@@theracistcookie9253 Yes, it is a whole course on just that, and it focuses on problem formulation, software technologies and analytical methods for optimization serving, which sounds really interesting, for sure!
@@theracistcookie9253 Yes, it is its own separate course which focuses on problem formulation, software technologies and analytical methods for optimization serving as an introduction to a wide variety of optimization problems and techniques, which sounds really interesting!
I love when smarts topics are explaining in smart videos using smart example, like a game. This is genius, my professors need to see that like of video.
I started learning calculus few weeks ago and I managed to do it myself after 1 or 2h of correcting wierd mistakes. Very fun puzzle I would say. Thank you for the video
Very small correction at 4:50, local/absolute minimums and maximums need not *only* occur when the derivative is equal to zero. Take f(x) = | x |, whose derivative is never zero for all inputs x. Great video regardless! Love the applications and problem solving break downs! Keep up the great work!
@padfoot9445 Unfortunately, it's not enough to only have a continuous function, since your derivative isn't necessarily continuous. Cusps and vertical tangents can cause a derivative to be discontinuous. Including undefined values of dy/dx COULD work, however you should also check to see if the original function is defined at that point, like the function f(x) = 1/x, where it's value and derivative are both undefined at x = 0. If you find your function is continuous on your interval (which in most first year calculus courses, they will be), then it's perfectly reasonable to include undefined points of your derivative as critical points, since mostly like they are either cusps or vertical tangent lines, and are still defined at said point.
Ah of course I forgot about that, thank you so much for the correction! Since I took the earlier calculus courses, there was only really a need to check for when the derivative equals 0, so that part didn't cross my mind, thank you so much though!
Max min of a continuous function on a compact def set is found either in points where the derivative is zero, edge points or where derivative doesnt exist.
I love math, but being unmedicated ADHD, it makes it very hard to focus in class and my teacher's methods don't resonate with me. that's why I love this video. thanks, I have always been wondering (as I play a lot of Roblox) how to find the optimal routes for certain games and whatnot. you earned my subscribe! :)
Thank you so much! I also have had a lot of times where the teacher's efforts didn't work all that well for me, and I found that imagining the concepts in a different way helped get the topics through into my head, and that's what I'm trying to replicate here haha thank you though!
Holy shit the youtube algorithm is showing me this video right as im learning this topic! I solved a problem thats essentially this same problem, just that it was about the cost of laying pipes along a river with underwater pipes being more expensive.
This time, I started watching but stopped because I want to try to solve it first myself tomorrow before I finish the video. I’m sure it will be spectacular…
i love this problem but unfortunately it is flawed. in the video 4.07 seconds is his answer and its good mathematically. However if you stay off the soulsand, you travel 19 meters total at 5m/s which come out to a time of 3.8 seconds. so there is no point in crossing the soulsand in this problem at all.
That’s definitely my bad, the problem was meant to have the soul sand much further out on both sides so going purely on the grass wasn’t an option, this question is running off the assumption that the soul sand is unavoidable.
I just discovered your channel and this is amazing! I've been studying calculus and physics and your videos are a great recap. So underrated this stuff but keep it up. I think you will soon get more viewers :D
Vídeo maravilhoso. Faça algo relacionado a maximização de produção (como função de produção, da microeconomia) se for possível, por favor. Seria muito legal ver uma maximização de produção de uma farm. Abraços do Brasil
I have another problem which came out from my game. We have two variables Multiplier & MT value. Multiplier by default equals to 1 & MT = 0 We have a value which we want to optimize named "Action" which I'll refer as A now. If we increase Multiplier by 1 we add 1 to A or we increase MT value by Multiplier. The question is what is the least action required to get MT from 0 to some value x ? Here's solution: Setting up the equation: I started by setting up what's action equal to? Action for the multiplier is equal but we assume that multiplier equals by default 1 so... A(m) = M - 1 However we have also action for increasing MF value which I'm gonna call f from now. I tested how M relates to wanted number (I tested for 15) So f = 0 by default & we want to get to the value 15 which is x After testing we can see that A(f) = x/M because A decreases as M gets bigger. So A = A(f) + A(m) Now we take the derivative of the function & solve for 0 & we find out that x = M^2 which means the minimum Action for M equals to √15 in that case. To calculate A(f) we just do A(f) = M-1 + x/M - √x which equals A(f) = √x - 1 since M cancelles out because it's equal to √x A = 2√x -1 which the lowest amount of action you can take to reach destinated value x (Note: all equations works only when M = 1 & starting value of f = 0 unless you want to find the solution for different values use this equation: A = M - M(s) + (x - x(0))/M )
and funny that light actually follows the optimization in order to save as much time as possible, bending when going through different mediums, so it has to spend as little time on travelling as possible, but then there's some quantum physics stuff
No need! I think you are talking about taking the derivative at a point using the limit definition in which case you do, but we’re taking the derivative of a function which means we don’t have to
Would it not be easiest to just normalise distance so grass disrance is 15 m And distance in soul sand is 15 m after mutliplyigj how mcuh longer you take to wlak so this much if soul sand is equal to that mvuh of grass distance meanign tine out of equations unles its realy necessary. Just guess and no thinking into it so feel free to roast me Edit: Got it! I aim to implement the A* algorithm in such a way that when transitioning from grass (cost multiplier 1) to soul sand (cost multiplier 10), the algorithm dynamically adjusts the heuristic to account for the reduced traversal efficiency. Specifically, distances between nodes on soul sand are scaled by how much slower you walked. This scaling inflates the distance between nodes making the distance bigger on soul sand Then a* algorithm will find shortest path as it doesn't care how the nodes are placed as long as the heuretics are given Edits: Just get total distance and do binary search For value of x between 0 and 15 and I believe y of 7 you get distance in 2d And distance/(speed / speed multiplier of material) for first and second node of path Goal is the point on 0 , 7 and you're at 15, 0 And x represents x position and you can do binary search by getting total distance of grass distance and soul sand distance and multiply our speed on that materials You can do binary search algorithm that will find always the best path regardless where goal is We just do heuristic if the point is closer by getting last best distance and x value for it and swapping for new if it is smaller time to travel
That’s actually what I thought too 😭 I originally wrote the script doing it that way but then you end up having to square the (15-x) term and then it just takes super messy, but it definitely is possible!
@gragbuilds like I asked chat gpt but it requires space bending to work so basically you must make it on paper and fold the paper to be as long so the time spend walking it would be same as on grass for same horizontal distance
@gragbuilds Got it! I aim to implement the A* algorithm in such a way that when transitioning from grass (cost multiplier 1) to soul sand (cost multiplier 10), the algorithm dynamically adjusts the heuristic to account for the reduced traversal efficiency. Specifically, distances between nodes on soul sand are scaled by how much slower you walked. This scaling inflates the distance between nodes making the distance bigger on soul sand Then a* algorithm will find shortest path as it doesn't care how the nodes are placed as long as the heuretics are given
Speaking of which, I'll start taking a course specifically on optimization theory in just 10 days, so wish me luck!
oh yeah best of luck with that!! thank you for all your comments haha but definitely good luck
@@gragbuilds Thanks so much!!! And you're welcome! I'm always willing to provide feedback whenever necessary!
Woah like a whole course on just optimization? Not just part of a calc course?
@@theracistcookie9253 Yes, it is a whole course on just that, and it focuses on problem formulation, software technologies and analytical methods for optimization serving, which sounds really interesting, for sure!
@@theracistcookie9253 Yes, it is its own separate course which focuses on problem formulation, software technologies and analytical methods for optimization serving as an introduction to a wide variety of optimization problems and techniques, which sounds really interesting!
I love when smarts topics are explaining in smart videos using smart example, like a game. This is genius, my professors need to see that like of video.
Thank you! I'll continue making these better and better
Fucking A! Great idea, presenting problems in this fun and practical way is much more engaging that the current meta
Thank you so much!! It’s definitely a lot more fun to make too haha
I started learning calculus few weeks ago and I managed to do it myself after 1 or 2h of correcting wierd mistakes. Very fun puzzle I would say. Thank you for the video
Very small correction at 4:50, local/absolute minimums and maximums need not *only* occur when the derivative is equal to zero. Take f(x) = | x |, whose derivative is never zero for all inputs x. Great video regardless! Love the applications and problem solving break downs! Keep up the great work!
would restricting it to continous functions/expanding the requirement of d/dx = 0 to also include d/dx is undefined work?
@padfoot9445 Unfortunately, it's not enough to only have a continuous function, since your derivative isn't necessarily continuous. Cusps and vertical tangents can cause a derivative to be discontinuous.
Including undefined values of dy/dx COULD work, however you should also check to see if the original function is defined at that point, like the function f(x) = 1/x, where it's value and derivative are both undefined at x = 0.
If you find your function is continuous on your interval (which in most first year calculus courses, they will be), then it's perfectly reasonable to include undefined points of your derivative as critical points, since mostly like they are either cusps or vertical tangent lines, and are still defined at said point.
Ah of course I forgot about that, thank you so much for the correction! Since I took the earlier calculus courses, there was only really a need to check for when the derivative equals 0, so that part didn't cross my mind, thank you so much though!
Max min of a continuous function on a compact def set is found either in points where the derivative is zero, edge points or where derivative doesnt exist.
man that's an AMAZING content idea!! I hope your channel grows bigger and bigger everyday
Im awful at problem solving in calculus this actually helped a lot! Thanks dude :)
I love math, but being unmedicated ADHD, it makes it very hard to focus in class and my teacher's methods don't resonate with me.
that's why I love this video. thanks, I have always been wondering (as I play a lot of Roblox) how to find the optimal routes for certain games and whatnot.
you earned my subscribe! :)
Thank you so much! I also have had a lot of times where the teacher's efforts didn't work all that well for me, and I found that imagining the concepts in a different way helped get the topics through into my head, and that's what I'm trying to replicate here haha thank you though!
Great video, I don't usually comment, but you deserve it for the algorithm, congrats, and thank you for this wholesome explanation!
Thank you so much man, hopefully al lthe explanations helped!!
This is really an underrated TH-cam channel. Wish you all the best in your TH-cam career!
Thank you man! I'm always going to keep pushing!!
i have been waiting your videos for past month. and i am surprised that you only have 970 subs
wow really?? thank you so much for watching all these videos haha, im sure with a lot of work i'll grow!!
You can also see at 6:07 that solution for x is dependent on the ratio of the velocities
Holy shit the youtube algorithm is showing me this video right as im learning this topic! I solved a problem thats essentially this same problem, just that it was about the cost of laying pipes along a river with underwater pipes being more expensive.
Yeah!! This problem or at least the theme of it is quite common haha
Can you do work and hookes law for calculus next? I love how simple you make these concepts sound. Super easy to digest.
Of course! I’m planning to do a shorter video about tangent lines but afterward I’ll definitely tackle work and hookes law :)
This time, I started watching but stopped because I want to try to solve it first myself tomorrow before I finish the video.
I’m sure it will be spectacular…
Here's a reminder to check & share your answers!
I immediately recognized snell's law
Great job! Hope your channel grows so you continue on making such vidoes.❤
thank you so much!! I'll continue to make these for you guys!!
i love this problem but unfortunately it is flawed. in the video 4.07 seconds is his answer and its good mathematically. However if you stay off the soulsand, you travel 19 meters total at 5m/s which come out to a time of 3.8 seconds. so there is no point in crossing the soulsand in this problem at all.
That’s definitely my bad, the problem was meant to have the soul sand much further out on both sides so going purely on the grass wasn’t an option, this question is running off the assumption that the soul sand is unavoidable.
Laying the foundation for Fermat's principle.
Thank you
This video is phenomenal!
Answer: just run+jump in a straight line to the finish and place blocks under you to prevent stepping in soul sand
I just discovered your channel and this is amazing! I've been studying calculus and physics and your videos are a great recap. So underrated this stuff but keep it up. I think you will soon get more viewers :D
Thank you so much!! I’m so glad you got a lot of help from these, you got this!!!
Awesome video man thanks alot!!!
ah the first qs reminded me of snells law in kinematics , tho finding the angles can be a bit weird in Minecraft
Vídeo maravilhoso. Faça algo relacionado a maximização de produção (como função de produção, da microeconomia) se for possível, por favor. Seria muito legal ver uma maximização de produção de uma farm. Abraços do Brasil
I have another problem which came out from my game.
We have two variables Multiplier & MT value.
Multiplier by default equals to 1 & MT = 0
We have a value which we want to optimize named "Action" which I'll refer as A now.
If we increase Multiplier by 1 we add 1 to A or we increase MT value by Multiplier.
The question is what is the least action required to get MT from 0 to some value x ?
Here's solution:
Setting up the equation:
I started by setting up what's action equal to?
Action for the multiplier is equal but we assume that multiplier equals by default 1 so...
A(m) = M - 1
However we have also action for increasing MF value which I'm gonna call f from now.
I tested how M relates to wanted number (I tested for 15)
So f = 0 by default & we want to get to the value 15 which is x
After testing we can see that A(f) = x/M because A decreases as M gets bigger.
So A = A(f) + A(m)
Now we take the derivative of the function & solve for 0 & we find out that x = M^2 which means the minimum Action for M equals to √15 in that case.
To calculate A(f) we just do A(f) = M-1 + x/M - √x which equals A(f) = √x - 1 since M cancelles out because it's equal to √x
A = 2√x -1 which the lowest amount of action you can take to reach destinated value x
(Note: all equations works only when M = 1 & starting value of f = 0 unless you want to find the solution for different values use this equation:
A = M - M(s) + (x - x(0))/M )
Gotta show my calc teacher this so he can teach next year bc calc with minecraft
is that zero from the hit game katana zero 😱
Great video! Peace out
great vid
and funny that light actually follows the optimization in order to save as much time as possible, bending when going through different mediums, so it has to spend as little time on travelling as possible, but then there's some quantum physics stuff
I did hear about that! It's super cool, and by adding an infinite number of mediums you get some sort of most optimal curve in gravity right? I forget
@@gragbuilds yeah, it created a cycloid which is pretty much the perfect slide
@@gragbuildsbrachistochrone
Great video idea, try making an Integration question
integration is the next video!
That’s actually lit
BRACHISTOCHROME
shouldn't we prove that the function is continuous before taking the derivative?
No need! I think you are talking about taking the derivative at a point using the limit definition in which case you do, but we’re taking the derivative of a function which means we don’t have to
@@gragbuilds hmm ok thank you !
In this example, the function is definitely continuous because it's composed of basic (continuous) functions, which implies its derivability
9:36 If you got all the way to there, you might as well just go around the soul sand
True I probably should have extended the soul sand 😭
@@gragbuilds also, if you just sprint jump, it would be way faster. I think it would be better if you used cobwebs there
@3141minecraft i think you are missing the point of the experiment
Im sorry but is that Zero skin from Katana Zero??!?
YES I love that game
@@gragbuilds Big W man, both of us still waiting for the DLC lmao.
I love this kinda Math
ooo notifications were turned off that's it!
i think you should jump probably
Would it not be easiest to just normalise distance so grass disrance is 15 m
And distance in soul sand is 15 m after mutliplyigj how mcuh longer you take to wlak so this much if soul sand is equal to that mvuh of grass distance meanign tine out of equations unles its realy necessary.
Just guess and no thinking into it so feel free to roast me
Edit: Got it! I aim to implement the A* algorithm in such a way that when transitioning from grass (cost multiplier 1) to soul sand (cost multiplier 10), the algorithm dynamically adjusts the heuristic to account for the reduced traversal efficiency. Specifically, distances between nodes on soul sand are scaled by how much slower you walked. This scaling inflates the distance between nodes making the distance bigger on soul sand
Then a* algorithm will find shortest path as it doesn't care how the nodes are placed as long as the heuretics are given
Edits:
Just get total distance and do binary search
For value of x between 0 and 15 and I believe y of 7 you get distance in 2d
And distance/(speed / speed multiplier of material) for first and second node of path
Goal is the point on 0 , 7 and you're at 15, 0
And x represents x position and you can do binary search by getting total distance of grass distance and soul sand distance and multiply our speed on that materials
You can do binary search algorithm that will find always the best path regardless where goal is
We just do heuristic if the point is closer by getting last best distance and x value for it and swapping for new if it is smaller time to travel
That’s actually what I thought too 😭 I originally wrote the script doing it that way but then you end up having to square the (15-x) term and then it just takes super messy, but it definitely is possible!
@gragbuilds like I asked chat gpt but it requires space bending to work so basically you must make it on paper and fold the paper to be as long so the time spend walking it would be same as on grass for same horizontal distance
@gragbuilds Got it! I aim to implement the A* algorithm in such a way that when transitioning from grass (cost multiplier 1) to soul sand (cost multiplier 10), the algorithm dynamically adjusts the heuristic to account for the reduced traversal efficiency. Specifically, distances between nodes on soul sand are scaled by how much slower you walked. This scaling inflates the distance between nodes making the distance bigger on soul sand
Then a* algorithm will find shortest path as it doesn't care how the nodes are placed as long as the heuretics are given