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Core 1

... two points are joined by a line segment of finite length: the distance formula is a straightforward application of Pythagoras, but again the formula looks impressive! Mid-points were dealt with in Key Stage 3 and students often remember the result as the “average” of the two co-ordinates. The form y ...
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= · = = / / 5x + 1 = 4 -→ 5x + 1 = 16 -→ x = 3 / / 3x + 1 = 4
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Partial differential equation



In mathematics, a partial differential equation (PDE) is a differential equation that contains unknown multivariable functions and their partial derivatives. (A special case are ordinary differential equations (ODEs), which deal with functions of a single variable and their derivatives.) PDEs are used to formulate problems involving functions of several variables, and are either solved by hand, or used to create a relevant computer model.PDEs can be used to describe a wide variety of phenomena such as sound, heat, electrostatics, electrodynamics, fluid flow, elasticity, or quantum mechanics. These seemingly distinct physical phenomena can be formalised similarly in terms of PDEs. Just as ordinary differential equations often model one-dimensional dynamical systems, partial differential equations often model multidimensional systems. PDEs find their generalisation in stochastic partial differential equations.
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