At the end of the typical one quarter course on power series the students lack the means to decide 2 whether 1/(1]x ) has an expansion around any point 0, or the tangent has an expansion anywhere and the means to evaluate and predict errors. In using power series for computation the main problems are: 1) To predict a priori the number N of terms needed to do the computation with a specified accuracy; and 2) To find the coefficients aO, ., a N These are the problems addressed in the book. Typical computations envisioned are: -6 calculate with error 10 the integrals If/2 J (If/2-x)tan x dx o or...