Mathematical Methods in the Physical Sciences · Problem 10.25

FUNCTIONS OF A COMPLEX VARIABLE — Mary Boas

Mathematics — Methods · miscellaneous-pde-steady-state-temperature

Problem

Find the steady state temperature in a semi-infinite plate covering the region

0 \leq y \leq 1

x > 0

, if the edges along the

x

axis and

y

axis are insulated (see Chapter 13, Problem 2.14) and the top edge is held at

u(x,1) = \begin{cases} 100^\circ, & 0 < x < 1, \\ 0^\circ, & x > 1. \end{cases}

Hint: Look for a solution as a Fourier integral. Leave your answer as an integral (just as we usually give answers as series.)