Overview
Power series are like infinite polynomials. Can they be added? Multiplied? Integrated? If so, we can use power series to approximate functions like the error function.
Lecture Video and Notes
Video Excerpts
» Clip 1: Power Series Multiplication (00:03:00)
From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006
» Clip 2: Derivative of a Power Series (00:02:00)
From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006
» Clip 3: Integral of a Power Series (00:04:00)
From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006
» Clip 4: Substitution of Power Series (00:04:00)
From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006
Worked Example
Summing Infinite Series by Comparing to Taylor Series
Lecture Video and Notes
Video Excerpts
» Clip 1: Power Series Expansion of the Error Function (00:03:00)
From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Power Series Expansion of the Error Function
> Download from iTunes U (MP4 - 87MB)
> Download from Internet Archive (MP4 - 87MB)
Recitation Video
Integration of Taylor's Series
> Download from iTunes U (MP4 - 17MB)
> Download from Internet Archive (MP4 - 17MB)