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Lecture# MATH-305: Lecture 21-09-2021 first part

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Elliptic partial differential equation

Second-order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic. Any second-order linear PDE in two variables can be written in the form
:

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function.
The function is often thought of as

Hyperbolic partial differential equation

In mathematics, a hyperbolic partial differential equation of order n is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the firs

Sobolev space

In mathematics, a Sobolev space is a vector space of functions equipped with a norm that is a combination of Lp-norms of the function together with its derivatives up to a given order. The derivative

Laplace's equation

In mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as

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