[Math] Complex form of Fourier Series

fourier seriesintegrationreference-requestself-learning

So, the last part of the university syllabus in the chapter of Fourier Series is: 

3.3 Half range sine and cosine Fourier series, Parsevel’s (without proof).
3.4 Orthogonal and Ortho-normal functions, Complex form of series.
3.5 Fourier Integral Representation.

I am done with orthogonal functions and orthogonal set of functions. I am ok with Parseval's identity. I can calculate half range sine and cosine series.

So what is left is two more topics:

  • Complex form of series
  • Fourier integral representation

    Can someone please tell me what they are? Possiblly point to beginner-level resources

    • Best Answer

    Maybe the following would be of help (at least as a starter, for your reference request):

    "Complex Form of Fourier Series" (Math24.net), this page goes through the derivations and provides a worked example. It also has quite a bit of explanation of what they are.

    This Youtube clip: "Lecture 4: Complex Form of Fourier Series Part 1 of 2", and the second part is here.

    This Youtube clip: "Mod-03 Lec-29 Fourier Integral Representation of a Function", and this Wolfram explanation and derivation of Fourier integral representations, also provide an explanation and derivations.

    I hope this is some help.

    Related Question