Here's an example of finding the curvature of y=x^2 at (1, 1) kzbin.info/www/bejne/hIbKeJWwf8iBY9U
@abacaabaca81313 ай бұрын
Hello Mr, do you have a video about Newton-Raphson method which is one of the ways to get the root of a complicated equation. The output does not have to be a number, but it can also be an expression. Because the other day I talk to AI how do I convert a single parameter function into a function that relies on two dependent variables. This is because I have a Bezier equation which is dependent on parameter t which can also be expressed as f(x,y). But to do this it says I need to use Newton-Raphson method which is also an iterative method and is one of the numerical method to find the root of an equation. I want to do this, because then I want to apply Green's theorem to find the area of a closed curvature. From there maybe I can find the volume by applying triple integral with parameter z. From volume, I can find mass, if I know the density. From, mass I can find force. From force, I can find Power and Work done and also momentum. If I know all that I can create a football game. Woo wee. Haha lol.
@tobybartels84263 ай бұрын
If you leave out the absolute value, the sign tells you which way it's curving, to the right or to the left (as the parameter increases).
@algorithminc.88503 ай бұрын
I think these are some of my favorite topics in calculus ... Thanks. Cheers
@guilhermerocha28323 ай бұрын
Amazing. Now do the 3d cruve version hahaha
@ianfowler93403 ай бұрын
Here's a fun problem I cooked up. Find the differential equation that must be satisfied to find the point on y = f(x) where the curvature is a maximum. It involves only y ' , y ' ' and y ' ' '. Next, use this DE to find the exact x-value where the curve f(x) = x^3 - 3x reaches maximum curvature. Very cool answer!
@fsisrael92243 ай бұрын
What field of math is that? Vector calculus?
@Gremriel3 ай бұрын
That's a lot of x's and y's.
@ianfowler93403 ай бұрын
Here is a way of developing this formula from scratch - 2D. No vector functions needed. Only basic calculus. 1) Sketch a general curve in the first Quadrant and label a point P(x,y) on that curve. 2) Sketch in a tangent line at P and sketch a horizontal line from P to the right. (// x-axis) 3) You now have defined an angle A between the tangent and the horizontal. 4) The Curvature at P can be defined the following way: Remember, we are trying to obtain a measure of how "bent" the curve is at P independent of it's orientation. As you move along the curve you want to measure how fast A changes per unit of ARC LENGTH. So k = dA/ds. You can use absolute value if you insist on a positive curvature. But negative curvature is O.K. - just indicates concave up or down. 5) Tools: k = dA/ds ds^2 = dx^2 + dy^2 ====> ds/dx = sqrt[ y ' )^2 + 1] y ' = tan(A) =====> sec^2(A) = ( y ' )^2 + 1 dA/dx = [dA/ds)] [ds/dx] y ' = tan(A) y ' ' = sec^2(A) * dA/dx y ' ' = [ (y ' )^2 + 1 ] * [ (dA/ds) * (ds/dx) ] Now solve for dA/ds using ds/dx = sqrt[ (y ' )^2 + 1] and you will get: k = [y '' ] / [ (y ' )^2 + 1] ^ (3/2)] Parametize: x. = dx/dt and y. = dy/dt giving: y ' = y. / x. (Newton's x_dot and y_dot) d( y ' )/dt = [ y..*x. - x..*y.] / [ (x.)^2 AND d(y ' )/dt = [d(y' )dx]*[dx/dt] = (y '')( *x.) Equating, substituting, re-arranging and a little work gives your formula. k = [x.y.. - y.x..] / [x.^2 + y.^2]^(3/2)
@bprpcalculusbasics3 ай бұрын
Thank you very much for this wonderful method! And I just recorded a video today too! Thanks. kzbin.info/www/bejne/oYq9dIdmjbSMq7s
@ianfowler93403 ай бұрын
@@bprpcalculusbasics You are very welcome. Thanks for the shout out. Very nice of you to do that in your new video! Cheers.
@jamescollier33 ай бұрын
That escalated quickly
@sebastiangudino93773 ай бұрын
Can we calculate the curvature to see just how quickly did it escalate?
@SterlingChaseStubblefield3 ай бұрын
Might be a case where the “dot” notation for derivative is a little cleaner. Love your videos!
@bprpcalculusbasics3 ай бұрын
Thanks!
@cdkw23 ай бұрын
That's a curved ball to my brain
@abacaabaca81313 ай бұрын
If its about geometry I am willing to listen.
@hassankhamis773 ай бұрын
I was searching for this ❤
@mugger85092 ай бұрын
Thank you so much! This is the only video I could find for this
@nathanoher48652 ай бұрын
Same! I always wondered but I feel like I have so many questions that have definitely been answered somewhere… but nowhere that I can access! Until now…
@Asiago93 ай бұрын
That's a nice new eraser
@urluberlu27573 ай бұрын
Thank you! 🤩👍
@bernarddoherty40143 ай бұрын
Holy cow! After “eating’ all of that ‘Math meal’ my mind feels like my belly would feel after eating 2 large pizza’s’ a bucket of KFC chicken and a liter of coke! I don’t have to ‘eat’ anymore math for 2 days,, 😂😂😂😂😩😩😩😳😳
@cdkw82543 ай бұрын
I remember some guy from your Instagram reel saying that if this is math where are the numbers?