Multivariable Calculus | The tangent plane of a level surface.

[@Al.2]

This video seems to be put too early in the playlist. Chain rule as of 2:40 not proved yet, gradient not defined.

[@fredrickelvis7883]

Great explanation. Love from Canada

[@declanwk1]

so clear, thank you

[@riemann4151]

These series is really good. Can you recommend textbooks on multivariable calculus in IR^n

[@alijoueizadeh2896]

Thank you. Greetings from Iran.

[@nailabenali7488]

Hey! There is on my course a notion called tangent vectors over a subset!! It's really different from this, do you have any idea on it?

[@MichaelPennMath]

I am not really sure about this - I would have to see how it is precisely defined.

[@nailabenali7488]

@@MichaelPennMath This is the definition I have: Let X be a subspace of a space E ( E can be a normed one) an element v from E is said to be a tangent vector to X in x if there existe epsilon strictly big than 0 and a parametric arc (gamma) defined from the open interval (-epsilon,+epsilon) to X differentiable in 0 such that gamma(0)=x and the derivative of gamma in 0 equal v. I did my best in the translation..

[@MichaelPennMath]

It still feels like this is a tangent vector at a point x\in X. If I am understanding: E is some "large" ambient space (like R^n or C^n) and X is a subset (probably like a smooth manifold), then v\in E is tangent to X at x if (your definition). One thing that you can do is put all of these vectors together into a tangent space -- the tangent space of X at x, sometimes denote T_x(X). This is an important concept in Lie theory -- the Lie algebra of a Lie group is the tangent space at the identity.

[@nailabenali7488]

@@MichaelPennMath for example if I wanted to find all the tangent vector to [-1,1]^2 at (0.0) should I look for a tangent space? ( I'm still learning this concept so I'm not very comfortable with)

[@MichaelPennMath]

@@nailabenali7488 From your definition, any curve in R^2 is tangent to this space at (0,0). You can take your curve to be a line through the origin in the direction of whatever vector you want. I think this may be an example of something that is very simple, but not realistic so it makes it tricky.

[@PianoMysteries]

so you ignore the k?

[@manuel3494]

Great vid

[@mathCS1233]

awesome bro thanks!!

[@uea4066]

how and why did you scale = , thanks by the way, great videos

[@fuvet]

I presume because he said the magnitude doesn't matter and since the x and z were equal to each other and the y would always be 0, he just set it to 1,0,1 for simplicity

[@aristo7051]

I wish you were my multivariable calc. lecturer