ABSTRACT
This chapter focuses on two basic methods — an “algebraic method” and a “Taylor series method” — for computing our power series. The main interest will be in the algebraic method. It is more commonly used and is the method extended to obtain “modified” power series solutions when we do not quite have the desired analyticity. But the algebraic method is not well suited for solving all types of differential equations, especially when the differential equations in question are not linear. For that reason (and others) the Taylor series method is introduced. The individual steps in algebraic method are, for the most part, simple and only involve elementary calculus and algebraic computations — but there are a lot of the elementary computations, and an error in just one can throw off the subsequent computations with disastrous consequences for student final answer.
