Differential equations in physics

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SUMMARY

Differential equations are integral to understanding various physical theories, particularly in electromagnetism and quantum physics. Key topics include Fourier analysis, which utilizes the Fourier transform to solve differential equations, and Green's functions, both of which are essential for grasping the underlying principles of these theories. Additionally, partial differential equations and boundary value problems are critical, with the Sturm-Liouville problem being a notable example that frequently arises in physics applications.

PREREQUISITES
  • Fourier analysis and Fourier transform
  • Green's functions
  • Partial differential equations
  • Boundary value problems
NEXT STEPS
  • Study the application of Fourier transforms in solving differential equations
  • Explore the concept and applications of Green's functions in physics
  • Investigate partial differential equations and their role in physical models
  • Learn about the Sturm-Liouville problem and its significance in boundary value problems
USEFUL FOR

Students and professionals in physics, mathematicians focusing on applied mathematics, and anyone interested in the mathematical foundations of physical theories.

kent davidge
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Can someone list to me (and whoever is going to view this thread) what topics in differential equations should be studied so that we can have a decent knowledge of the general physical theories in which they occur? (And I believe, they appear in all theories.)

So far, I believe the two most important for physics due to their occurrences in electroagnetism and quantum physics is

- Fourier analysis/ Fourier transform to solve diff equations

- Green's functions

Am I right that they are the two most important?
 
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There’s also partial differential equations and boundary value problems Which pops up in many areas of physics
 
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Exact, and the Sturm-Liouvilles problem
 
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