In this chapter, we use the series discussed in Chapter 11 to solve partial differential equations that arise in problems of mathematical physics.
- 12.3: Laplace's Equation in Rectangular Coordinates
- This section deals with a partial differential equation that arises in steady state problems of heat conduction and potential theory.
- 12.4: Laplace's Equation in Polar Coordinates
- Previously, we solved boundary value problems for Laplace’s equation over a rectangle with sides parallel to the x,y -axes. Now we’ll consider boundary value problems for Laplace’s equation over regions with boundaries best described in terms of polar coordinates.