Solving Ordinary Differential Equations Using Power Series. Basics, Concepts & Methods

      Аннотация: The study of differential equation equations is a beautiful application of the ideas and techniques of calculus to our everyday lives. Unfortunately, the number of differential equations that can be solved by analytic techniques is very limited since most of the equations are cumbersome and complex. Their solutions can only be approximated using numerical techniques with appropriate initial and boundary value conditions. Applying power series technique however, is more systematic and standard basic method of arriving at the solutions of such differential equations analytically and thus the reason for this concisely presented book. In this book, some special second order ordinary differential equations are reviewed. Power series technique is described at ordinary points as well as at singular points (which can be removed called Frobenius Method) of differential equations. several examples are presented and special second order ordinary differential equations are solved and explained logically for easy understanding, to meet College and University students' need and extend hand to tutors of differential equations in solving ordinary differential equations with variable coefficients.

Ключевые слова: Bessel functions, Differential Equations, Legendre Polynomials, ordinary differential equations, power series, Series Solutions of Differential Equations, Frobenius Method