My Math Forum Can someone show me some examples of partial differential equations ?

 Differential Equations Ordinary and Partial Differential Equations Math Forum

 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
Math Team

Joined: Jul 2013
From: काठमाडौं, नेपाल

Posts: 878
Thanks: 60

Math Focus: सामान्य गणित
examples:
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
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,737
Thanks: 606

Math Focus: Yet to find out.
Quote:
 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
Math Team

Joined: Jul 2013
From: काठमाडौं, नेपाल

Posts: 878
Thanks: 60

Math Focus: सामान्य गणित
Quote:
 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
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,737
Thanks: 606

Math Focus: Yet to find out.
Quote:
 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
Senior Member

Joined: Feb 2016
From: Australia

Posts: 1,737
Thanks: 606

Math Focus: Yet to find out.
Quote:
 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
Member

Joined: Jun 2017
From: India

Posts: 65
Thanks: 3

Quote:
 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
Math Team

Joined: Jan 2015
From: Alabama

Posts: 3,261
Thanks: 894

Quote:
 Originally Posted by MATHEMATICIAN examples:
????
NONE of those is a partial differential equation!

 Tags differential, equations, examples, partial, show

### linear algebra forums

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post rishav.roy10 Differential Equations 0 August 21st, 2013 07:12 AM roshe Differential Equations 0 April 21st, 2013 11:26 PM maximus101 Differential Equations 1 February 21st, 2011 03:52 PM rajanm1 Differential Equations 0 March 2nd, 2010 03:45 AM rajanm1 Differential Equations 0 March 2nd, 2010 03:39 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top