Unformatted text preview: 42 Chapter 3 Partial Diﬀerential Equations in Rectangular Coordinates
Note that A is a ﬁnite number because f is bounded, so its absolute value
is bounded and hence its integral is ﬁnite on [0, L]. We have
bn sin nπ −λ2 t0
L 2 ≤ Ae−λn t0 = Ae−
≤ A e− c2 π 2 t0 c2 π 2 t0
L2 c2 π 2 t0 2
L2 n = Arn , where r = e− L2 < 1. Take Mn = Arn . Then a holds and
convergent because it is a geometric series with ratio r < 1. Mn is ...
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This note was uploaded on 12/22/2011 for the course MAP 3305 taught by Professor Stuartchalk during the Fall '11 term at UNF.
- Fall '11