Vector calculus in curvilinear coordinates! (a helpful intro)

In this video, we learn about how to do derivatives, or differential calculus, in different types of coordinate systems, like spherical coordinates! We'll focus on the gradient of a function.

Rather than simply giving you the equations (you can look them up!), we will look at *where* the equations come from by building out a generic coordinate system to figure out how we translate the gradient.

Questions about this or other math topics? Leave a comment and let's tackle it together!

[priyanshusorout]

Benefits of having less subscribers - mostly everyone will get answer of their questions 😁😁

[itskarudo]

I love your energy! best video I've seen on the subject by far, thank you 😄

[thevegg]

Hi, you make math fun! So let's see if you can make answering my question fun. :)
I'm an extremely visual learner. That being said I'm trying to visualize Christoffel symbol 'values'.

So if I have a very messy curvilinear csys, how can I visually see or plot the coordinates of a derivative vector (one that represents the change in a given vector before and after being parallel transported an infinitetesimal distance dx.

Should I...
a) plot the coordinates of the derivative vector on the messy curvilinear csys (no idea how to do that)
or
b) plot the coordinates of the derivative vector on cartesian coordinate csys, aka known as the tangent plane...(I know how to do that).

The issue is that a cartesian csys has a nice grid to count lengths of coordinates...but messy curvilinear cys is usually not represented as such (just four curvy lines.
Where are my cury line grids!!! How do I make them. And, on the off chance that both of them are required, how do we size them such that they match? ie. If my cartesian csys has small grid units of one inch, but my messy curvy csys had them as one mile...you see what I mean. I feel like the metric tensor has something to do with matching them up.

Thank you if you try to answer this.

Rocky (big fan)

[mdmouzakkirhossain]

If F(x_, y_, t_) is a function in Cartesian coordinate system, then can you tell me please, what will be the form of del F/del x_ and del F/del y_ in curvilinear coordinate system.
The curve is (x_, cos(x_)).
x_, t_ in Cartesian coordinate,
"
x, t in curvilinear coordinate.
Please help me to rectify this problem.

[lucasf.v.n.]

it's much better (and easier) to learn this in general curvilinear coordinates rather than orthogonal ones; also, u need to stress the importance of using unit basis vectors rather than unscaled basis vectors; and if I may compliment u, u r hot;

[EricPham-grpg]

Instrumentation may simulate better because it interactively and limited of integration unless...

[smftrsddvjiou]

silly question. is it not dl suqared ? Or is dl not the length ?

[chamelious]

Your vids are really good, but the camera constantly autofocusing is distracting, maybe it has a manual mode that will stop it doing that?

[mnada]

It's helpful. What's your book? Are you going to make a separate video for each coordinate system ?

[priyanshusorout]

Can anyone do phd in particle physics after getting master's in chemistry??

[EricPham-grpg]

Maybe newton method on each dimension separately or differential equations systems of equations may easier

[AbDullAHMoHAAmeD]

This is a lil advanced class for me I'll come back later but thanks

[Sumit-zbuj]

We can confirm that she is not confirm when when she was laughin but we weren't.

[lucientdaemon]

I don't remember subscribing here

[jimmyt_]

Let's New episode!!! <grabs beer and watches>

[danielzlotin]

Hey Jen thanks for the videos, they are great and easy to understand. would be nice if you will arrange them in the right order.

[selamselam]

I would join every class with your lecture

[binita]

Thank you so much. This was very helpful 💓