Calc 2, Lec 30A, Error in Taylor Approximation to e^(x), Using Series for Differential Equations

Calculus 2, Lecture 30A.

(0:00) Announcements and class plan.
(1:43) Example 1: Error estimates for f(x) = e^(x): how big should n be so that the error in using a Taylor polynomial to approximate f(x) is less than or equal to 0.001 for all x between -0.5 and 0.5?
(14:57) Example 2: Power series solution of the differential equation dy/dx = y with initial condition y(0) = 1 (initial-value problem IVP).
(21:58) Example 3: Solve dy/dx = y^2, y(0) = 1 by separation of variables first and then by using power series.
(26:13) Example 3 (continued): Solve dy/dx = y^2, y(0) = 1 by using power series.