Mr. Integral

THE BIG IDEA

Power Series and Taylor Approximation

How can a polynomial stand in for a complicated function?

A power series packages a function into coefficients near a center. First find where the series works, then differentiate, integrate or truncate it while tracking endpoints and error.

Begin the first lesson →See the lesson route ↓

3 lessons · No deadlines or locked lessons

SEE THE CONNECTIONS

How the ideas fit together.

A map of the main ideas. Follow a node to its lesson.

  1. Start with01Convergence region
  2. inside that region, transform with02Series operations
  3. matching derivatives constructs03Taylor models

YOUR LEARNING ROUTE

One idea at a time.

Read the explanation, use the visualization, then try the check before opening its reasoning.

Keep the unit cheat sheet handy →
Lessons in this unit3 lessons
  1. 01Power Series and Endpoint TestsFind a radius of convergence and test each boundary point separately.
  2. 02Differentiating and Integrating Power SeriesBuild new series from a known geometric series while tracking constants and convergence.
  3. 03Taylor Polynomials and RemaindersApproximate a smooth function near a center and justify accuracy using an explicit remainder bound.