1. Limited time only! Sign up for a free 30min personal 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!

Fourier series

  1. Apr 13, 2016 #1
    1. The problem statement, all variables and given/known data
    is the author wrong ? i was told that the f(x) = 0.5(a_0) +Σ(a_n)cos (nπx / L ) ........ but , in the example(photo2) , the author ignore the L , which the author gave f(x) = 0.5(a_0) +Σ(a_n)cos (nπx ) +......

    2. Relevant equations

    3. The attempt at a solution
    P/ s : i have tried to make some correction beside the working , is it correct ?

    Attached Files:

    Last edited: Apr 13, 2016
  2. jcsd
  3. Apr 14, 2016 #2


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Don't know what photo 2 is, but in 154002 the author carefully uses L = 2.
    And in 1550002 L is ##\pi##
  4. Apr 14, 2016 #3
    So, the author is wrong, right? In155002, the L should be 2, right??
  5. Apr 14, 2016 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If 150 says ##n\pi\x\over L## and 154 says ##n\pi\over 2##, doesn't that mean the author did take L = 2 ?

    As for 155, I'm not so sure: does the definition in your book agree with

    The Fourier series of the function f(x) is given by
    $$f(x)={a_0\over 2}+\sum_{n=1}^\infty \{a_n\cos nx+b_n\sin nx\}$$
    where the Fourier coefficients ##a_0##, ##a_n##, and ##b_n## are defined by the integrals$$
    a_0={1\over \pi} \int _{−\pi}^\pi f(x)\, dx,\quad a_n={1\over \pi} \int _{−\pi}^\pi f(x)\cos nx\,dx,\quad b_n{1\over \pi} \int _{−\pi}^\pi f(x)\sin nx\,dx$$
  6. Apr 14, 2016 #5
    no , as you can see it 150 , the author gave $$f(x)={a_0\over 2}+\sum_{n=1}^\infty \{a_n\cos nπx / L+b_n\sin nπx\/L}$$

    Attached Files:

    • 150.jpg
      File size:
      66.5 KB
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Fourier series
  1. Fourier series (Replies: 10)

  2. Fourier Series (Replies: 1)

  3. Fourier Series (Replies: 6)

  4. Fourier series (Replies: 1)

  5. Fourier Series (Replies: 10)