hi, Dr Peyam i just passed all my calculus courses but i still have some problems with Parametric Equations in 3 dimentions. Can you make some videos about that?
Hay una parte en este video, que puede ser útil en Regresión Lineal...voy a investigarlo. Gracias, su video es inspirador de áreas de investigación en otras disciplinas.
Thanks for the videos you help me out a lot but can you please explain why t=1 at the end of the line in the second example because I thought that should be the distance of the line
this is legit awesome, but I have a question, can you parametrize a 3d function? for example if you had a sphere of radius 1 in the first octave of R3 (x^2+y^2+z^2=1) could you parametrize x, y and z to make them all a function of t? my guess is no but please surprise me
hey dr peyam to parmetrize the line can't we just find the actual equation of the line and then put x=t and y=f(t) like in the example where line goes from (1,2) to (3,4) the actual equation is y=x+1 so we can take the coordinates of any random pt. on the line as (t, t+1)
@@wyrmhero4275 Actually no, that would give the line through the points. Not the line segment between the points. The only way to express a line segment is with a vector and an initial point which leads to the parameterization of the line segment.
Counter clockwise and anti clockwise are the same, but I'm assuming you meant clockwise. We go CCW because that is the direction the function moves through. We follow dtheta around the unit circle, which is inherently CCW.
x = (1 - t^2) / (1 + t^2) y = (2t) / (1 + t^2) for t in the rationals. favorite circle parameterization! You've done the cycloid right? and a sphere? en.wikipedia.org/wiki/Cissoid_of_Diocles en.wikipedia.org/wiki/Tractrix Those are pretty fun. Thank you Dr. Peyam!
Dr Peyam you’d said at the start that there’s a link to a future video, but I think it could’ve been that that video maybe was already posted and I watched them in reverse. Nvm, mb
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Parametric equations are also useful when you want to turn an implicit curve into a function.
Not only in life, but also in mathematics 😂😂
The timing is pretty funny for me as I just started learning parametrization in bc calc last friday
Also, great video. I have not looked at parametrization for a long time, so this is nice!
Parametrise hyperbolas, ellipse and a flowers plzz!
Where is blackoenredpen
Dr. Peyman please make video in polish. i am your big fan !!
u r so happy and great thanks m8 big up to this one
Thank you !!
wow Thank you for this playlist!
Very helpful to me as I continue reviewing math topics for machine learning
hi, Dr Peyam i just passed all my calculus courses but i still have some problems with Parametric Equations in 3 dimentions. Can you make some videos about that?
Hay una parte en este video, que puede ser útil en Regresión Lineal...voy a investigarlo. Gracias, su video es inspirador de áreas de investigación en otras disciplinas.
De nada, fue mi placer
Always good to review the basics sometimes. Great video. Viele Grüße aus Deutschland!!
Danke :)
Thanks for the videos you help me out a lot but can you please explain why t=1 at the end of the line in the second example because I thought that should be the distance of the line
What if using u-substitution (u = t-1) for the parabola equation to get starting point to u=0? (Also might work for the line case)..
Exactly what I needed!
Nice Sir 👍
this is legit awesome, but I have a question, can you parametrize a 3d function? for example if you had a sphere of radius 1 in the first octave of R3 (x^2+y^2+z^2=1) could you parametrize x, y and z to make them all a function of t? my guess is no but please surprise me
Yep, but with 2 variables u and v; it’s called a parametric surface
mano desculpa o linguajar mas tu e muito foda
hey dr peyam
to parmetrize the line can't we just find the actual equation of the line and then put x=t and y=f(t)
like in the example where line goes from (1,2) to (3,4) the actual equation is y=x+1
so we can take the coordinates of any random pt. on the line as (t, t+1)
Yes, that would work
@@wyrmhero4275 Actually no, that would give the line through the points. Not the line segment between the points. The only way to express a line segment is with a vector and an initial point which leads to the parameterization of the line segment.
@@StreuB1 i further checked the answer in the video
the equations are x=2t+1
y=2t+2 which are of the form
x= k y=k+1, her k=2t+1
What would happen if you would integrare a contour clockwise? Why is it important to integrate anti-clockwise?
Counter clockwise and anti clockwise are the same, but I'm assuming you meant clockwise. We go CCW because that is the direction the function moves through. We follow dtheta around the unit circle, which is inherently CCW.
x = (1 - t^2) / (1 + t^2)
y = (2t) / (1 + t^2)
for t in the rationals.
favorite circle parameterization!
You've done the cycloid right? and a sphere?
en.wikipedia.org/wiki/Cissoid_of_Diocles
en.wikipedia.org/wiki/Tractrix
Those are pretty fun.
Thank you Dr. Peyam!
Love those ones!
parametrize´ em all
There’s no link the the desc
Link to what? I forgot what I was mentioning
Dr Peyam you’d said at the start that there’s a link to a future video, but I think it could’ve been that that video maybe was already posted and I watched them in reverse. Nvm, mb
Probably this one: What is a Line Integral ? th-cam.com/video/c_GxshGtOLE/w-d-xo.html
First
Enthusiasm
2:50 why did you mention that a circle is one-dimensional object?
Why not?
@@drpeyam As far as I know ,a circle is a 2D object.
It’s a 1D object living in a 2D space. A disk is 2 dimensional
@@drpeyam Sorry ,I was mistaken . I confused space inclosed in a circle and a circle itself
I think the last one is a bit pointless, because is a 1 to 1 definition
You should say “parametrize the graph of a function”, not “parametrize a function”