Question: A one-meter long bar is heated unevenly, with temperature in °C at a distance x meters from one end at time t given by
H(x, t) = 100e-0.1t sin(Πx) 0 ≤ x ≤ 1
(a) Sketch a graph of H against x for t = 0 and t = 1.
(b) Calculate Hx(0.2, t) and Hx(0.8, t). What is the practical interpretation (in terms of temperature) of these two partial derivatives? Explain why each one has the sign it does.
(c) Calculate Ht(x, t). What is its sign? What is its interpretation in terms of temperature?