How can this discrepancy be explained?

[vze3bbyp]

@All,

I've attached a short text demonstrating a discrepancy in the numerical calculation of an integral and series supposed to describe the same thing. What are your thoughts? What might this discrepancy be due to?

 

[Office_Shredder]

It's kind of confusing to read you calculation of the derivative, because your variables keep changing names. At one point you have E(t) when you mean E(T), you have these functions I_in and V_in whose difference from I and V is unclear (if there is one).

Then you say capital T is the period, which would seem to indicate that it's a constant and not a variable. I can't really figure out what your function is

 

[vze3bbyp]

Iin and Vin and I and V are the same quantities.

 

[Office_Shredder]

And what about the fact that the definition of E(t) is not a function that actually depends on t? I would assume that it was intended to read E(T) but you later define T to be the period of your voltage so that wouldn't be a function either

 

[vze3bbyp]

Correct, it's E(T) where, T, before defining it as the period is a variable. I should've started with $$E(\tau) = \int_0^\tau I_{in}V_{in} dt$$ instead.

 

[vze3bbyp]

Another correction. Please replace the word 'integral' with the word 'series' in the following part of the last paragraph:

For values of F < 0 not only the integral tends towards zero but after a certain F it becomes negative. The opposite is observed when F > 0. In this case the integral becomes more and more positive with the increase of F.