I studied entry level maths at uni level - a prerequisite course for most STEM degrees to cover the relatively small amount of maths common to nearly all science fields.
Chapter 11 of 12 were Taylor polynomials and series, and it was listed as “optional”.
I looked at it once, read it aloud for my young son to fall asleep to, and never looked at it again.
Most aspects of our daily lives rely on Taylor series, polynomial expansion, and approximation theory in general. Everything built or planned using computer modeling software, down to the trig functions on your calculator… they all use polynomial approximations to allow a discrete mathematical machine to get us to within a certain error percentage of a continuous function in a timely manner.
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Ah yes, that tracks with the very surface level overview that I picked up from it. It was only when I saw the magic “optional” tag that I was like noooope!
Maybe I’ll have a look at it in more detail when I get a free summer 😊
Think of The Taylor Series as a way of systematically approaching the estimation other more difficult functions by starting from a particular point and reconstructing a graph function by stacking polynomials/exponents centered on that point like legos until you get a close enough shape.
Brook Taylor was absolutely brilliant though
