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Taylor and MacLaurin Series

A series of free Calculus Video Lessons from PatrickJMT.

Taylor and Maclaurin Series - Example 1
An example of finding the Maclaurin series for a function is shown.

Taylor and Maclaurin Series - Example 2
A complete example of finding a Taylor series for the function ln(x) centered at a = 2 is shown.

Using Maclaurin/Taylor Series to Approximate a Definite Integral to a Desired Accuracy
This video uses Maclaurin/Taylor series and the Alternating Series Estimation Theorem to approximate a definite integral to within a desired accuracy.

Taylor's Inequality
Examples are shown using Taylor's Inequality. The first part shows that a series expansion is valid using Taylor's Inequality. The second part shows how to use Taylor's Inequality to estimate how accurate a Taylor Polynomial will be.

Taylor / Maclaurin Series Expansion - Proof of the Formula
Taylor / Maclaurin Series Expansion - Deriving the Formula. In this video, I show how to find the Taylor series expansion for a function, assuming that one exists! It is nothing too heavy: we just take derivatives and plug in the value at which we are centering the function. I do not find any Taylor series of specific functions in this video, nor do I justify when a Taylor series expansion is valid (not all functions have power series expansion!).

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