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kring_c14
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Homework Statement
just wondering if anyone knew a website that has solved problems about Fourier expansion??
all i can find are notes and discussions about it..
a gazallion thanks everyone
A Fourier expansion is a mathematical technique used to represent a periodic function as a sum of simpler trigonometric functions. It is based on the concept that any function can be expressed as a combination of sine and cosine waves at different frequencies and amplitudes.
Fourier expansion is important because it allows us to analyze and understand complex functions by breaking them down into simpler components. It is widely used in fields such as signal processing, image processing, and quantum mechanics.
One common problem with Fourier expansion is the Gibbs phenomenon, which refers to the oscillations that occur at the edges of a Fourier series approximation of a discontinuous function. Another problem is the convergence of the series, as some functions may not have a finite Fourier expansion.
The coefficients in a Fourier expansion can be determined using the Fourier series formula, which involves integrating the function with respect to the appropriate trigonometric function. This process may vary depending on the type of function and the interval over which it is being approximated.
Yes, Fourier expansion can be extended to functions with multiple variables through the use of multidimensional Fourier series. This involves expanding the function in terms of multiple trigonometric functions, each corresponding to a different variable. It is commonly used in fields such as differential equations and partial differential equations.