Session 100: Operations on Power Series

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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

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» Clip 1: Power Series Multiplication (00:03:00)

» Accompanying Notes (PDF)

From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 2: Derivative of a Power Series (00:02:00)

» Accompanying Notes (PDF)

From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 3: Integral of a Power Series (00:04:00)

» Accompanying Notes (PDF)

From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006

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» Clip 4: Substitution of Power Series (00:04:00)

» Accompanying Notes (PDF)

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

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» Clip 1: Power Series Expansion of the Error Function (00:03:00)

» Accompanying Notes (PDF)

From Lecture 39 of 18.01 Single Variable Calculus, Fall 2006

Recitation Video

 

Integration of Taylor's Series

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