Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Practical application of partial,simple differential equation

  1. Apr 30, 2005 #1
    can anybody tell with equation,the practical applications of partial
    differential equation and ordinary differential equation. If it is in
    mechanical engineering statics etc will be helpful
  2. jcsd
  3. Apr 30, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    Most of the equations of Mathematical Physics are in terms of not only partials but non-linear ones to boot. I mean really, we do easy ones in school to just learn how to work them but in real-life, the equations include more variables (hence partials), since as you know "everything is connected to everything out there", and if our mathematical models are to have any chance of genuinely reflecting the real world out there, then they usually need to be non-linear since of course it's a non-linear world out there as well. However, non-linear ones are really tough to work with so just so that we can get a handle on things, we often "linearize" them just to cope.

    As far as "practical", well we live in a "changing world". Derivatives represent change. Ergo: Differential equations are good at modeling the world.
  4. Apr 30, 2005 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    Dearly Missed

    As for statics, partial differential equations naturally occurs in elasticity theory.
    If you want to find out how much a beam is going to bend, or find the stress distribution within it when subjected to some load, you're in the middle of some ugly non-linear partial diff.eq. problems.
  5. Apr 30, 2005 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Here are some statics and dynamics applications to get you started... google these

    beam deflection "differential equation"
    "virtual work" "differential equation"
    "finite element method" "differential equation"
    catenary "differential equation"

    for dynamics:

    oscillator "differential equation"
    "least action" "differential equation"
    kepler "differential equation"

    maxwell "differential equation"
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook