ABSTRACT
This chapter reviews analytic methods for solving partial differential equations (PDEs). Analytic solutions are of major interest as test models for comparison with numerical techniques. The emphasis has been on the method of separation of variables, the most powerful analytic method. The most commonly used analytical methods in solving EM-related problems include separation of variable, series expansion method, conformal mapping, integral methods, and perturbation methods. Coordinate geometries other than rectangular Cartesian are used to describe many EM problems whenever it is necessary and convenient. 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. Although Hermite, Laguerre, and Chebyshev functions are of less importance in EM problems than Bessel and Legendre functions, they are sometimes useful and therefore deserve some attention. The chapter concludes by remarking that the most satisfactory solution of a field problem is an exact analytical one.
