- #1
frozenguy
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Homework Statement
Find the Fourier series of f on the given interval:
EDIT: For the result of an, it should be multiplied by [tex]\frac{2}{1+n^{2}}[/tex]. That has been corrected.
Last edited:
Diff eq Fourier Series Stuck halfway through,
- Thread starter frozenguy
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In summary, The task is to find the Fourier series of a function on a given interval. The result of an should be multiplied by \frac{2}{1+n^{2}}. The conversation includes a correction and a comment about the answer not matching the book's, with a suggestion to fix the sign of bn. The final response expresses gratitude for the help.
Find the Fourier series of f on the given interval:
EDIT: For the result of an, it should be multiplied by [tex]\frac{2}{1+n^{2}}[/tex]. That has been corrected.
- #2
vela
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So far, so good.
- #3
frozenguy
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Hey Vela thanks for your response. How about now? Is my answer in a different form or did I screw up somewhere? Note the books answer.
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vela
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You messed up the sign of bn. Fix that and your answer will match the book's.
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frozenguy
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vela said:
Oh ok. I see that now, and the two factorizations I have to make.
Thanks for your help!
What is a differential equation?
A differential equation is a mathematical equation that relates a function to its derivatives. It is used to describe how a system changes over time and is commonly used in physics, engineering, and other fields.
What is a Fourier series?
A Fourier series is a way of representing a periodic function as a sum of sinusoidal functions. It is used to analyze and approximate functions that are periodic in nature.
Why am I stuck halfway through my Fourier series?
There could be several reasons for getting stuck halfway through a Fourier series. It could be due to errors in the calculations, incorrect assumptions about the function, or limitations of the chosen method. It is important to carefully check all steps and reassess the problem to find the cause of the issue.
How do I solve a differential equation using Fourier series?
The process of solving a differential equation using Fourier series involves breaking down the equation into a series of simpler equations, solving for the coefficients of the Fourier series, and then using those coefficients to find the solution to the original equation. It requires knowledge of both differential equations and Fourier series techniques.
Can I use a computer to help me with my Fourier series problem?
Yes, there are many software programs and online tools available that can assist with solving Fourier series problems. However, it is important to have a good understanding of the concepts and techniques involved in order to use these tools effectively and verify the results.
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