Calculus 3: Directional Derivatives and the Gradient Vector (Video #16) | Math with Professor V

[@valeriereid2337]

I highly recommend this to anyone looking for help with this level mathematics. Well explained, straightforward and super helpful.

[@0.Abdulrahmannn]

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.

[@mathwithprofessorv]

Thank you sooooo much!!! ☺️☺️🫶🏻🫶🏻🫶🏻

[@vashon100]

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?

[@aizarana8665]

same i will also highly recommend these lecs , thanks maam ...

[@mathwithprofessorv]

Thank you so much ☺️☺️☺️

[@sphelelendiyaza7682]

Your Videos Prof Are The Best

[@mathwithprofessorv]

Glad you like them! :)

[@omarbailey2369]

Your videos always make it easy to understand. Thank you!

[@mathwithprofessorv]

Yay you’re so welcome!

[@omarbailey2369]

@@mathwithprofessorv question, do you do differential equations as well?

[@mathwithprofessorv]

The playlist is not complete but I have 13 videos so far: Differential Equations Video Lectures kzbin.info/aero/PLl-Np5U6u5E5kGFz9LrlUy77fOgAKKSOt

[@justintheballer3733]

Could you explain at 14:18 why you did a^2+b^2=1

[@berkaycosgun8901]

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💕💕)

[@melihugurlu291]

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.

[@RahulChauhan-zz1nt]

Best video

[@mathwithprofessorv]

Thank you!!!

[@samyount2546]

At 57:00 could you explain how (25/2)k^2=1 I got 37/2k^2=1. (Awesome video btw)

[@setsototitipana8433]

When computing the directional derivatives, why do we use unit vectors not not just any vector that has the direction you want?

[@ziadbinfars7188]

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

[@benudharasatapathy6625]

Suppose Z=f( x(t), y(t) ) , Then (dz/dt)=(dz/dx)(dx/dt) also (dz/dt)=(dz/dy)(dy/dt) , is it correct ?

[@benudharasatapathy6625]

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 ?