Differential equations in physics

In summary, the topics in differential equations that should be studied to gain a good understanding of their occurrences in general physical theories are Fourier analysis/transform, Green's functions, partial differential equations, boundary value problems, and the Sturm-Liouvilles problem. These topics are especially important in electromagnetism and quantum physics.
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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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1. What are differential equations and how are they used in physics?

Differential equations are mathematical equations that describe how different quantities change over time. In physics, they are used to model and predict the behavior of physical systems, such as the motion of objects, the flow of fluids, and the behavior of electric and magnetic fields.

2. What is the difference between ordinary and partial differential equations?

Ordinary differential equations involve only one independent variable, such as time, and describe the rate of change of a single variable. Partial differential equations involve multiple independent variables and describe the rate of change of a function with respect to each variable.

3. How are differential equations solved in physics?

There are a variety of methods for solving differential equations in physics, including analytical methods (such as separation of variables, variation of parameters, and Laplace transforms) and numerical methods (such as Euler's method and Runge-Kutta methods).

4. Can differential equations be used to model real-world phenomena?

Yes, differential equations are widely used in physics to model and understand real-world phenomena. They have been successfully applied to a wide range of fields, including mechanics, electromagnetism, thermodynamics, and quantum mechanics.

5. Are there any limitations to using differential equations in physics?

While differential equations are a powerful tool for modeling physical systems, there are some limitations. In some cases, the equations may be too complex to solve analytically, requiring the use of numerical methods. Additionally, the accuracy of the models depends on the assumptions and simplifications made in the equations.

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