# Tagged Questions

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### The difference between m and n in calculating a Fourier series

I am studying for an exam in Differential Equations, and one of the topics I should know about is Fourier series. Now, I am using Boyce 9e, and in there I found the general equation for a Fourier ...
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### Partial Differential Equation Eigenvalue of zero question

In the event that I'm solving a partial differential equation through separation of variables, if I end up with an eigenvalue of zero, what do I do with the corresponding eigenfunction? That is to ...
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### Theoretical Understanding of Fourier Series

I understand mathematically how it is derived, and how it works (ie how it is applied and the significance of Fourier Series in solving PDEs). What I want to know is why it works, theoretically and ...
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### Check my solution - Modelling of a spring with Differential Equation

I am doing some work with differential equations. I have solved the following problem but am uncertain if I'm doing it correctly. Could someone look over it for me and check if I'm doing something ...
Find the Fourier tranform of $f(x)=x^2e^{-x^2}$ In a previous question when I found the Fourier transform of $f(x) =e^{-x^2}$, I used the formulas $F(f')=i\omega F$ and $F(xf)=iF'$. Will they be ...
### Solving $f''+f=\sin x$ with Fourier series
Does there exist a twice differentiable periodic function $f$ such that $f''(x) + f(x) =\sin(x)$ for all $x \in [-\pi, \pi]$? How to solve this differential equation using Fourier series? I ...