Mathematical Methods (10/24.539)

VII. Power Series Solution Method

Introduction

For second or higher order systems, except for some special cases, we have only been able to generate analytical solutions for linear constant coefficient systems. This section of notes highlights the Power Series solution scheme, which gives a fairly general procedure to handle linear variable coefficient systems. In practice, however, this method is very tedious to apply and the resultant infinite series solutions are often difficult to use in subsequent manipulations and analyses. Sometimes a closed form solution can be written, but this is a special case rather than the rule.

Although not the method of choice in most practical applications, the Power Series solution method is the primary tool for solving a wide range of classical second order systems which give rise to many of the special functions that are used routinely in engineering design and analysis. Thus, we will study this technique as a tool for solving some model second order variable coefficient systems, and as background so that the study of Special Functions can be addressed in a logical manner (in the next section of these notes).

After a brief theoretical overview, the material here on the Power Series method focuses on the illustration of the method via actual applications to three specific problems, as follows:

10/24.539 Lecture Notes by Dr. J. R. White, UMass-Lowell (updated October 1998).

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