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Series: Calculus: Power Series Function Representations

About this Series

  • Lessons: 4
  • Total Time: 0h 23m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/29/2009
  • Last Updated At: 07/20/2010

In this four-lesson series, we'll learn about the calculus behind power series and how we can use the power series to integrate functions that we otherwise are unable to integrate.

Inside its interval of convergence a power series defines a function that you can differentiate and integrate. Using calculus on a power series is a powerful tool for finding alternate representations of functions. That is, you can find power series for new functions by applying calculus to known power series. Integrating known power series results in alternative representations of new functions.

Not all functions can be integrated, but you can use power series to evaluate some integrals that you couldn't evaluate before. If a function has a difficult integral, you may want to integrate its power series expression instead. In this way, power series allow you to integrate functions you could not integrate with the other methods you have learned. The disadvantage of using power series to integrate is that the result is not a recognizable function. Instead it's a power series. But if none of the other integration techniques work, that's a small price to pay.

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

2174 lessons

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Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

None of the lesson in this series have been reviewed.

Below are the descriptions for each of the lessons included in the series:

Supplementary Files: