1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Is the function odd, even or neither?

  1. Apr 20, 2007 #1
    The function f(x) 1, -pi < x < 0

    0, 0 < x < pi

    now after sketching the function i believe i am correct in saying it is neither symmetrical about the x axis or the origin and therefore is neither odd nor even?

    It is a square wave?

    Am i correct? Also how should i now go about finding its fourier series?

    Thankyou
     
  2. jcsd
  3. Apr 20, 2007 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Assuming you mean f(x)= , then, yes, it is neither even nor odd.

    You could find its Fourier series by using the usual formulas:
    [tex]A_n= \frac{1}{\pi}\int_{-\pi}^0 sin(nx) dx[/itex]
    and
    [tex]B_n= \frac{1}{\pi}\int_{-\pi}^0 cos(nx)dx[/itex]
    where An and Bn are the coefficients of sin(nx) and cos(nx) respectively for n> 0.
    [tex]B_0= \frac{1}{2\pi}\int_{-\pi}^0 dx= \frac{1}{2}[/tex]
    is the constant term.

    Or you could write f(x)= 1/2 + g(x) where g(x)= 1/2 for [itex]-\pi \le x\le 0[/itex] and g(x)= -1/2 for [itex]0< x \le \pi[/itex]. g(x) is an odd function so the calculations are little simpler.
     
  4. Apr 20, 2007 #3

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    I'm going to be more abrupt than the lovely mentors here. What is the bloody definition? Sorry, cabellos, but I'm truly fed up with the number of questions which are answerable with 'look at the definition'.
     
  5. Apr 20, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "Lovely", moi? Oh, how sweet of you!

    Actually, I think the first sentence of just about every response should be "look up the definition"!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Is the function odd, even or neither?
  1. Odd and even function (Replies: 5)

Loading...