Even if you never need Calculus, the Mathematical Competency, Logic, and Problem Solving Skills gained by it's study are indispensable.

Calculus is so useful for engineering, you can't just build an engine with algebra and not know where the heat goes or the pressure on beams in a bridge, but calculus and differential equations do that. I can't predict the weather with algebra or even think about landing on the moon without calculus. You just can't have a modernized world like this without calculus, algebra is just the tool we use to understand it. There's not much real world applications of algebra, but there's a lot of calculus applications.

I’ve been waiting 35 years for this explanation. Thank you !

i learned calculus at school to a fairly advanced level, i could score highly on calculus in exams, but i never really got a good feel for practical applications - thanks for this video.

Calculus takes algebraic math to the next higher level of abstraction. It hints and still higher levels. It solves exactly problems that previously could only be approximated. It teaches you how to think about huge and very tiny things--how to mentally zoom in and out of problems. It's a powerful intellectual tool in your technical problem-solving arsenal.

As a chemist, we use calculus basically for everything. To calculate how fast a reaction could go, to solve Schrodinger's equation and derivate lots of equations that serve kinda like a model to represent some nature's behavior. My mathematicians friends don't like when I say that, but Calculus it's a really strong tool.

better question, what is calculus not used for?

"what is calculus used for?" where do I begin......

School system asked me to memorize formulas and I got out with A. Now I'm feeling bad that was not guided into the right way. 😢😢

Amazing speech. I knew some applications of math and calculus etc being a mechanical engineer, but the possibilities are truly far reaching. I'm really excited to find out more and help fellow people. Everyone should try it and give it a shot.

Having (barely) passed college level calculus 1 & 2, here I am 11 years later still trying to understand what calculus even is, and what it's used for.

If anyone else is also forced to watch this for an assignment, just know that you're not alone and I feel your pain.

"It had to be completely walled off, with a door that would open and close." Most doors open and close. LOL

I truly appreciate the comments that show the usefulness of calculus. Studying this stuff made me wonder whether or not life involves differentiation, integration, optimization, etc., and without even watching the video I already see the importance of learning these complex concepts; thx strangers

if you're an engineer or studying engineering and you still don't find calculus useful, find another thing to do in your life.

Terrible choice of name for this video!! Makes calculus seem like something boring, only used in some specific areas of science. Calculus is the shit... learning it is like getting an extra set of senses. Humans only see the present and in 3d, calculus makes us able to see past and future, and in endless dimension. We use it to explain everything that is in some kind of motion or change. Which is pretty much everything that exist!!

I'll taking AP calc the next two years, and I'm super excited. I love math, and I've already learned a little calc, but to get classes from the amazing teacher that my school has... I'm really, really looking forward to that.

Oh cool, I did my Masters of Engineering research on developing a simulation of tissue thermal damage and thermally induced stresses during radio-frequency thermally ablative procedures. Pretty much the last topic he discussed as he finished.

I hated maths at school but as I was interested in practical Engineering, I took a 4 year industry apprenticeship. With day release I had to study for the ONC and HNC and maths is a big part of mechanical engineering. I would say that when you can see how it is applied to real problems, you can learn it much faster. I ended up with my own consulting business and projects included teaching industrial statistics at a major Australian University.

It can also be used to calculate light reflections on a 3d object, using partial derivatives, cross products and dot products, in a computer simulation or a video game. It can also be used to determine how much material is used to craft an object, using integrals, so that way companies do not have to spend extra money on extra material that they do not need.

I appreciated all the examples. Wish my prof. back 55 years ago had taken the trouble to give even just 1 example where calculus could help.

Calculus is extremely useful for all applications of engineering. Position and vector functions, integrals, and derivatives. All these fields help us construct the world around us as well as our modern technologies.

Could you explain more about the equations used to perform these experiments?

What is Calculus Used For? (at this point you sit watching the video hoping to learn some practical day-to-day uses for it and all you see is what you already know they are used for: niche applications)

He was an engineering undergrad and he didn't get a satisfactory answer to the question "What is calculus used for?" until grad school? Did he sleep through college or something? :-P

Excellent presentation. This inspired me to continue my calculus studies and it is great to see how calc. can be used in real world scenarios that can potentially impact mankind on an immense level. Thank you for sharing this...

So it's used for very academic, theoretical applications. It sounds like the work of PhDs, but how is it applied by people who aren't in research fields but had to take it as an undergrad?

This was one of the reasons why mathematics seemed so daunting: Much of it was so abstract for me, I had no idea why stuff like algebra and calculus even existed. Only now am I getting why this stuff is important. Of course, it didnt help that I could never pay attention to anything beyond what I was interested in at the moment.

When I need to use math in real life beyond basic math and pre-algebra, it's usually algebra or calculus. Like when I need to determine the dimensions of a field given certain parameters, or how quickly I am going at a certain moment in time. Both are equally useful depending on the situation. And of course, multivariable calculus, ordinary differential equations and linear algebra have a certain elegance to them. Also, I would like to learn more about partial differential equations besides just the very basics.

It's true that manipulated equations are a useful outcome of learning calculus. But calculus contains basic concepts to help explain how the world works. Students can learn equations, but not the concepts. An interesting example of calculus not understood concerns 9/11 doubters, who include students who've taken calculus. After learning trade tower structural members melt at temperatures higher than burning jet fuel presents, they suppose a nefarious heat source was introduced. Only then did structures melt and buildings collapse. Calculus explains why this wasn't the case. Key structural supports failed due to rate of weakeness change, and its second derivative (in calculus-speak.) Planes hit 1/4 kilometer high. Supports heated, weakened. Non-structural top floors collapsed. Structural member stress increased. That stress surge initiated collapse. Stress cascaded down, accelerating lower floor weakening. The derivative of the rate of weakening surpassed well-defined structural integrity threshold. Its second derivative led to immediate failure. Calculus maps how change rates, not absolute values, can cause events. It shouldn't be over-sold. Fourier transforms, cellular autonoma, probability, topology, and neural networks may arguably be used more than traditional calculus, in academia, industry, and government.

Every science is just applied mathematics. So that means learning the abstract format of mathematics would not only be the most efficient form but it would also allow for immense versatility -- an attribute characteristic of a polymath, or the ideal human being.

because I thought you were going to show some real useful examples of its everyday use but all you do is state obvious facts

My son is taking calculus. I think it is just as important to teach why we use calculus as much as the math itself.

I didn't like math in general, but when I took "Calculus I" I started really enjoying studying it and I felt like I am challenging myself like in paper-game. I am taking "Calculus II" and I don't need Calculus III for my degree but I will take it later when I have a free time.

HERE IN MY GARAGE< JUST BOUGHT THIS NEW LAMBORGHINI Can I please watch something on youtube without all these ads?

The chemical engineer in me says to just use a vacuum pump to generate a partial vacuum and discharge the smoke removed to the outside of the restaurant. But that kind of defeats the point of the talk :P

Calculus is used for complicated curves. The simplest example is a car which accelerate from 0 to 60 mph in 12 seconds. What is the speed at 4 second or 9 seconds. What is the distance covered by the car after 4, 9 or 12 seconds Once the car run at constant speed, it is easy. It covers 60 miles every hours. But during acceleration and break, calculus find simple equations. Consider statistics : a bacteria invade your body and multiply every hour. So, 2 bacteris at 1 o clock, 4 at 2, 8 at 3, etc. The number of bacteria is 2^hours, the constant 2 elevated to the power of the number of hours elapsed. Now, the immune system declare war to the invader. A section of the genetic code is made of codon which are mixed randomly, affecting the efficiency to recognize invaders. The best tagger win the right to rest and multiply as fast as possible. Those clones are all efficient taggers. When does the immune system catch up with the invader? These are two curve raising exponentially. What if another strain of bacteria take 48 minutes to double their number? How long it will take to the adaptative portion of the immune system to make enough of these antigene? Calculus concentrate a lot on "complex numbers" with one axe representing the square root of negative one. This strange definition actually represent cyclic event, oscillation which repeat. The fourier analysis tell us that any complex wave is made of many sinusoidal wave. The related Taylor series tell software engineer how to write equations to compute logarithm, sinus and the invert sinus and many other functions. Instead of using sliding rulers or hundreds of pages in table giving the answer for the most important values, the series allow a machine to compute those functions. Calculus goes even farther by predicting the amount of error that is expected depending on the equation selected.

So far in calculus 1 I've learned more about algebra than I ever did as well.

Great information for students in secondary schools and college.

Well done, sir. There are thousands of uses, Science and engineering would b e set back immeasurably without it. Love you

I'm so excited to start calculus next semester

When I think of models, Calculus is needed because most of our world is modeled by differential equations, and partial differential equations. That's what I think.

without calculus, we wouldn't have gone to the moon !!

I'm in business calculus...for business applications obviously. I'm doing pretty well it in. I see how useful it can be, even for business majors. Pretty much gets more into the economic side of things though.

Great explanation!

Thank you. Now it's more complicated

I love calculus and maths not just cause it is useful but cause it is beautiful.

I teach calculus in college in Nicaragua (third world country), and sadly, I would say that less than 10% of my pupils get to understand the very basics of calculus, there is a huge opposition in them to study it and the biggest complain I get is "where in real life will I use this?", and it is a difficult question to answer in a honest way, being in Nicaragua, we don't have NASA or high tech industries where there is a chance to need derivatives and integrals, and the students aren't happy with the response "calculus will develop your mind", the only thing it comes to my mind is that we are pointing high and calculus will help you to understand other sciences such as statistics, physics, economics and others

I'm teaching high school calculus now. It's profoundly challenging getting students engaged with this material. There is an economic "as if" function to the teaching of math. Let E be effort, V perceived value, and D difficulty. Then E=V/D (students put forth effort based on their valuing divided by their difficulty with the material). Though a part of V is their GPA, a much bigger part seems to be relevance and fun. D is huge the way textbooks present calc thus the V/D ratio (and E) -> 0.

I have heard of a story of a young woman at a dinner with many famous people; she wound up sat next to Einstein, although she didn't know who he was, she asked what he did and he said he was a student of physics and this was after the creation of the atom bomb; I don't know how she couldn't have known him then, the story is prolly B S but when I was a student of Calculus my twin daughters were born and I used half- life decay expectations and weight gain expectations for that age to predict their weight gain while they were premies in the prenatal I C U and it wound up being quite accurate

Awesome talk!

The problem with how this is typically taught is; they don't give you a practical problem to solve, so the purpose is opaque. I tend to learn much better when I can understand what I'm doing. It's like memorizing times tables without knowing the process of how to get the answer or it's use. Sure you can know 9x9=81, but what happens when you have to figure out 286×932? You can only memorize so much and when you're asked to figure something outside of the range of what you memorized it's completely worthless.

Good Question. Many fields of engineering use calculus as a basis of the subject. Specifically Mechanical and Industrial Engineering. Mechanical Engineering courses in college have a large emphasis on calculus such as Mechanics and Dynamics. Industrial Engineering is based upon maximizing output and making ways where industries need maximum productivity this requires a lot of application of calculus.

Thanks, in my school, all we do is just learn blindly how to perform the calculations and never had any insights on how to apply them, why learn them etc

I went to MSU too and I took all the calculus for engineering. I am very sad that this was the only subject I did not understand through my studies. I have never been able to use it in anything I have ever done, because I never learned how to apply it. I could do all the math, but attaching it to something that mattered was never understood.

This is how I "get" math. Lets say you want a way to add up all the numbers after 0 ye preceding something like, say, 5. So you want to add up 1 and 2 and 3 and 4. Previous to computers, without an easy formula, you'd have to add them up yourself. However, there's a summation equation to answer this question: n(n+1)/2. It's simple and elegant to get an answer for enormous numbers. If one had not the availability of this equation, one would have to sit and wiat as a computer slogs through all of the sums to give you a result. Put to the task, it'd likely store answers up to X in a ROM chip to save time. (something similar happens in fact when we want to know prime numbers - but they're easy to compute) Broadly the summing up of the whole process above is what math is to me. Any problem, pick one! It resembles the one above. We need to do something, but our answer is poor and slow. Math comes to the rescue and gives us a relatively sleek formula and suddenly we're applauding and jumping up and down like kids wiht big smiles on our face! The ultimate goal is a sleek simple formula which stands as a testament to the power of math! Like a Marilyn Monroe of the beauty queens

but without solving calculus equations, i can predict the future that i'm going to blow up the calculus exam tomorrow

Still can't get how exactly calculus is used in these predictons

Im still in doubt,coz i have just started differentation and doing a lot of y= and dy/dx and i dont get the use of it

this needs an update from Jeff Heys to see where we are 11 years later.

I recently completed a math degree... don't ever do a math degree.

That's some creative (vertiginous) cinematography there, buddy.

I'm about to to take Calculus of Business and Social science for my major in Accounting. This is actually my first time taking calculus ever and I'm a little worried because I have no idea how its going to go or what I'm going to expect. Do you guys have any tips? I would really appreciate that.

Those that conquer calculus and chemistry truly rule the world

Algebra is used for solving problems that have very well defined behavior. Calculus not only solves problems involving change and motion in time, but is also great a deriving general solutions to broad classes of problems. With calculus we can derive the specific equations needed to launch a space shuttle from Earth to achieve a specified orbit. We can also re-solve for different payloads, orbits, launch sites and even launching from other planets!

Mesmerizing.

There's so many variables to so many different problems. Finding such a model would take decades.

Truly inspiring

so what was calculus use for? is there a part 2 to this video with an answer?

Does anyone else start off with the Real life application word problems after studying the concepts instead of jumping straight into problems? i usually do this and THEN attempt the problem set because i think that if you have working real life model then its easier to tell yourself that the concept isnt too abstract anymore. Not too mention that the word problem I did sometimes involves applying more than one concept which actually helps me on the harder problems later on in the problem set.

am still waiting for the example!! he is just giving that it could be used again and again, just show an example, at least I really wanted to know how to calculated the smoke coming out of that room -.-

i will learn calculus right now!

Caculus is a walk on Cake, if you know what is meant by a function, and what is meant by continuity - not in mathematics but in Real life, every where around us. The problem is that Human brain can only speculate Discretely, at some intervals, while the Nature never provides such facility for us. Dealing continuity in terms of Discrete human thought, assuming the interval between discrete knowledge of something to infinitely small, makes it continuous. That's calculus

I watch this video 2023 I asm so excited this lacture I love math specially apply mathmatics model in different disciplines and really life I graduated economics right now I started jonney to ehenced mathmatics skills for applying economics and other disciplines

Does calculus help to show how a community can grow and how fast it can grow

Calculus is difficult, yes, but it's definitely a branch of mathematics one needs to learn. For example, if your function models the rate of flow of water (in gal/hr) between 12 pm to 8 pm, you can find the total amount of gallons within that time frame by finding the area under the curve. Why? Because of the relationship between derivatives and integrals, the Fundamental Theorem of Calculus.

Ngl I passed math and I’ve forgot nearly everything I learnt in my final year of school

Wow! I'm just as disinterested in continuing to Calc. after Trig. as I was before I watched this video.

I always asked that question, but never got a good answer.

This is why I learn calculus even though I don't take it in curricular

Excellent!

Neither do I. But for me non-mathematician, personally, the fact that you can do SO MUCH with efficiency in Calculus -- be it calculating the likelihood of a launched banana hitting you on the head OR creating flying-robots that can carry your glass of water OR curing cancer -- makes me all the more excited to learn it! :D

what jobs of any kind require the use of calculus, diff equations .. etc?

Essentially Calculus teaches us how irregular shape relate to each other. There is a specific section called related rates. How fast will the ladder drop to the ground after I kicked it?

How do we model something without sample data from experiments for comparison? If the experiments are unethical and expensive, then how do we even start?

Calculus is used for considering the rate of change of any variable of any functions, classically, and usually, time is continuous in many, many models, ranging from models in biology and chemistry to economics and communications. Calculus wouldn't really be effective at "predicting the future", it is only effect if the scenario is limited, severely. If you're interested in "predicting the future", you would be looking at probability, statistics and chaotic theory instead. Although it would remain the case that integral calculus is useful in considering the probability of probability functions given a section of the probability functions.

I'd imagine we'd need to compare the results of our models to the actual data taken from the experiments which are impossible (too expensive or unethical) to conduct.

I listen to this when I need to sleep.

that was awesome

Sounds like computer modeling is the real important part.

I feel like there are more than just the two options he gives in both examples.

math and life never identical, but they were together ever since

Interesting and never occurred to me because we barely understand the basics on a molecular level and these models would all have to be molecular level because you can't assume anything in the body, you can only make shortcuts if you know the underlying laws. Calculus can be summed up in derivatives and the chain rule, don't need a 1 year university course for that. The name of the game for models, which are used everywhere, from games to engineering to prediction to AI, is 'linear approximations' which is replacing a short curve by a line, and for that you need to calculate with derivatives, chain rule, matrices, and probabilities.

Montana state university? I'm from Montana! :D

predicting the weather over the course of years is impossible

guys, the same mathematical models are also what drives the entire social media world. calculus has it's own consequences. it is upto us how we want to deal with them.

math guys are always positing their usefulness in society

What is Calculus Used For? Sleeping.

When he speaks about the smoking room, i gave a small laugh to myself then said to myself, why da fuk would'nt you just take the table farthest away....

Can you predict the winning combination of lottery through calculus?