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June 18th, 2017, 02:39 PM   #1
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Can someone show me some examples of partial differential equations ?

Khan Academy is supposed to have some tutorial on partial differential equations, but instead I only found a YouTube video of PDE.

I have never seen a differential equation containing partial derivatives




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June 18th, 2017, 04:39 PM   #2
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examples:
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June 18th, 2017, 05:25 PM   #3
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Thanks .

A partial differential equation (PDE) is a type of differential equation involving unknown function(s) of several independent variables, in addition to partial derivatives with respect to those variables.

In PDEs, it is common to denote partial derivatives using subscripts

Can somebody please translate this subscripts $\displaystyle u _t = u _{xx}$ to the other form of representing it?
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June 18th, 2017, 08:24 PM   #4
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Originally Posted by awholenumber View Post
Thanks .

A partial differential equation (PDE) is a type of differential equation involving unknown function(s) of several independent variables, in addition to partial derivatives with respect to those variables.

In PDEs, it is common to denote partial derivatives using subscripts

Can somebody please translate this subscripts $\displaystyle u _t = u _{xx}$ to the other form of representing it?
$u_t = u_{xx}$ is shorthand for $\dfrac{\partial u}{\partial t} = \dfrac{\partial^2 u}{\partial x^2}$.
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June 18th, 2017, 09:13 PM   #5
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That means ,

The partial derivative of u with respect to t = The second order partial derivative of u with respect to x ?

If a function u(t,x) is sufficiently differentiable, separation of variables and basic integration serve as two methods of solving them ?
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June 18th, 2017, 09:27 PM   #6
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That means ,

The partial derivative of u with respect to t = The second order partial derivative of u with respect to x
yes
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June 18th, 2017, 11:46 PM   #7
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Originally Posted by awholenumber View Post
That means ,

The partial derivative of u with respect to t = The second order partial derivative of u with respect to x ?

If a function u(t,x) is sufficiently differentiable, separation of variables and basic integration serve as two methods of solving them ?
Might be worth noting that the PDE here is a generic form of a parabolic PDE;

$u_t (x,t) = c^2 u_{xx}(x,t)$ where $c^2 = 1$, also known as the 'heat equation'.
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June 19th, 2017, 01:13 AM   #8
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Might be worth noting that the PDE here is a generic form of a parabolic PDE;

$u_t (x,t) = c^2 u_{xx}(x,t)$ where $c^2 = 1$, also known as the 'heat equation'.
Sorry. Didn't realise this was discussed in the video.
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June 19th, 2017, 08:53 AM   #9
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Quote:
Originally Posted by Joppy View Post
Might be worth noting that the PDE here is a generic form of a parabolic PDE;

$u_t (x,t) = c^2 u_{xx}(x,t)$ where $c^2 = 1$, also known as the 'heat equation'.
So this is how a multivariable partial differential equation with partial derivatives looks.

Thanks a lot.

Last edited by skipjack; August 25th, 2017 at 08:24 AM.
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June 21st, 2017, 04:39 AM   #10
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examples:
????
NONE of those is a partial differential equation!
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