Definition of order of a partial differential equation

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  • #1
Kashmir
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How is the order of a partial differential equation defined?

This is said to be first order: ##\frac{d}{d t}\left(\frac{\partial L}{\partial s_{i}}\right)-\frac{\partial L}{\partial q_{i}}=0##

And this second order :##\frac{d}{d t}\left(\frac{\partial L}{\partial \dot{q_{i}}}\right)-\frac{\partial L}{\partial q_{i}}=0##

What's the proper definition?

Thank you
 

Answers and Replies

  • #2
mathman
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The dot over the q makes the second line second order.
 
  • #3
Kashmir
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The dot over the q makes the second line second order.
Thank you, could you please tell me the definition of second order for partial D.E ?
 
  • #4
Astronuc
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The order for partial D.E., like an ordinary D.E., refers to the highest order derivative in the D.E.

For example, a D.E. with ##\partial^2{y}/\partial{x}^2##, would be 2nd order if no higher derivatives were present, and similarly with d2y/dx2.

Unfortunately, I've gone blank about mixing time and position/space derivatives, and ordinary with partial.

There are many online tutorials concerning DEs, both ODE and PDE.
https://users.aber.ac.uk/ruw/teach/260/classification.php
https://tutorial.math.lamar.edu/classes/calciii/highorderpartialderivs.aspx

https://www.math.toronto.edu/jko/APM346_summary_1_2020.pdf
https://www.csc.kth.se/utbildning/kth/kurser/DN1213/numme06/utdelat/kap10.pdf
 
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