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!

Homework Help: Partial Differential Equations (odd&even functions)

  1. Sep 23, 2011 #1
    1. The problem statement, all variables and given/known data:

    A function f : R → R is called “even across x∗ ” if f (x∗ − x) = f (x∗ + x) for every x and is called “odd across x∗ ” if f (x∗ − x) = −f (x∗ + x) for every x. Define f (x) for 0 ≤ x ≤ ℓ by setting f (x) = (x^2) . Extend f to all of R (i.e., define f (x) for all real x) in such a way that it is odd across x∗ = 0 and even across x∗ = ℓ.


    2. Relevant equations:

    1. conservation equations (transport): concentration, flux
    (a) flow (flux = vu ) — fluid, traffic, etc.
    (b) mixing: diffusion/dispersion (probability; flux = D ∇u )
    reaction/diffusion systems
    2. mechanics (Newton’s 3rd Law): force, potential energy, momentum
    (a) wave equation; ICs and BCs
    (b) beam, plate equations
    3. steady state (equilibrium: balance equations)
    4. some other examples . . . (e.g., Cauchy-Riemann equations)

    **Also studying the heat equation/etc**


    3. The attempt at a solution:

    I understand the difference between "even" and "odd". I have created the following:
    f(ℓ-x)=f(ℓ+x) even at "ℓ"
    f(0-x)=-f(0-x) OR f(-x)=-f(x) odd at "0"

    I think I need to use the above IC's to setup the BC's. Once I have the BC's determined I am not sure how to combine them to find the full equation for f (x) or where to start with f (x) = (x^2).

    Please help!!!
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted



Loading...