What is Calculus Used For? | Jeff Heys | TEDxBozeman
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- čas přidán 19. 04. 2012
- This talk describes the motivation for developing mathematical models, including models that are developed to avoid ethically difficult experiments. Three different examples from the field of human health are presented.
Jeffrey J. Heys is an assistant professor of chemical engineering at Montana State University. He received his B.S. in chemical engineering in 1996 from Montana State University, and his M.S. and Ph.D. from the University of Colorado at Boulder in 1998 and 2001,respectively. His research area is computational transport and computational fluid dynamics in biological systems with an emphasis on fluid-structure interaction and multiphase flows.
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Even if you never need Calculus, the Mathematical Competency, Logic, and Problem Solving Skills gained by it's study are indispensable.
So true!!
True❤
what if my future is in writing knitting patterns? Is Calculus going to help me make a 3d model of a human bodice and help me find the proper compression of a stitch for the garment that will be worn by a post-surgical woman who is pregnant?
Or do I just take business math?
Yes, the 7% of students that (put in the work to) gain these skills enjoy them.
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.
No real world application for algebra? Do you know about compound interest? Can you figure out Celsius from fahreheit without a c
Alfred Collins key words are “not much” 😂 Also, kinda insignificant compared to the amount calculus has done for the modern world.
Math is used for everything no matter what it is
Algebra is used in finding equations in Calculus.
You can't have calculus without algebra, and you contradicted yourself with the last sentence about that.
I’ve been waiting 35 years for this explanation. Thank you !
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.
Mathematics is a practical guided tool for practical thinkers following scriptures
@@bilkangbol333 Is mathematics scripture? Is it delivered unto man by God? Great question! It is a language, a tool, a system of thinking and modeling, an abstract construct, perhaps the greatest invention of the human mind AND/OR our greatest discovery. Is it divinely inspired and revealed? Hmm…
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.
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.
Me too man. That's not our fault. That's our education system that failed us. They made us number ninjas but left out the important application and why we do it part
@@Jay-fv1hc is not the education fault, if you want to apply the knowledge look for your self.
@@robertokalinovskyy7347 why should i, a non-expert, look for stuff by myself when i paid the university, professionals who know a lot, to teach me?
"what is calculus used for?" where do I begin......
If you're really interested, you can use some reference books(just Google reference books) or you can see various lectures online on CZcams and various other sources
Anwesh Mohapatra I think he was making the point that it has almost an unlimited number of applications
Monty maybe, I'm not sure either way.
deathwilldie much like the limit of x^2/x as x approaches infinity, the limit does not exist
***** How? As x gets larger or smaller, x^2/x also gets larger or smaller respectively, and does not approach 0.
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.
Same
better question, what is calculus not used for?
Human Love
Jesus Gil Might or might not be the case. The biochemical processes that describe the feeling of 'love', the emotional state of 'being in love' might or might not be modelled using calculus.
+Aashish Bharat i mean some people might find calculus or someone doing calculus arousing.....
+Jesus Gil Baby false
If you were a function and I were a derivative, I'll be tangent to your curves
The limit for my love for you is like the limit of 1/x as x approaches 0, it doesn't have a limit
+Marcus Fenix I was going to ask the same question.
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 use Calculus to find areas of stuff. I use hyperbolic functions to find out how long rope i need to install to the balcony to hang wet clothes without touching the ground.
Advanced mathematics possess the key to illumination, and becoming god.
Science can only prove material truths. This existence cannot be explained with science (at least not completely)
R=>0 is the formula for existence. All monads can be represented by a number between 0 and infinity. 0 represents a mathematical point, and contains all numbers (see the limit of 0)
0 represents photons, ideas, the astral realm of thought, the spirit, and the soul..... god.
I can say that 0 represent pankdonka... the sentence doesn't mean shit!
H3000 These ideas soar right above the heads of low iq materialist empiricists.
You simply do not have the brain power required to dissect the formula's that create reality.
That's ok, go play some video games, maybe in your next carnation you will be brilliant.
H3000 Scientists are materialists. You know nothing of philosophy. I was referring to your IQ. Mine is 160, what's yours?
if you're an engineer or studying engineering and you still don't find calculus useful, find another thing to do in your life.
George Farah
I still don't get why it's useful. I'm doing a businesd degree, and feel like if I understood why it was important I would learn it better. (im an emotional meaningful existential type of learner lol)
I study business as well, and calculus is extremely important in this field (unless you're mainly studying marketing/management etc.)
At least in finance and economics we use calculus a lot. It's extremely useful in optimization, equilibrium analysis, profit maximization problems etc. I find myself using it every day
I studied 5 semister of maths in engineering which was mostly calculus. I still don't know how to apply it in practice. I don't feel like I'm missing something.
Damn i'm an engineer and i dont know the real applications of calculus..do i really need to change my major? Lol..please, instead of telling other people what should they do, just give your ideas if u know any..i mean the real applications
Maybe instead of giving up people could study the subjects of engineering more deeply and finding out why it’s useful. Engineers are curious, if they are not curious then they should find something else to do.
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. 😢😢
"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
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.
If anyone else is also forced to watch this for an assignment, just know that you're not alone and I feel your pain.
My own free will brought me here
because I thought you were going to show some real useful examples of its everyday use but all you do is state obvious facts
If by "obvious facts" you mean "perfectly applicable uses for Calculus", then YES. These are "obvious" (not really) "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.
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)
Well, those niche applications are the ones behind our modern day-to-day life.
We got better car engines because of it, more efficient fuel combustion, etc.
So, you can just oversimplify the answer it with: to design airplane, design cars, etc
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.
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.
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.
Did that research begin with a hotdog in a microwave?
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.
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
probably he wasn't satisfied with the typical text book examples of bacterium growth and carbon dating
probably he wasn't satisfied with the typical text book examples of bacterium growth and carbon dating
Hussam Ali What about all of the applications of calculus in his engineering courses? You know: dynamics, thermo, circuits...
+Tom Mattson So far, I've only been exposed to algebra in physics and electronics. I've done some very complex stuff without a single derivative or integral. It really speaks to how broken the math departments are when a student can sit in a classroom for years and leave with nothing.
+Tom Mattson Differential equations. Absolutely essential for many problems in physics. Quantum mechanics uses differential equations (mainly the Schrodinger Equation). Capacitor discharge equations are solutions of differential equations, same with nuclear decay.
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.
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.
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.
More power to you. Going into engineering?
+Renegade For Life yep! Going into computer engineering. And, by the way, I'm absolutely loving my AP Calc and AP CompSci classes this year. I can't wait to be doing these things full time. :)
Have you started computer engineering yet? I plan to start computer and electrical engineering in one year.
SogMosee I start University in the fall! I'm going for a dual degree in mathematics and computer engineering. I signed up for my classes Wednesday. I'm super excited.
That is awesome man! So sort of programming do you do now?
HERE IN MY GARAGE< JUST BOUGHT THIS NEW LAMBORGHINI
Can I please watch something on youtube without all these ads?
Funny you brought that up, but that happened to be the one ad I decided to watch in over a year.
+Renegade For Life same
Renegade For Life well if it's motivating
Adblock
That guy is most likely a con artist so don't fall for his false promises of grandeur.
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?
+George Rosebush Well, mechanics would be a practical example of calculus usage. If you want to model anything, really, you'll need to evaluate the three quantities that are acceleration, velocity and position. You need calculus for that. In particular, all robots and engineered system use such calculations. Sometimes a computer is used to simulate something and for that to be possible, you'll need to give it an algorithm, based on some formulae that were derived using calculus to get your result. Sometimes, at the beginning of the project, you make the calculation by hand and then see if it's actually something doable. Even if you're not building anything concrete like a robot or a wheel or something, you may find yourself fidling with an equation and have to evaluate an integral or a derivative or something. Then, calculus knowledge becomes useful because you'll get the profound result without being stuck by some petty integral. (Cases where you can't evaluate also exist, that's why simulations exist after all.)
All of that seems pretty concrete and unacademic to me. ;)
+George Rosebush the speaker was mainly encouraging people who might end up having potential to do quality research and breakthroughs
Have you taken differential equations yet?
@@alalize yeah, let me do some calculus to replace a radiator or rebuild a transmission......
@@Sebastian_Hahn Yeah and good luck building that bridge without it.
but without solving calculus equations, i can predict the future that i'm going to blow up the calculus exam tomorrow
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.
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.
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.
+Brian Coyle Can it explain building 7? lol
Can it explain how the planes didn't crumble on impact?
Basically calculus seem to say us how change in input becomes the reason and validates the results of outcomes.
+Brian Coyle. Is all that stuff you said at the bottom not derived from calculus or at least makes use of some of it?
What sort of life did you live to get to this point Brian... to be able to write so eloquently and explain complex topics in that way... incredible...
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
Erik Anderson A partial vacuum would be near impossible to create in a restaurant, the windows would have to be airtight and the doors would not open due to the pressure differential, and if the doors opened, the vacuum would be terminated.
Wouldn't a simple exhaust fan be a better solution? Along with an intake duct also from outside?
Could you explain more about the equations used to perform these experiments?
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.
Yes. I recently finished differetial equations and linear algebra. All of the previous couple years of math sorta fell into place during that semester.
Yea, so far I'll be taking intro to Linear Algebra and Diff. Eqns. From the looks of it, it seems more abstract, and in one of the videos, whose topic was vector space, left me mind blown. When I hear the term Vector, I see arrows, but it turns it is defined differently in linear algebra.
Fernando Gallardo
Is that a combined Diff Eq and Linear algebra semester? I know some schools do that. I had a semester of each separately. Personally i think both of the courses are easier to understand at first than Calc 1,2,3. Linear Algebra is pretty cool. It will be a challenge to "see" the arrows in n-dimensional space where n>3. lol Have fun.
yes, it is a combined course, although I've been researching what math is transferable in specific U.C.'s, and they only accept Linear Algebra, or the Differential Equation, but not both.
ah, yeah the requirements for the mechanical engineering program at my place, University of Michigan, are Calc 1,2,3 - Linear Algebra, and Diff Eq. All separate, 5 semesters.
without calculus, we wouldn't have gone to the moon !!
Have we?
You and I --we haven't..... but the astronauts have!
Oh yea, right!
no single astronaut has ever landed on moon!
@@ASWAJA2023 You're right, it was the rocket
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.
+Kason Durham Biology as applied mathematics? Not sure I agree. Economics or physics though are both essentially applied mathematics.
+blownspeakersss biology is absolutely applied mathematics; just on a broader scale. You don't use equations as often but thats not where the thinking is being done anyways is it? genetic engineering, mutations, complex systems they are formalized and analyzed through the basic principles of mathematics
Kason Durham To me, what you're referring to is bioengineering -- which is not the same as biology. I would imagine one could become an evolutionary biologist, or a zoologist, for example, without learning much calculus or advanced mathematics. But yes, genetics, biomedical engineering, bioengineering, etc. all rely heavily on mathematics.
+blownspeakersss thats a fair point, my rebuttal would go along the lines of those fields being the product of simple math (mathematics nonetheless) but that would be off topic considering this is a calculus video
+Kason Durham Physics is not "applied maths". Physics uses maths as a language to describe the universe. There's more to physics than equations and abstract maths.
this needs an update from Jeff Heys to see where we are 11 years later.
I'm so excited to start calculus next semester
@@parthbhatt8762 yea I went up to calc two which was how much I needed for my chem major
I love calculus and maths not just cause it is useful but cause it is beautiful.
Well done, sir. There are thousands of uses, Science and engineering would b e set back immeasurably without it. Love you
Those that conquer calculus and chemistry truly rule the world
That's a little too far don't you think ?
So far in calculus 1 I've learned more about algebra than I ever did as well.
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...
Great information for students in secondary schools and college.
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.
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
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.
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
this is best and correct answer imo. i think as educators we need to collaborate with other departments and teach calculus that is relevant to the institution and national goals (where there is no NASA). but about NASA i infact have all counttries should have some sought of NASA type institutions to help develop other industries. developing countries import techologies where calculus is used to engineer those products. So we cant say calculus doesnt apply in third world countries, we are not applying it and are buying foreign objects which were made using it. To compliment you nice answer I will point out calculus is really a set of algorithms ( mathametical modeling is really a form of programming). Models are ubiquious imo. I am from CS and I am interested in math modeling and what I found out is that calculus enable to write all functions. derivative is like recursion and integrations is like iteration. programming is about writing functions and similarly calculus is way of writing any functions. differential calculus is like functional programming imo while integration calculus is like procedural programming(iterative). Most of calculus is interested in finding analytic solutions, programming does not care about analytical solutions(only numerical ones). bottom line calculus is a form of computation, albeit an old one. It is my strong believe math dept should introduce other paradigms like programming together with traditional math.
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.
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
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.
I recently completed a math degree... don't ever do a math degree.
+Joe McDicksmack does your diploma say Joe McDicksmack?
But why?
+John Gray Why not?
Probably because there's not a lot you can do with just a pure math degree. Math is essential to things like engineering, the physical sciences, programming etc. but by itself, the only thing you can really do is teach.
+jtlbb2 He never specified witch area of mathematics. If it is a degree in applied mathematics, he could for example become an economist, or something else dealing with calculations. But if he has a degree in pure mathematics, it may be necessary to get a Ph.D and work with research in academia. I still think it's harsh to advice random people to never get a maths degree.
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.
Thank you. Now it's more complicated
Great explanation!
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.
Still can't get how exactly calculus is used in these predictons
Mesmerizing.
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.
yes engineering schools and math dept do a bad job at this. they will spend so much time on something and then ditch it along the way. which shows the deptments heads did not plan the cillabus properly this is why you were left hanging. But if we see you down on your course we could derive all of the principles in it(your course) using calculus(that is from first principles of physics which are a set of differential equations). but the connections is usually skirmed or left for you to read on your own which thanks to your calculus you should be a ble to to do on your own.
That's some creative (vertiginous) cinematography there, buddy.
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!
Truly inspiring
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
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
Nice explanation
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
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.
i will learn calculus right now!
Martin Ibarra oh its to hard, maybe tomorrow
+Martin Ibarra how's your PhD coming...?
+Martin Ibarra lol calcs not that hard. takes some time to get around why you do all the differentiation/integration but after that its just how can you use this knowledge?
YESTERDAY YOU SAID TOMORROW. JUST DO IT! DON'T LET YOUR DREAMS BE DREAMS.
Get to Stokes' Theorem yet?
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.
Did you ever wind up taking calculus?
This is why I learn calculus even though I don't take it in curricular
There's so many variables to so many different problems. Finding such a model would take decades.
You're right, but in the large scale a lot of variables become insignificant so you can simply ignore them. If you are making large scale predictions, you can solve a lot of modeling equations to give you pretty accurate results. This is why scientists can predict how the climate of Earth will change in 100 years, yet your local weatherman can't tell you if it will rain or not next week.
BYSMA4th great point!
math guys are always positing their usefulness in society
what jobs of any kind require the use of calculus, diff equations .. etc?
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
Sounds like computer modeling is the real important part.
+Bloodmoon And what's that based on according to you ?
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?
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.
Excellent!
By watching this it seems calculus is an ethical answer to unethical questions. A safer way to conduct experiments.
Does calculus help to show how a community can grow and how fast it can grow
Teaching it is fun. Most of the trouble that student's have with Calculus is the algebra involved. I always tell students you learn algebra by doing Calculus.
That's why the engineers relays the mathematical calculations and modeling because save experiments costs, time and also save life.
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.
Awesome talk!
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....
so what was calculus use for? is there a part 2 to this video with an answer?
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?
math and life never identical, but they were together ever since
everyone needs calculus. even if you're not an engr. it's our armor against idiocy :)
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 -.-
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 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
that was awesome
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.
I always asked that question, but never got a good answer.
What is Calculus Used For?
Sleeping.
😆😆😆
hmm if i could find out an equation to represent the side of my vase i could find out exactly how much dirt i need to fill up the bottom 4 inches without wasting any if of course i have a measurement tool exact enough to measure that dirt, or i could just wing it
Most of the time, companies need just 1 mathematician and all the other people can do nothing with the math they learned.
One engineer who developes something, and that's it. So, math is needed, but only a few people can do something with it in life. The construct I-phones, smartphones and all these things, you just need a few people. Most people cannot do anything with the math they learned.