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 June 18th, 2017, 02:39 PM #1 Member   Joined: Jun 2017 From: India Posts: 65 Thanks: 3 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 Last edited by skipjack; July 18th, 2017 at 02:32 PM. June 18th, 2017, 04:39 PM   #2
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Attached Images Eqn1.jpg (17.1 KB, 16 views) June 18th, 2017, 05:25 PM #3 Member   Joined: Jun 2017 From: India Posts: 65 Thanks: 3 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? June 18th, 2017, 08:24 PM   #4
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 Originally Posted by awholenumber 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 $\dfrac{\partial u}{\partial t} = \dfrac{\partial^2 u}{\partial x^2}$. June 18th, 2017, 09:13 PM #5 Member   Joined: Jun 2017 From: India Posts: 65 Thanks: 3 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 ? June 18th, 2017, 09:27 PM   #6
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 Originally Posted by awholenumber That means , The partial derivative of u with respect to t = The second order partial derivative of u with respect to x
yes June 18th, 2017, 11:46 PM   #7
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 Originally Posted by awholenumber 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'. June 19th, 2017, 01:13 AM   #8
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 Originally Posted by Joppy 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. June 19th, 2017, 08:53 AM   #9
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 Originally Posted by Joppy 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. June 21st, 2017, 04:39 AM   #10
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 Originally Posted by MATHEMATICIAN examples:
????
NONE of those is a partial differential equation! Tags differential, equations, examples, partial, show ### linear algebra forums

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