How To Find The Fourier Series Of Absolute Value

In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series.
In This Video, You'll Learn;
1. How To Identify the function: Whether the given function is odd function or even function? Identify the function's type from its expression or waveform or graph.
2. Identification of function's type (that is odd or even function) will reduce the calculation of Fourier series.
3. If function is odd then Fourier coefficient a0 and an equals to 0 (zero). and if function is even then Fourier coefficient bn equals to 0 (zero). If function is neither odd nor even then you have to calculate all three coefficients a0, an and bn of Fourier series one by one.
4. How To Remember the formulae of Fourier series and coefficients of Fourier series with period 2l or 2c.
5. Once you will get the values of all three Fourier coefficients (a0, an, bn) then Fourier series expansion can be done by just simply replace the values of this Fourier series coefficients to the formula of Fourier series with period 2l or 2c.
6. How To get the Fourier series of any periodic function with period 2l or 2c.
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[@yenye120]

Nice one

[@AVITECHNOLOGIES]

Thank you very much.

[@natalyarregoitia9228]

Just wanted to say thank you. I haven't touched any math in years and decided to go back to college for engineering and your videos are super helpful.

[@AVITECHNOLOGIES]

@@natalyarregoitia9228 You're welcome 😊

[@wangamanga2128]

when you were solving for a_0, why is f(x)=x, wasn't f(x) a piecewise function? 10:07

[@AVITECHNOLOGIES]

When finding the Fourier coefficients, things could be made easier if you know the symmetry of the function. In this case, the function is even. Hence, we could reduce our integral and solve by just one of its function values. To understand better, watch my video on even and odd functions.