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: 911 Thanks: 64 Math Focus: सामान्य गणित 
examples:

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: 1,847 Thanks: 661 Math Focus: Yet to find out.  Quote:
 
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: 911 Thanks: 64 Math Focus: सामान्य गणित  
June 18th, 2017, 11:46 PM  #7  
Senior Member Joined: Feb 2016 From: Australia Posts: 1,847 Thanks: 661 Math Focus: Yet to find out.  Quote:
$u_t (x,t) = c^2 u_{xx}(x,t)$ 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: 1,847 Thanks: 661 Math Focus: Yet to find out.  
June 19th, 2017, 08:53 AM  #9  
Member Joined: Jun 2017 From: India Posts: 65 Thanks: 3  Quote:
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: 3,264 Thanks: 902  

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