Calculus 2     Lesson 11.9     Representation of Functions as Power Series
The following topics are the most important. Typical exercises from Calculus, 7th edition-Early Transcendentals, by James Stewart, are assigned at the end of each objective.  

In smaller print following the objective is a guide for the reading assignment in the form of page numbers in the text and notes regarding the reading about the objective.
1. Form new power series from existing power series using the following operations on power series and tell the radius or convergence of the new series.
1a. replace (x-a) by b( cx d)k in a series p751#3,4,6
P747 The definition of the sum of a geometric series is given in box 1 on this page.  From the basic formula, a/(1-u) = a + au + au 2 + ... decide what a and u are in the process.  Look at Example 1 if there is a 1 + u in the denominator.  Look at Example 2 if there is a constant b, not equal to 1, in the b + u in the denominator.
  P747 Look at the video in the ebook on Webassign. Example 1
1b. multiply or divide a series by b(x-a)k p752#17,23
P748 Look at Example 3 if there is a variable term in the numerator.
1c. add or subtract two series p751#11
P747 After using partial fractions, use this definition in box 1 on this page for each of the fractions and combine as needed.
1d. differentiate a series p751#13
P748 The theorem governing differentiating the power series term by term is given in box 2 on this page.  Note that this process is only valid on the interval of convergence of the power series.  Look at Examples 4 and 5.
  P749 Look at the video in the ebook on Webassign. Example 5
1e. integrate a series p752#20,27,29
P749 The theorem governing integrating the power series term by term is given in box 2 on this page.  Note that this process is only valid on the interval of convergence of the power series.  Look at Examples 6 and 7.
  P750 Look at the video in the ebook on Webassign. Example 7
P750 Write the integrand as a power series, integrate term by term if the limits are within the interval of convergence, and then evaluate (or estimate) the result with the limits of integration.  Look at Example 8.
Maple Assignment:  none