Mathematical Methods in the Physical Sciences · Problem 2.8

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · laplace-equation-rectangular-plate

Problem

Find the steady-state temperature distribution in a rectangular plate 30 cm by 40 cm given that the temperature is

0^\circ

along the two long sides and along one short end; the other short end along the

x

axis has temperature

T = \begin{cases} 100^\circ, & 0 < x < 10, \\ 0^\circ, & 10 < x < 30. \end{cases}