MATH 2ZZ3 Lecture Notes - Lecture 9: Eigenfunction, Thermal Diffusivity, Heat Equation

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Math objects made using mathtype; graphs made using winplot. We"ll focus on 2nd order pde"s and look for. Example 1 aem x u x y u. 0 m (2 distinct, real roots) cosh 2. Recall from math 2z03: cosh 2 cosh 2 x. 2 y sin 2 x u are solutions to homogeneous linear pde, then linear combo. , where ci, a constant, is also a solution. If 1 u u u an infinite set{ } 1. 1 1 c u i i c u k u i u k i. Solution is an equation of u x t. Heat equation models the flow of heat, through this rod. Take a string of length, l, and stretch it between 2 points that correspond to respectively. When string moves, it moves perpendicular to x-axis. Then ( displacement of any point on string, measured from x-axis at time t > 0 x x l.

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