Boundary-Value Problems in Rectangular Coordinates Chapter 12 Boundary-Value Problems in Rectangular Coordinates

FIGURE 12.2.1 One-dimensional flow of heat

FIGURE 12.2.2 Flexible string anchored at x = 0 and x = L

FIGURE 12.2.3 Steady-state temperatures in a rectangular plate

FIGURE 12.2.4 Plucked string

FIGURE 12.3.1 Temperatures in a rod of length L

FIGURE 12.3.2 Graphs of (17) when one variable is held fixed

FIGURE 12.3.3 Rod losing heat in Problem 5

FIGURE 12.4.1 Frames of a CAS “movie”

FIGURE 12.4.2 First three standing waves

FIGURE 12.4.3 Initial displacement in Problem 7

FIGURE 12.4.4 Initial displacement in Problem 8

FIGURE 12.4.5 Initial displacement in Problem 9

FIGURE 12.4.6 Initial displacement in Problem 10

FIGURE 12.4.7 Vibrating bar in Problem 11

FIGURE 12.4.8 Vibrating string in Problem 12

FIGURE 12.4.9 Simply supported beam in Problem 17

FIGURE 12.5.1 Steady-state temperatures in a rectangular plate

FIGURE 12.5.2 Surface is graph of partial sums when f(x) = 100 and a = b = 1 in (10)

FIGURE 12.5.3 Solution u = Solution u1 of Problem 1 + Solution u2 of Problem 2

FIGURE 12.5.4 Plate in Problem 11

FIGURE 12.5.5 Plate in Problem 12

FIGURE 12.6.1 Plate in Problem 11

FIGURE 12.7.1 Twisted shaft in Example 2

FIGURE 12.7.2 Surface is the graph of a partial sum of (17) in Example 2

FIGURE 12.7.3 Angular displacements as a function of time at various cross sections of the rod in Example 2

FIGURE 12.7.4 Vibrating cantilever beam in Problem 11

FIGURE 12.8.1 (a) Rectangular plate and (b) rectangular membrane

FIGURE 12.8.2 Rectangular parallelepiped in Problems 5 and 6

FIGURE 12.R.1 Initial velocity g(x) in Problem 5

FIGURE 12.R.2 Square plate in Problem 7

FIGURE 12.R.3 Semi-infinite plate in Problem 8

FIGURE 12.R.4 Infinite plate in Problem 10