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#1 2012-10-26 03:13:51

Karrl
Guest

Taylor series

How do I find taylor series of a function?Is there analysis method,formula or something else?

#2 2012-10-26 03:20:00

bob bundy
Registered: 2010-06-20
Posts: 8,155

Re: Taylor series

hi Karrl

Welcome to the forum.

Yes, there is a formula.  Have a look at:

http://en.wikipedia.org/wiki/Taylor_series

Bob

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2012-10-26 03:30:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

Hi;

What is the function?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#4 2012-10-26 03:30:28

Karrl
Guest

Re: Taylor series

If you meant the first formula,then what are the variables x and a?

#5 2012-10-26 03:31:19

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

Helps a lot to see the particular function you have in mind and what is the point of expansion.

x is the independent variable and a is the point of expansion.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#6 2012-10-26 04:00:05

Karrl
Guest

Re: Taylor series

So for f(p),p=x,and a is any point I want?And will there be taylor series for every function

#7 2012-10-26 04:04:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

Any function that has derivatives that exist at the point of expansion. You can pick any point but that does not mean it will converge.
Sometimes the usual method will not work and you must use another.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#8 2012-10-26 04:29:02

Karrl
Guest

Re: Taylor series

Could you show me an example of taylor series(not the e^x,I know that)and explain how the series is found.

#9 2012-10-26 04:38:18

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

That is a Taylor series expanded around zero. When it is expanded around zero it is called a Mclaurin series.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2012-10-26 04:44:55

Karrl
Guest

Re: Taylor series

What is the difference in expanding around different points?

#11 2012-10-26 04:48:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

The formula or method used is slightly different. Here it is expanded around a and is called a Taylor series.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2012-10-26 04:57:41

Karrl
Guest

Re: Taylor series

So,all values of a will estimate same?if not then what is the best value for a?

#13 2012-10-26 05:07:23

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

The purpose of the series is to numerically evaluate a value of a function.
An example will make all of it clearer.

Supposing you want to evaluate sin(.1)? Taylor series usually only converge a small distance from the point of expansion. We choose zero because it is close to .1.

Now you plug into x the value that you are looking for. x = .1

The actual value of Sin(.1) is 0.09983341664682815

The approximation is a good one. This is an easy one. In practice they are usually trickier.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#14 2012-10-26 12:44:29

Karrl
Guest

Re: Taylor series

So the close a is to x,the better

#15 2012-10-26 15:25:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Taylor series

Hi;

So the close a is to x,the better

Exactly. The Taylor polynomial has a limited range from the point of expansion.

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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