Partial differential = the change?

[rsaad]

partial differential = the change??

Homework Statement

How is
Δy/Δx = \partial y / \partial x ?

I just don't know the logic behind this.

 

[lurflurf]

That is only approximately or asymptotically true. If Δy and Δx are small Δy/Δx will be near ∂y / ∂x.

 

[SammyS]

Homework Statement

How is
Δy/Δx = \partial y / \partial x ?

I just don't know the logic behind this.

Do you understand how \Delta y/\Delta yx\approx dy/dx\ ?

Usually, x & y are independent variables -- and often there are additional independent variables.

If f is a function of independent variables, x and y, then we write f(x,y).

\partial f/\partial x\ \ is essentially \ \ df/dx\ \ if we treat y as being held at some fixed value.

Then \ \ \Delta f/\Delta x \approx \partial f/\partial x\ \ keeping y fixed at some value.



By the Way: If x & y are independent variables, then \ \ \partial y/\partial x=0 \ .