MathHelp

Fourier Series def, from Meta:

                                     

                      

Got a helpful reference from Copilot, this morning, in reference to the math on

Fouries series and the transform:

The Fourier Transform and Its Math Explained From Scratch - Programmathically

The Fourier Transform:                                               

                                                 *     *     *

I know that integrals seem daunting. I fully understand the difference between the

length of a fence and the area of a yard, because there are units!!. With integrals, 

one ends up conjecturing speeding cars, filling fish tanks and the like. Essentially, 

we are changing the 'space'...

WhichIsIt

 Meta:

https://meta.ai/s/2XeUZTVYQ3MVb9FK/

https://meta.ai/s/tJg2nqfgPmSk45TF/

https://meta.ai/s/pBzmhwMjQHjUiBQr/

https://meta.ai/s/Th4pSCYxuU38EDdY/

https://meta.ai/s/rdBigFYpWM5k23Sj/

Copilot:

https://copilot.microsoft.com/sl/f2zm9zytBw4

https://copilot.microsoft.com/sl/eHYvR8QNtoO

https://copilot.microsoft.com/sl/jOkpGnBbMGG

https://copilot.microsoft.com/sl/kJ1ZnaEV5Pg

Dangerous

 Asked Copilot to explain about the importance of the contant of integration C.

                                                                          

Indeed!

 

https://www.desmos.com/calculator/zv8ghd2hsj?lang=fr

(Type 'int' to make the integration symbol appear!)

Merlin:

                                                                                  

     

                                                                                 

*     *     *

                                                                                   

                                                                                

Boxcar

 

Fourier_desmos

 Having a moment, this morning, putting the square wave demo of the

Fourier Series in a graph. For a few terms:

The constituent waves:

Amplitude:

Power:

The series up to 100:

(To access the summation symbol, type 'sum' in the entry box.)