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differential equation and ordinary differential equation. If it is in

mechanical engineering statics etc will be helpful

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In summary, the practical applications of partial differential equations and ordinary differential equations can be found in various fields such as mathematical physics, mechanical engineering, and elasticity theory. These equations are used to model the changing world and are particularly useful in analyzing statics and dynamics problems, such as determining the stress distribution in a beam or studying the behavior of an oscillator. However, dealing with non-linear equations can be challenging, so linearization techniques are often used.

- #1

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differential equation and ordinary differential equation. If it is in

mechanical engineering statics etc will be helpful

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chandran said:

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.

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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.

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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"

A partial differential equation (PDE) is an equation that involves multiple independent variables and their partial derivatives. It is used to describe physical phenomena in fields such as physics, engineering, and economics.

A simple differential equation involves only one independent variable, while a partial differential equation involves multiple independent variables. This means that the solution to a PDE is a function of more than one variable.

Partial differential equations have a wide range of practical applications, including in physics, engineering, economics, and biology. They are used to model and analyze complex systems and phenomena, such as fluid dynamics, heat transfer, and population dynamics.

There is no general method for solving all types of partial differential equations. However, there are various techniques that can be used, such as separation of variables, method of characteristics, and numerical methods.

To apply partial differential equations in real-world problems, one needs a strong understanding of mathematical concepts such as calculus, linear algebra, and differential equations. Additionally, knowledge of the specific field in which the PDE is being applied is also necessary.

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