What are some online resources for learning Fourier expansion/series?

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In summary, the speaker is taking a course on vector calculus and their professor mentioned that Fourier expansion/series is covered, but it is not included in the textbook. They have tried searching online for resources, but have not found anything helpful. They are asking for recommendations for online texts on Fourier expansion/series for beginners and greatly appreciate any help. Two potential resources are Wikipedia's page on Fourier analysis and a website called Sunlightd.com that also covers Fourier analysis. The speaker also mentions that many engineering textbooks touch on Fourier series.
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Brown Arrow
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well I am taking the second part of vector calculus. my prof told me that Fourier expansion/series is part of the course but its not covered I am our textbook; he did not refer any book to study from.. i tried googling it. i did not get anything which can help me...so I am asking if you guys know any online text that i can use to study Fourier expansion/series...like for beginners...

i greatly appreciate your help

BA
 
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umm anyone?
 
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Many engineering textbooks deal with Fourier series, but not too in depth. You can start there.
 

FAQ: What are some online resources for learning Fourier expansion/series?

What is a Fourier expansion/series?

A Fourier expansion, also known as a Fourier series, is a mathematical method for representing a periodic function as a sum of sine and cosine functions with different frequencies. It is used in many areas of physics and engineering to analyze and model periodic phenomena.

What is the difference between a Fourier expansion and a Fourier transform?

A Fourier expansion is used to represent a periodic function as a sum of sine and cosine functions, while a Fourier transform is used to represent a non-periodic function as a sum of sine and cosine functions with different frequencies. Essentially, a Fourier expansion is for periodic functions and a Fourier transform is for non-periodic functions.

How is a Fourier expansion calculated?

A Fourier expansion is calculated by using the Fourier series formula, which involves integrating the function over one period and solving for the coefficients of the sine and cosine terms. These coefficients represent the amplitudes of the different frequencies in the function.

What is the significance of the Fourier coefficients?

The Fourier coefficients represent the amplitudes of the different frequencies present in the function. This allows us to analyze the function in terms of its frequency components, which can be useful in understanding the behavior and properties of the function.

What are some applications of Fourier expansion/series?

Fourier expansion/series has many applications in physics and engineering, such as signal processing, image and sound compression, and solving differential equations. It is also used in areas like heat transfer, vibration analysis, and quantum mechanics.

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