Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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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.
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I'm having trouble understanding why these two conditions imply that c1=c2=c3=c4=0.  Wouldn't both equations still hold if c3=c4=0 only?  Or just c1 and c2?  Why do all four of them have to be 0?

use initial conditions и (0, t) — 0 and u (п, t) — 0 u (0, t) = (c1 + c2) (c4 + c3t) = 0 → (c1 + c2) (c4 + czt) = 0 u (T, t) (ci + cze) (c4 + c3t) = 0 C2e (ci + cze-*) (c4 + c3t) = 0 this condition is only possible if c1 = c2 = C3 = C4 = 0
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Transcribed Image Text:use initial conditions и (0, t) — 0 and u (п, t) — 0 u (0, t) = (c1 + c2) (c4 + c3t) = 0 → (c1 + c2) (c4 + czt) = 0 u (T, t) (ci + cze) (c4 + c3t) = 0 C2e (ci + cze-*) (c4 + c3t) = 0 this condition is only possible if c1 = c2 = C3 = C4 = 0
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