MATH 250 Lecture Notes - Fourier Series, Ordinary Differential Equation, System Of Linear Equations
Document Summary
One-dimensional undamped wave equation; d"alembert solution of the wave equation; damped wave equation and the general wave equation; two- dimensional laplace equation. The second type of second order linear partial differential equations in 2 independent variables is the one-dimensional wave equation. Together with the heat conduction equation, they are sometimes referred to as the. Evolution equations because their solutions evolve , or change, with passing time. The simplest instance of the one-dimensional wave equation problem can be illustrated by the equation that describes the standing wave exhibited by the motion of a piece of undamped vibrating elastic string. Consider a piece of thin flexible string of length l, of negligible weight. Suppose the two ends of the string are firmly secured ( clamped ) at some supports so they will not move. Then, the vertical displacement of the string, 0 < x < l, and at any time t > 0, is given by the displacement function u(x, t).
