2. A hyperbolic equation: the wave equation
2.1 Vibrating string equation
This was one of the first partial differential equations to be demonstrated.
It was studied in the first half of the 18th century by d'Alembert :
where v denotes the velocity of wave propagation in the string and u (x, t ) the ordinate of the point of abscissa x on the string at time t (this ordinate being...
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A hyperbolic equation: the wave equation
A parabolic equation: the heat equation
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