What's your favourite type of differential equation

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SUMMARY

The discussion centers on various types of differential equations, with a particular emphasis on partial differential equations (PDEs) and their applications. The user expresses a preference for the several variable complex heat equation, highlighting Riemann's theta function as a fundamental solution. Additionally, the mention of equations featuring a small \(\epsilon << 1\) in front of the highest order term indicates an interest in perturbation methods. The conversation encourages the exploration of other types of differential equations that may have been overlooked.

PREREQUISITES
  • Understanding of differential equations, particularly partial differential equations (PDEs).
  • Familiarity with Riemann's theta function and its applications in complex analysis.
  • Knowledge of perturbation methods in mathematical analysis.
  • Basic concepts of multi-variable calculus.
NEXT STEPS
  • Research the applications of Riemann's theta function in solving PDEs.
  • Explore perturbation techniques in differential equations.
  • Study the properties and solutions of the several variable complex heat equation.
  • Investigate other types of differential equations, including those with delays.
USEFUL FOR

Mathematicians, physicists, and engineering students interested in advanced differential equations and their applications in various fields.

?DE


  • Total voters
    12
J77
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Just a small list, mark up any others I have neglected... :cool:

edit: already see, I should've put in PDEs with delay...
 
Last edited:
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my fave is the several variable complex heat equation, to which riemann's theta function is a fundamental solution.
 
I've started to enjoy those equations with a small [tex]\epsilon<<1[/tex] just in front of the highest order term...:biggrin:
 

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