A Collection of Problems on Mathematical Physics by B. M. Budak, A. A. Samarskii, A. N. Tikhonov, I. N. Sneddon, PDF

By B. M. Budak, A. A. Samarskii, A. N. Tikhonov, I. N. Sneddon, M. Stark and S. Ulam (Auth.)

ISBN-10: 008010021X

ISBN-13: 9780080100210

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11). Find the deflection of the string u{x, t) for ί > 0, if the string is excited at time r = 0 by a transverse impulse I = MVQ, transmitted to the mass Μ and directed along the axis of the spring. 26 COLLECTION OF PROBLEMS ON MATHEMATICAL PHYSICS [80 80. The mass Μ of the preceding problem, in oscillating, ex­ periences a frictional resistance proportional to the velocity. Find the reflected and transmitted waves, taking the wave u^(^x, t) = f(x—at) travelhng from the region x < 0 as the initial condition.

Solve the problem of propagation of electrical vibrations in an infinite conductor for the condition that GL=CR, (1) where G, L, C, R are the leakage conductance, self-inductance, capacity and resistance per unit length of the c o n d u c t o r t . The voltage and the current in the conductor at the initial time are given. 2. Problems for a Semi-infinite Region If only one end of a string* is far enough from the part of it under investigation so that a reflection from that end is n o t im­ p o r t a n t in the oscillations of this part, at least during the time interval being considered, then we arrive at the problem of the vibrations of a semi-infinite string 0 < x < + o o , where x = 0 corresponds to the " n e a r " end of the string.

192. igi are odd. and ^ ( . ) = Σ ^ ^ 44 COLLECTION OF PROBLEMS ON MATHEMATICAL PHYSICS [193 193. Prove that a representation of the solution of the b o u n d a r y value problem Utt = a'u^^+c^u+f(x, Akj^ t), = 0, w(jc,0) = 0 , 0 < X, ί < + 0 0 , 0<í<+cx), wXx,0) = 0, x = 0, 0

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A Collection of Problems on Mathematical Physics by B. M. Budak, A. A. Samarskii, A. N. Tikhonov, I. N. Sneddon, M. Stark and S. Ulam (Auth.)


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