Don't understand the taylor expansion?

[Lengalicious]

Not sure under which forum this should have gone under, anyway can someone who really understands it explain it to me in as simple terms as they can, from what I'm getting its approximates something for a function or something? No idea.

 

[zhermes]

http://en.wikipedia.org/wiki/Taylor_series
http://mathworld.wolfram.com/TaylorSeries.html
http://cinderella.de/files/HTMLDemos/2C02_Taylor.html

 

[mathman]

Not sure under which forum this should have gone under, anyway can someone who really understands it explain it to me in as simple terms as they can, from what I'm getting its approximates something for a function or something? No idea.

It belongs in either general math or calculus. To understand Taylor series you need to understand calculus at least on an elementary level. It is very hard to explain otherwise.

 

[Claude Bile]

A Taylor series basically calculates a bunch of derivatives at some point in a parameter space and then extrapolates them to other points close to the initial point in the space.

The more derivatives you figure out the better you can predict what some function (of which said derivatives are taken) will be at some distance from the initial point.

Claude.

 

[pmacias]

Sure, I'd be happy to explain the concept of Taylor expansion to you. Taylor expansion, also known as Taylor series, is a mathematical tool used to approximate a function using a series of terms. It is named after the mathematician Brook Taylor who first described it in the 18th century.

In simple terms, Taylor expansion allows us to represent a complicated function as a sum of simpler functions, known as Taylor polynomials. These polynomials are built around a specific point, called the center, and the more terms we include in the expansion, the closer the approximation will be to the actual function.

This tool is particularly useful in situations where the function is too complicated to be easily evaluated or when we need to approximate a value that is not explicitly given. For example, if you want to know the value of a function at a certain point but only have information about the function at a nearby point, Taylor expansion can be used to approximate the value at the desired point.

I hope this explanation helps you understand the concept of Taylor expansion better. Please let me know if you have any further questions.