Boundary-Value Problems in Other Coordinate Systems Chapter 13 Boundary-Value Problems in Other Coordinate Systems

FIGURE 13.1.1 Polar coordinates of a point (x, y) are (r, )

FIGURE 13.1.2 Dirichlet problem for a circle

FIGURE 13.1.3 Semicircular plate in Example 2

FIGURE 13.1.4 Infinite plate in Problem 5

FIGURE 13.1.5 Quarter-circular plate in Problem 8

FIGURE 13.1.6 Wedge-shaped plate in Problem 10

FIGURE 13.1.7 Annular plate in Problem 11

FIGURE 13.1.8 Semiannular plate in Problem 14

FIGURE 13.1.9 Quarter-annular plate in Problem 17

FIGURE 13.1.10 One eighth-annular plate in Problem 18

FIGURE 13.2.1 Initial displacement of a circular membrane in Example 1

FIGURE 13.2.2 Standing waves

FIGURE 13.2.3 Frames of a CAS “movie”

FIGURE 13.2.4 Cylindrical coordinates of a point (x, y, z) are (r, , z).

FIGURE 13.2.5 Circular cylinder in Example 2

FIGURE 13.2.6 Infinite cylinder in Problem 11

FIGURE 13.2.7 Composite circular plate in Problem 13

FIGURE 13.2.8 Oscillating chain in Problem 15

FIGURE 13.3.1 Spherical coordinates of a point (x, y, z) are (r, ,  ).

FIGURE 13.3.2 Dirichlet problem for a sphere in Example 1

FIGURE 13.3.3 Hollow sphere in Problem 5

FIGURE 13.3.4 Container of fluid in Problem 10

FIGURE 13.R.1 Wedge-shaped plate in Problem 5

FIGURE 13.R.2 Infinite plate in Problem 6

FIGURE 13.R.3 Circular plate in Problem 7

FIGURE 13.R.4 Cylinder in Problem 15