Consider the heat problem that is described by: 0.9urr = Ut, 0 < x < 5, t > 0 u(0, t) = 0, u(5, t) = 0, t>0 u(x, 0) = 5x – a² 0 < x < 5 (a) Identify the heat diffusivity constant a?, the length of the bar L, and the initial temperature distribution f(x). (b) Plug a? and L into u(x, t) to describe the solutions to this problem. u(x, t) = Cne-a²n²x?t/L² sin ("T* ) n=1 (c) Plug L and f(x) into the following equation to describe the coefficients Cn. f(2) = Cn sin (T) n=1

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.