partial differential equations
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Answer:
A partial differential equation (or briefly a PDE) is a mathematical equation that involves two or more independent variables, an unknown function (dependent on those variables), and partial derivatives of the unknown function with respect to the independent variables
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Answer:
Many physically important partial differential equations are second-order and linear. For example: uxx + uyy = 0 (two-dimensional Laplace equation) uxx = ut (one-dimensional heat equation)
Step-by-step explanation:
In mathematics, a partial differential equation is an equation which imposes relations between the various partial derivatives of a multivariable function.
Partial differential equations are used to mathematically formulate, and thus aid the solution of, physical and other problems involving functions of several variables, such as the propagation of heat or sound, fluid flow, elasticity, electrostatics, electrodynamics, etc.
Partial differential equations (PDEs) have just one small change from ordinary differential equations - but it makes it significantly harder. In general the vast majority cannot be solved analytically. But a small class of special partial differential equations can be solved analytically.