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#1 2012-10-27 02:13:51
- Karrl
- Guest
Taylor series
How do I find taylor series of a function?Is there analysis method,formula or something else?
#2 2012-10-27 02:20:00
- bob bundy
- Moderator
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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
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
#3 2012-10-27 02:30:18
- bobbym
- Administrator
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Re: Taylor series
Hi;
What is the function?
In mathematics, you don't understand things. You just get used to them.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#4 2012-10-27 02:30:28
- Karrl
- Guest
Re: Taylor series
If you meant the first formula,then what are the variables x and a?
#5 2012-10-27 02:31:19
- bobbym
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#6 2012-10-27 03:00:05
- 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 2012-10-27 03:04:51
- bobbym
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#8 2012-10-27 03:29:02
- 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 2012-10-27 03:38:18
- bobbym
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#11 2012-10-27 03:48:51
- bobbym
- Administrator
Offline
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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#12 2012-10-27 03:57:41
- Karrl
- Guest
Re: Taylor series
So,all values of a will estimate same?if not then what is the best value for a?
#13 2012-10-27 04:07:23
- bobbym
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.
#15 2012-10-27 14:25:25
- bobbym
- Administrator
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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.
90% of mathematicians do not understand 90% of currently published mathematics.
I am willing to wager that over 75% of the new words that appeared were nothing more than spelling errors that caught on.