Practical application of partial,simple differential equation

[chandran]

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

 

[saltydog]

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

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.

 

[arildno]

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.

 

[robphy]

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"