Fourier series: odd & even extensions

[RosanelladC]

I'm setting up a couple of worksheets (though ideally I'd like to have 2 in 1) that will enable me to work out Fourier series, the respective odd & even extensions and display the graphs.

Questions:

1) Is there a way to display a function g(t) in one set of curly brackets? e.g. (something looking like this but inside the culry brackets)

1 (0 < t <= 1)

g(t) = {

2 - t (1 < t <= 2)

2) Calculations are flagged in red (actually, nothing is being calculated at all!) when I try to work out the Fourier series of g(t) symbolically. I'm not sure what it is that I've missed?!?

N.B. I have used the necessary parts from a worksheet that came with my MathCad package 14.0 M020 and trying to make some sense of it.

[Werner_E]

Ad 1) Use the if from the programming palette. No curly brackets but as near as you can get. See attached

Ad 2) You have no functions A() and B() defined, therefore the error. See attached

[RosanelladC]

Werner Exinger wrote:

Ad 1) Use the if from the programming palette. No curly brackets but as near as you can get. See attached

Ad 2) You have no functions A() and B() defined, therefore the error. See attached

I see. Thank you very much!

[Werner_E]

One word of caution: If you want to use the function definition with the programming structure to calculate the Fourier coefficients replace the NaN for 0. Otherwise the integrals won't even evaluate numerically.

[ptc-6649671]

Hi! Hope you can help me with one also.

The integral I set-up for the sine and cosine series always gets this non-coverging error message. I believed I've stated all parameters needed already.

[ValeryOchkov]

With help this Mathcad web-sheet http://twtmas.mpei.ac.ru/mas/Worksheets/Fourier.mcd

[Werner_E]

Why don't you open a new thread for a new question and most important - attach your worksheet.

Its hard to debug a picture rather than the sheet itself.

Apart from the unnecessary definition of the range t and a[0, best guess is that you have used the wrong indices for a and b - you have to use vector indices and not the literal index.

[ValeryOchkov]

See please http://twtmas.mpei.ac.ru/mas/Worksheets/Fourier.mcd