1. ## Partial Differntiation, Wiki

I'm just in first year calc, but I sat in on a PDE class. I got interested and looked it up on wikipedia. I noticed that when choosing one of the infinitely many tangent lines on the surface of a function and finding it's slope the lines of most interest are often the on the xz and the yz planes. Can someone tell me why the lines on these planes are so interesting?

2. Hello,

I'm sorry, I don't understand your question at all, makes no sense...
Plus, I'm sorry too for this, but are you sure you have the necessary knowledge to do PDEs ?
Because I saw your other question : http://www.mathhelpforum.com/math-he...ean-f-x-y.html, and if you didn't know that, you can't possibly understand what a PDE is...
Another remark, that may explain why your question looks weird : is a derivative equivalent to a tangent to you ?

Again, sorry to say that, it may look rude, but you've gotta go back to reality.

Please correct me if I'm thinking wrong.

3. This is what I was referring to (quoted from wiki) in my original post:

"It is difficult to describe the derivative of such a function, as there are an infinite number of tangent lines to every point on this surface. Partial differentiation is the act of choosing one of these lines and finding its slope. Usually, the lines of most interest are those that are parallel to the xz-plane, and those that are parallel to the yz-plane."

I just wanted to know why the slopes of these lines (i.e. those lines on the xz and yz) are so..."interesting", and what sort of applications they have.

4. Oh gosh, you said PDE in your post, but it was about partial derivative... Which is not the same at all . I had to type your sentence in google to find it

Anyway, sorry for the trouble !

As for the sentence, here is how I understand it :

Since you're dealing with a three dimensional space, the tangents to the curve at a given point forms a space. (for your culture, it's called the Tangent space - Wikipedia, the free encyclopedia, but that's an outlying notion)
There's a nice picture in the link of the tangent space, with the example of a sphere.
Any line in this plane that passes through the point you're interested in will be a tangent to the curve.
Whereas when dealing with a 2 dimensional space, there's one (or several in the worst cases) tangent at a given point.
That's why it's difficult with 3 dimension, since you have an infinity of lines to deal with.

As for the xz, yz planes, we consider the tangents parallel to these planes, because for the following things, it's like we fix a given y, and we consider the curve with this given y (which gives the parallel with the xz plane). Same thing for the yz plane, while fixing x.

If you continue reading, you'll see that while differentiating with respect to x (or to y), y (or x) is considered as a constant.

I hope it's a bit clearer

5. yep, i think i understand that quite well thanks

but... when you say:
"Since you're dealing with a three dimensional space, the tangents to the curve at a given point forms a space."

do you mean plane/hyperplane instead of space?

6. Originally Posted by Noxide
yep, i think i understand that quite well thanks

but... when you say:
"Since you're dealing with a three dimensional space, the tangents to the curve at a given point forms a space."

do you mean plane/hyperplane instead of space?
A space that is a plane. I said a space, to say "the space (or set) of all the tangents to the curve", and it appears that this space is a plane :P
And since it's a plane taken from a three dimensional space, it's also a hyperplane
You can substitute space by plane in my posts if it disturbs you !

I also understand why I confused and thought you were talking about PDEs, because you put this thread in differential equations. I'll ask for it to be moved