Reminding students about Taylor series: Index

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 f(x) = e^x, and a numerical investigation of speed of convergence.

Part 5: Application to f(x) = \displaystyle \frac{1}{1-x} and other related functions, including f(x) = \ln(1+x) and f(x) = \tan^{-1} x.

Part 6: Application to f(x) = \sin x and f(x) = \cos x, and Euler’s formula.




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