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categoryالرياضيات schoolبكالوريوس event_available2026-07-15

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Solve Laplace's equation მłu მłu + + ay2 аги az² = 0 ax² for the steady-state temperature u(x, y, z) in the rectangular parallelepiped shown in the figure below. x (a, b, c) The top (z = c) of the parallelepiped is kept at temperature f(x, y) and the remaining sides are kept at temperature zero. u(x, y, z) = ∞ + Ẻ 00 Amn sinh(comm2) sin( 2 x) sin() ΜΠ where (@mn)² = a m1n 1 b a 4 and Amn = ab sinh(@mnC) f(x, y) dx dy.

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