This is the best mathematics channel for practical and theoretical explanations I've come across so far. This is a golden last-minute savior channel and a very effective, through-course-understanding alternative source. A very recommended and very lovely channel.
52:12 Confused....I can do the mechanics of grad f with these examples, but I am confused graphically how the grad f vector can be a normal vector to the surface and also a vector that gives greatest rate of increase/decrease for the surface? A normal vector is not also indicating surface rate of change. So it does one thing for some surf equations and another thing for other surf equations?
The playlist is not complete but I have 13 videos so far: Differential Equations Video Lectures th-cam.com/play/PLl-Np5U6u5E5kGFz9LrlUy77fOgAKKSOt.html
bro i wanted to reply after 1 year because I didn't understand either :D if u= you need unit vector normalization. u_hat=u/||u|| (u direction vector, u_hat same direction but magnitute 1 so unit vector) u_hat=()/(sqrt(a^2+b^2)) definition of unit vector is "magnitute equal to 1" so a^2+b^2=1 (yes we dont need a and b exact value) if you go to 16:04 you can check v1 and v2 vectors magnitute are equal to 1 (note: we loveeeee proffesor v💕💕)
41:24 I consider u unit vector as (cos(alpha), sin(alpha)), then I did dot product. To make this expression the biggest, I took derivative then I found that tan(theta)=3.2 This is different than your solution can u explain which one is true because my professor solved a different question in this way. Thank you.
We don't want to alter the change rate of the gradient vector as any vector not a unit vector the magnitude of it ( the value regarding the direction ) is not 1 and if u multiplied any constant with any value but 1 u will eventually change the constant
According to chain rule, (dz/dt)=(dz/dx)(dx/dt) + (dz/dy)(dy/dt) . I will be greatfull , on knowing that , why a '+' sign is in between them ,why they are being added ?
I highly recommend this to anyone looking for help with this level mathematics. Well explained, straightforward and super helpful.
This is the best mathematics channel for practical and theoretical explanations I've come across so far. This is a golden last-minute savior channel and a very effective, through-course-understanding alternative source. A very recommended and very lovely channel.
Thank you sooooo much!!! ☺️☺️🫶🏻🫶🏻🫶🏻
52:12 Confused....I can do the mechanics of grad f with these examples, but I am confused graphically how the grad f vector can be a normal vector to the surface and also a vector that gives greatest rate of increase/decrease for the surface? A normal vector is not also indicating surface rate of change. So it does one thing for some surf equations and another thing for other surf equations?
same i will also highly recommend these lecs , thanks maam ...
Thank you so much ☺️☺️☺️
Your Videos Prof Are The Best
Glad you like them! :)
Your videos always make it easy to understand. Thank you!
Yay you’re so welcome!
@@mathwithprofessorv question, do you do differential equations as well?
The playlist is not complete but I have 13 videos so far:
Differential Equations Video Lectures
th-cam.com/play/PLl-Np5U6u5E5kGFz9LrlUy77fOgAKKSOt.html
Could you explain at 14:18 why you did a^2+b^2=1
bro i wanted to reply after 1 year because I didn't understand either :D
if u= you need unit vector normalization.
u_hat=u/||u|| (u direction vector, u_hat same direction but magnitute 1 so unit vector)
u_hat=()/(sqrt(a^2+b^2))
definition of unit vector is "magnitute equal to 1" so a^2+b^2=1 (yes we dont need a and b exact value)
if you go to 16:04 you can check v1 and v2 vectors magnitute are equal to 1
(note: we loveeeee proffesor v💕💕)
41:24 I consider u unit vector as (cos(alpha), sin(alpha)), then I did dot product. To make this expression the biggest, I took derivative then I found that tan(theta)=3.2 This is different than your solution can u explain which one is true because my professor solved a different question in this way. Thank you.
Best video
Thank you!!!
At 57:00 could you explain how (25/2)k^2=1 I got 37/2k^2=1. (Awesome video btw)
When computing the directional derivatives, why do we use unit vectors not not just any vector that has the direction you want?
We don't want to alter the change rate of the gradient vector as any vector not a unit vector the magnitude of it ( the value regarding the direction ) is not 1 and if u multiplied any constant with any value but 1 u will eventually change the constant
Suppose
Z=f( x(t), y(t) ) ,
Then (dz/dt)=(dz/dx)(dx/dt)
also (dz/dt)=(dz/dy)(dy/dt) ,
is it correct ?
According to chain rule,
(dz/dt)=(dz/dx)(dx/dt) + (dz/dy)(dy/dt) .
I will be greatfull , on knowing that , why a '+' sign is in between them ,why they are being added ?