To generate the series solution of differential equations about ordinary points.
The series solutions to the initial value problems
| y'' + y = 0, | (1) |
| y(0) = 0, y'(0) = 1, | (2) |
and
| y'' - xy = 0, | (3) |
| y(0) = -1, y'(0) = 2, | (4) |
are found. The students are taking step by step through the procedure. The true solution for these IVP's as well as the first 5 distinct Taylor series approximations are plotted to show their correlation.
The assignments include a discussion on why the Taylor series of sin(x)
is given by 
in terms
of uniqueness of initial value problems. Students are also asked to find
the series solution of an initial value problem, the true solution of the
problem, and graph the first 5 distinct Taylor series approximations as
well as the true solution on a single graph and comment.
An example showing how Maple can be used to generate the Taylor series polynomial approximations for (1),(2) from the recurrence relation is provided for the students and the end of the lab.
Return to Differential Equations: Explorations
Through Technology.