Advanced Engineering Mathematics, 7th Edition

14.1 Polar Coordinates

INTRODUCTION

All the boundary-value problems that have been considered so far have been expressed in terms of rectangular coordinates. If, however, we wish to find temperatures in a circular disk, in a circular cylinder, or in a sphere, we would naturally try to describe the problems in polar coordinates, cylindrical coordinates, or spherical coordinates, respectively.

Because we consider only steady-state temperature problems in polar coordinates in this section, the first thing that must be done is to convert the familiar Laplace’s equation in rectangular coordinates to polar coordinates.

Laplacian in Polar Coordinates ...