I’m doing something that I should have done a long time ago: collect past series of posts into a single, easy-to-reference post. The following posts formed my series on how I remind students about Taylor series. I often use this series in a class like Differential Equations, when Taylor series are needed but my class has simply forgotten about what a Taylor series is and why it’s important.
Part 1: Introduction – Why a Taylor series is important, and different applications of Taylor series.
Part 2: How I get students to understand the finite Taylor polynomial by solving a simple initial-value problem.
Part 3: Making the jump to an infinite series, and issues about tests of convergence.
Part 4: Application to , and a numerical investigation of speed of convergence.
Part 5: Application to and other related functions, including and .
Part 6: Application to and , and Euler’s formula.