Can u-substitution be described as a Jacobian?

[Char. Limit]

So u-substitution is used to make an effective change of variables in one-dimensional calculus. Jacobian determinants are used to make a change of variables in two or higher-dimensional calculus. Can a u-substitution be thought of as a one-dimensional Jacobian determinant?

And on an entirely unrelated note, does anyone know how to make vertical dots in matrix? I was going to draw out the Jacobian determinant, but I couldn't figure that out.

 

[AlephZero]

You can think of it as the determinant of a 1x1 Jacobian matrix if you want. But apart from telling you that single-variable calculus is consistent with multiple-variable calculus, I'm not sure what that buys you.

does anyone know how to make vertical dots in matrix?

\vdots.

 

[Char. Limit]

It's always nice to know that things are consistent between the two areas, though. Thanks!

 

[micromass]

And on an entirely unrelated note, does anyone know how to make vertical dots in matrix? I was going to draw out the Jacobian determinant, but I couldn't figure that out.

What kind of "vertical dots"?? And did you type "matrix" instead of "LaTeX"??

 

[Char. Limit]

What kind of "vertical dots"?? And did you type "matrix" instead of "LaTeX"??

Typo, and, well, ellipses, but vertical, not horizontal. Like this:

$$\vdots$$

 

[micromass]

Typo, and, well, ellipses, but vertical, not horizontal. Like this:

$$\vdots$$

Did you just answer your own question?? Yes, vdots is the way to type vertical ellipses. And ddots is the way to type diagonal ellipses.

 

[Char. Limit]

Did you just answer your own question?? Yes, vdots is the way to type vertical ellipses. And ddots is the way to type diagonal ellipses.

I got vdots from AlephZero above, and ddots from you! Now I can type out n-size matrices!

 

[micromass]

I got vdots from AlephZero above

Oh, how did I miss that??

Also, don't forget hdots which is a nice way to type ...