Derivatives: Real Life Applications (two exercises)
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- čas přidán 30. 06. 2024
- In this video we look at two real life problems as application of derivatives. These are just two of the many problems, which we will tackle in future videos.
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Timestamps:
00:00 Intro and theory
00:52 Exercise 1: Fencing
10:42 Exercise 2: Pendulum
22:18 Outro
If you have any questions, remarks, or suggestions for future topics, let me know in the comment section below :)
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I really like the way you explained the use of derivative in real life.
Thanks for your help!
I'm really glad you liked it, and learned something :D
Thanks!
Awesome 🔥
Thank you :D
I find it infinitely complicated to understand the common thread with which you start your hypothesis. Im now more confused by derivatives!
Ouch, that's not what I had in mind. If you have any specific question, I'll see if I can explain it differently. In general:
1. Try to identify what it is you try to maximize/minimize (e.g. a surface)
2. Find a function that represents this surface, and try to write it as a function of 1 variable (e.g. the surface as a function of one of its sides).
3. Derive this function, and put it equal to zero.
4. Solve this algebraic equation for that one variable.
Hi how are you sir :)
I love your videos a lot because you explain really well.
I have a little request, can you do a video like that about conic sections in the future please?
❤️🔥❤️🔥❤️🔥❤️🔥❤️🔥❤️🔥❤️🔥
Hi Abather, thanks for the kind words :) Yes, I could make one on conic sections. I will add it on the (ever increasing) list of topics :D
👉 Hello fine people, here's a more advanced real life application --> czcams.com/video/K7qNvxhcOPc/video.html
Hello, thanks for the awesome explanation, do you know where I can find more resources on math real world applications with good explanations like yours? I'm really trying but they're hard to find.
Thanks! :)
Well, I get some of my exercises from high school math textbooks. Although they are in Dutch, I'm sure you can find them in any language. It's harder to find step-by-step explanations, which I why I started this channel :)
@@PenandPaperScience oh, okay then thanks ✨, keep it up then please😊
✨Thank you, Sir, 🙏✨
You are very welcome :D
@@PenandPaperScience ✨🙏🏼✨
I have a question, how is the derivation of sin -> -cos? Shouldn’t it just be cos.
You are completely correct, of course! Thanks for pointing it out!
I haven't been taught this yet. But it seems interesting can u refer me a video to study this?
These are application problems of derivatives. The theory used is that of basic derivatives. You can also look for "Extremum problems" which are always solved using derivates in the same fashion we did here.
1. Find the function describing the problem you want to optimise.
2. Derive this function to the variable you want to find the extremum of (max of min)
3. Equate this derivative to zero and solve for the variable.
4. The obtained value for the variable is the value that maximises (or minimises) the problem.
I will make more videos on extremum problems in the near future :)
@@PenandPaperScience Actually I'm in 9th standard so calculus and derivatives I know nothing on. So will u make a video explaining it like from start and basic.
@@abhinavmishra4039 If you want a really detailed quick rundown on Calculus, I highly recommend watching 3Blue1Brown’s series on The Essence of Calculus. He has awesome explanations on the core concepts of Calculus, and has really nice diagrams and animations to go with it. You might have to find other sources if you want to dig into the crevices of Calculus.
@@ghostoftoyman7896 thanks I will check it out.
@@ghostoftoyman7896 Yeah, thanks Patrick! 3B1B's videos are amazing! His animations are top notch :)
Shouldn't l(t) = α*cos(sqrt(g/L)t)?
Any math or similar study should start with a application use related to the student, generating a "need" to spike the eager and ability to learn. sounds simple but not often seen. that was a fundemental key stone in the teaching education i reviced on sergent school, i always have implemented it, and also tryed my self how well it works. as a real example i had for my self. doing a very desired recon course provided by our nations special forces, we where out in the freezing winter for 3 days without food or sleep. at first daylight on 3 day (we walked all nigth to the location) we where taugth to manouver a rubber boat into water and if turned over how as a team to flip the boat back around, even thoe the scenario was looking at the facts maby worst possible setup for learning, i and my colleagues was able to focus and learn all the technices precise and fast, (while in the back ground the other SF guys was making a hole in the ice on the lake to launch the boats :D), and as expected both the launch and the flip around technicque became handy very shortly after :D
That was interesting to read, especially in the comment section of a video on derivative applications :)
@@PenandPaperScience well today i am a mechanical engineer, and doing abit brush up in my evening time i saw your video and could relate :D
@@Jauertussen1 Cool, that's nice to hear :))
Isn’t there a faster way for the second question?
Since we are modelling the pendulum as just a normal sine function (there’s no energy loss in this scenario)
well we know that the period (time for 1 oscillation ) is just 2 pi / b
Where b is the coefficient of t inside sin, eg sin(bt)
Since our model is a sin ( sqrt(g/L) * t )
Well our b is sqrt(g/L)
So period = 2pi/b = 2 pi * sqrt(L/g)
No calculus needed
HOWEVER,
It’s a good problem nonetheless as it teaches u to think through the problem which is useful for more general cases where u cannot model the pendulum with a simple sine function.
In real life, obviously as the pendulum swings, it loses energy and has a lesser displacement over time
Using calculus can help find the time for 1 oscillation within this more complex functions
One of them that I can think of my head is e^(-t) * sin(t)
That is a clever way to tackle problem 2 yes. I like how you can get there without any computations :D Well done!
Please create a discord server for more interaction!
I will do so as soon as I am back at home. I'm currently on holiday abroad with just enough internet to respond to comments ;) I will keep everyone up to date about the discord server :) Thanks again for the idea.
@@PenandPaperScience Alright! No problem at all. I am there to support you and your channel!
Hi there, just wanted to let you know that I've created a designated Discord Channel now for any questions and discussions :)
discord.gg/mrdvf6VK6k
@@PenandPaperScience Great! I will join it asap.