presentation I come across on integration & differentiation. We learned at school but never were told why we do integration & differentiation. In school we had to just solve an equation involving integration (single, double or triple) and differentiation (full or partial). Both are very interesting specially when you try to convert these equations into linear system of equations and solve them by forming matrices and solving it using certain boundary equations.
I hope you hv such vlogs at an advance level e.g. solving an electromechanical problem using finite element method,
Great stuff!
Suggestion: add the second differential i.e. curvature. It would add so much more, and needs not take a lot of time.
Thank you so much for finally explaining to me what the actual thing was that we were supposed to be calculating . Had you been my first year calculus teacher my life would have been very different.
The Question should be,What is Calculus not good for?
When you have the answer to that Question,you will then know,what is Calculus good for.
The Alpha is the Omega.
Feeding you :D
I love your channel. I’m gonna start formally learning calculus thanks to you
How many of us could have ACTUALLY UNDERSTOOD calculus if the education system had bothered to teach us some of this. I'd have rathr not gotten so far in math and more thoroughly understood what we did. This is what we need. Thanks for the video!
Right, deriving physics equations you have memorized for years without knowing why is so satisfying
I honestly think they should start teaching calculus a lot younger, and with a more conceptual basis to prepare students for the technical hard bits, so that most people should at least have a handle on it by the end of high school. Because the degree to which people (or, I guess, from my experience, Americans) don't understand calculus is a TRAVESTY, and so many things in every day life would be easier if people thought about them in calculus terms instead of arithmetic terms.
Why would they want to make people smart? Population os supposed to be a bunch of sheeps. Ot's why education sucks. Thanksfully, there is Internet where there is a lot of websites to learn everuthing like math and programming.
@@quantumsoul3495 Since you seem like a person who wants to learn and become better, it is thankfully not thanksfully and everything is with a y not u but i guess that one is just a typo.
@@nicolaskoukoutsis8562 thanks
In india, we learn to do advanced calculus in high school
@Another Random Cuber It depends, it's the only true way to learn programming and khanacademy is actually quite efficient for math
Please teach us calculus!
Or anything for that matter, I’d listen every day!
In my country we learn calculus at high school math
Samee
Same
Same
Which country is that? and what grade? 12th grade or 9th grade.
Asia?
I actually did it. In 12 weeks, I managed to learn Algebra 2 and fundamental Calculus [for the first time in my life]. It was HELL. Time to tackle Mathematical Modelling. FML.
I am just wondering, say there is an alien civilization just as advanced as us, what kind of mathematical concepts did they invent to describe the universe.
Do you think their math would be similar to our math, but just with different symbols for representing numbers, addition, subtraction, multiplication, and division.
Or, they have invented some new form of arithmetic and a different way of doing the same thing calculus does.
A lot of mathematics arise quite naturally from simple concepts, so I believe that aliens would have similar ideas behind their mathematics. Of course the way of representing those ideas could be very different. Also, a civilization could not be as advanced as us without knowing quite a lot of mathematics.
Great video, keep up the good work. I was not taught calculus at school, I did not know that it even resisted, but I have been fascinated even since I discovered it. A really brilliant explanation
Sadly, my mind does NOT "work that way", I have trouble learning calculus without applying to something real. You're right, the pathetic American school system doesn't have time to teach application of calculus, instead we get "just do the formula"...my mind need to connect it with something (the motion of stars). What's more sad, I'm MORE prone to use advance math on a daily basis than any of my classmate from high school due to the type of hobby I have (designing airplanes, foils and hulls). Today, I still don't get calculus and hoping someone can explain it in such a way that my mind can connect it with "getting things done" in my life.
It's not only american education the same happends in western Europe. Even more sad was that half of the students on my school stopped their physics study at an university (which costs alot and takes away 1 full year of potential studying) after realising it was alot of math, because highschool fails to give a view of what physics is really about.
About your calculus problem I think that 3blue1brown has an awesome way of explaning it (you prob tried already since it get mentioned by everyone), but I also like the channel 'Michel van Biezen' this guy has alot of videos where he explains not specific calculus but he uses it alot and explains why he does that , this guy really helped me.
I think youre just slow, keep trying. I guarantee if you spent 12 hours of honest study you would learn it to a great degree
Hey, the country suffering most from unexplained Calculus is India.
Calculus is basically the rate of change. It basically plots out the gradient of a function. The basics are not that hard to understand.
this problem doesn't exist in India. here in india high level mathematics is taught at high school itself.
I'm currently a physics major and calculus becomes the algebra. What I mean by that is once you reach calculus, algebra should be second nature and it is one of the biggest reasons people fail calc. Well after calc, calculus becomes the new basic idea that you need for the rest of your math career! Calculus one through three are probably one of my favorite math classes thus far and I'm ready for more!
Swarthy One I'm actually taking Diffy Q over the summer. I should be fine though! I got an A in calc 2.
You start learning calculus in university ?
I was taught in the 11th grade .
Omg same. He got me confused ;__;
You are also asian i assume
@@arush6778 nah eastern European hahaha
10th grade
7th grade.Ye're all amateurs
I'm a math teacher and i like to learn calculus. Thakyou it is very clear 😀 greetings from papua
Momentum, p, is lowercase. Uppercase P is pressure.
H Sharma and curvy p is density
IMTHEDARKNIGHT - thats Greek rho
Thanks, for introducing me to 3B1B, It changed everything.
3Blue1Brown fans checking in :)
It brought back to me lovely memories of high school...It applies also to economy if you a cost function of x2 +3x +4 (just and example, the first derivative would be 2x +3 and the area between two points on the curve would be the total cost . Thank you for that memory
You didn’t explain how we know the integral of momentum with respect to velocity is Kinetic Energy. You explained how you got the equation, and I get that, but how do we know it’s for KE?
To show that in full generality would take a long series of videos. You can get some insight from an example problem, though. The most important feature of energy is that it's conserved (in many systems). If we start with an example system, say a weight of mass *m* on a spring of stiffness *k*. The motion of the simple system could be, with a particular starting condition, x=x0 cos[sqrt(k/m) t]. This described a simple oscillating motion, the frequency depending on the spring stiffness and mass.
If you calculate the kinetic energy of this system [1/2 m (dx/dt)^2], you'll see that it varies with time. If you calculate the potential energy of the system [1/2 k x^2] you'll find that it also varies with time. The sum of the two, though, does not change with time. In other words, it is conserved. This fact (more or less) justifies calling these two quantities "energies." And, of course, you can verify that the derivative of kinetic energy with respect to the velocity (= dx/dt) is, indeed, *m v*.
If you want a totally general answer to this question, you can study up on Lagrangian mechanics. Fair warning, though, this view of things is much more abstract, and also requires comfort with calculus.
you can deduct that using the original equation,
the slope is dy/dx and integral, in the simplest term, is y * x (the area under)
it's an established fact that Momentum * Velocity = Kinetic Energy
so in the graph of Momentum vs Velocity, if you find the integral (y * x) you get the Kinetic energy
it's not the exact explanation, but it serve well as a visualization
So now he's a mathematician I thought he just used to be an astronaught, firefighter, teacher and now he grew his hair up, such an inspiration.
I'm thinking about civil engineering, will I have to do calculus?
LegendofVII I dont know about you but I recommend learning calculus from now just in case. It wont hurt to learn besides you might change your mind about engineering
Il be honest with you. I am a dumbass at math but I am still going for engineering. I am in Calc 2 now and its hell. The amount of understanding needed is crazy. Calc 1 is not hard compared to calc 2. Dont be afraid and dont let anyone tell you, you cant do it. Who cares if you fail calc 5 times, at the end you will get your degree and you will be the winner. If you want to succeed, first dont worry about money, but still be considerable about it.
YUP
I got an EE but honestly calculus is used in all engineering.
Hash you are goint to need a lot of math especially integrals derivatives matrixes ( or tensors ) and of course differntial equations
I missed out on calculus in a good education. Thank you for being interesting, erudite and well spoken.
Calculus isn't hard. It's just taught horribly. Many just regurgitate what sone dry teacher or book told them. Relate it to real life, then everyone will love calculus.
Calculus is one of the highest achievements of human thought. That alone makes it a source of wonder. Those who understand it can appreciate the beauty that most are not able to know.
Im more surprised you learned calculus at uni. I was taught calculus when I was 16 (through to 18). That was still part of mandatory education. Now Im at the first year of uni in an engineering degree and we started with a very brief recap of calculus (1-2 classes) and then we did Analysis for the rest of the semester. In the second semester we had linear algebra. Also when we had physics at school we were always taught the derivations of the equations so we would understand them toroughly.
Anyhow, great video
That is great! You went to a good school. The UK system is a little different and we do '6th form college' ages 16-18 where you do learn calculus, but only if you take mathematics. So I did learn calculus before University, but only the derivations at University.
My high school didn't require calc or physics so my first 2 years of engineering were a bitch. You then get into your junior year and all you did algebra with short cuts to skip the calculus lol.
Excellent explanation which helps beginners dive into the beauty that is calculus
Map of Engineering please!
That map might be a little too big. Each branch of engineering has tons of subdivisions.
@Swarthy One that's a real train wreck of a comment
I've been looking for this equation the other day and uh THANK YOU FIRST FEW SECONDS!
My brain clocked out at the 47th second
I am fourteen years old and love math and physics with my life, but school is very slow so I've got to get books and study on my own.
I just discovered this channel and I am completly in love.
PD: If I have a mistake I'm sorry but I am spanish- speaking.
Calculus
Huh, yeah
What is it good for?
Absolutely everything.
say it again.
First Principle, ("first do no harm"), so if there's no derivivation of why this is a use-question of a particular observable cause-effect purpose, then this video is about the "how" technique in a 2D of 3D assumed coordination system that is the apparent "whatever" physical application seems relevant to "try".., and the original implied existence of what, how, when and why, an aspect of fitted location in a projected drawing of difference distribution is relevant.., is the why here-now-forever orientation of human participation?
In the holistic awareness of Perspective, differentiations and integrations are equivalent processes that "approaches the limits" of calculation, but the real-time wave-package envelope-shaping in Singularity Perspective Pointing to Positioning is inherent in the e-Pi-i sync-duration Eternity-now in logarithmic circularity, equating the sync-duration resonance @.dt, formulation formatting. (It's unlimited and "Mathemagical"!)
...... absolutely NOTHING !!!! bam bam bam
its just a song, chill
Got em! Lol
Great explanation, very easy to understand, thanks!
By the way, the pronunciation for p in p=mv is wrong. P is actually the Greek alphabet which is pronounced as Rho.
Either way you can use any letter under the sun. ρ is just the norm. You could use d for density if you want.
Man I think it's just P
Rho denotes density
And P momentum
This video explains much more clear than my uni professors
What is it good for?
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Absolutely everything (Except for my gpa)
I hated calculus in school, but i was decent in it, but in Engineering university i got see how its actually applied in real world and after working with different transformations, calculus feels normal math don’t even think about it.
: “The secret of getting ahead is gettingstarted
Ha! You recommended 3Blue1Brown's channel! I have been subscribed to that channel for months! That's exactly where I learned more about machine learning after you made some of your videos. His videos on linear algebra are superb. You're right, that whole channel is phenomenal. Admittedly, I don't watch as much of his videos as I'd like to be able to.
An electrical engineer, more of a hardware engineer, an ex hardware engineer for HP (one of the smartest men I've ever met before, actually taught me about Boolean algebra and how computer memory functioned and cry displays functioned) told me that if someone cannot explain something, anything, in a simple manner...it is because they do not fully understand it. That does not appear to be a problem for you so far:) Even if the video is scripted, it is the way in which you speak that confirms my suspicions about you.
A very well done video about a complex subject. Mathematics, not unlike physics, can easily intimidate individuals who are less educated on the subject. You see some of the more complicated examples of this and it's easy to understand why. You do a very good job of kind of enticing or inviting people to take a closer look at the subject, "it's not that hard" I feel you calling out. And while I wouldn't say it's always easy, most of the calculus I've encountered so far isn't nearly as difficult as I anticipated. Very well done.