ABSTRACT
This chapter briefly examines the common analytical methods and thereby puts numerical methods in proper perspective. The most commonly used analytical methods in solving electromagnetics (EM)-related problems include: separation of variables; series expansion; conformal mapping; and integral methods. The chapter emphasizes the method of separation of variables for solving a partial differential equation (PDE). It applies the method of separation of variables to PDEs in rectangular, circular cylindrical, and spherical coordinate systems. Orthogonal functions usually arise in the solution of PDEs governing the behavior of certain physical phenomena. These include Bessel, Legendre, Hermite, Laguerre, and Chebyshev functions. The chapter applies the idea of infinite series expansion to those PDEs in which the independent variables are not separable or, if they are separable, the boundary conditions are not satisfied by the particular solutions. In many practical situations, no solution can be obtained by the analytical methods, and one must therefore resort to numerical approximation or graphical or experimental solutions.
