Question

HELP! I'm in calculus class and they keep talking about Taylor series. I don't understand what's going on. Please explain what is Taylor series and what is Mclaurin series and how they are similar and how they are different.

Answer 1

Essentially, the Taylor series is the default equation whereas the Mclaurin series is one in which the p can change. Whereas both are used to write nonzero terms, only one has different p values.

Answer 2

Essentially the two series serve the same purpose. The only difference between the two is that in Mclaurin series the center is always zero.

Answer 3

Taylor series and the associated McLauran series are + x^5
series of infinite terms allowing us to find some common mathematical functions
eg
sin(x) = x - x^3/3! + x^5/5! - x^7/7! + .... , x must be in radians
e^x = 1 + x + x^2/2! + x^3/3! + ....
ln(1+x) = x - x^2/2 + x^3/3 - x^4/4 + ...., -1 < x < 1

They must converge, even though some of them might diverge initially.

google Taylor series, there are some really good youtubes from the KhanAcademy

Answer 4

First sentence should say:
Taylor series and the associated McLauran series are series of infinite terms allowing us to find some common mathematical functions.

Answer 5

Both are the same idea
Taylor expands starting at some point where x = a
terms are something times (x-a)^n

Maclaurin assumes a = 0, terms are in x^n

thus Maclaurin is a special case of Taylor where we start at x = 0