Science:Infinite Series Module/Units/Unit 3/3.2 Taylor Series

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What This Lesson Covers

In this lesson we will introduce a few concepts:

  • representation of functions with a power series
  • conditions for convergence of a power series
  • radius of convergence of a power series

Learning Objectives

After reading this lesson and completing a sufficient number of exercices on paper, you should be able to

  • expand a given function in a Maclaurin series
  • determine the radius of convergence of a Taylor series


  1. A motivating problem
  2. The Taylor and Maclaurin expansions
  3. The Maclaurin expansion of ex
  4. The Maclaurin expansion of sin(x)
  5. The Maclaurin expansion of cos(x)
  6. A list of Maclaurin expansions
  7. Videos on Taylor Series