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Board index > Departments > Mathematics
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Problems coming under other departments must be posted into the respective sections.
This section is a dedicated section for Maths only forum so please dont post problems under mechanical, electronics or any other in this category.



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sreenath
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#2
Sat Aug 29, 2009 8:02 pm
Post subject: Partial differential equation Post
In mathematics, partial differential equations (PDE) are a type of differential equation, i.e., a relation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables. Partial differential equations are used to formulate, and thus aid the solution of, problems involving functions of several variables; such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity. Seemingly distinct physical phenomena may have identical mathematical formulations, and thus be governed by the same underlying dynamic.
A relatively simple partial differential equation is

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This relation implies that the values u(x,y) are independent of x. Hence the general solution of this equation is

Image

where f is an arbitrary function of y. The analogous ordinary differential equation is
Image

which has the solution

Image

where c is any constant value (independent of x). These two examples illustrate that general solutions of ordinary differential equations involve arbitrary constants, but solutions of partial differential equations involve arbitrary functions. A solution of a partial differential equation is generally not unique; additional conditions must generally be specified on the boundary of the region where the solution is defined. For instance, in the simple example above, the function f(y) can be determined if u is specified on the line x = 0.
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#2
Sun Aug 30, 2009 11:40 am
Post subject: Re: Partial differential equation Post
Aaga avane thaa ya iva..
Sorry members for using non english language, but i have to express my surprise :D
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