The mother of all formulas, Taylor and Maclaurin Series are pretty intimidating when you first see them. But once you get in the swing and see just how plug-and-chug they are, you can relax and focus on not messing up negative signs. Which is really what calculus is all about, if you think about it.
Intro to Taylor & Maclaurin Series
This video introduces these complicated series, and tries to show you that they're really not that bad. Also included are a couple of hot tips to help you memorize the nasty-looking Taylor Series expansion formula, and for those who want to "understand stuff", I spend about a minute explaining how the Taylor & Maclaurin expansions are really just linear approximations with an extra couple terms thrown on.
Taylor & Maclaurin Series Examples
In this video we go through some more examples of working out the expansions of a few common functions. Hopefully by the end of this, you'll be getting the hang of these things so we can start calculating stuff with them.
Approximating Functions With Taylor & Maclaurin Series
Finally, it's time to start approximating some stuff! Why approximate anything when I can just type it into my calculator, you ask? Well, mister, put yourself in the shoes of someone in the 1700's, before they had calculators and slide rules (look it up), and you'd be thanking your lucky stars that you have a way to calculate ln(1.1) and e.1. Yeah, not so sassy now are you?
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