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#101 2011-11-08 22:50:56
- Maiya
- Member
- Registered: 2011-08-11
- Posts: 124
Re: Naturual Logarithms
ya that series okay but,
how did that series come into existence............
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#102 2011-11-08 23:01:35
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Naturual Logarithms
Hi;
That series is called a Maclaurin series and is result of two men. Brooke Taylor and Colin Maclaurin. It comes from the formula:
Want to see exactly how?
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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#103 2011-11-09 23:09:22
- Maiya
- Member
- Registered: 2011-08-11
- Posts: 124
Re: Naturual Logarithms
hello bobbym;
sure i'd like to see how.........
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#104 2011-11-09 23:23:26
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Naturual Logarithms
Start with the function:
This function is unique in continuous mathematics because it is the only one whose derivative is the function itself. In math speak:
Because of this it is easy to get the Taylor series of it.
We now plug in to the Taylor expansion of e^x.
To now get e, which is e^1 we plug into the above expansion with x = 1.
Which is how that series comes about as being equal to e.
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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#105 2011-11-09 23:33:41
- Maiya
- Member
- Registered: 2011-08-11
- Posts: 124
Re: Naturual Logarithms
thank you Bobbym
that was very useful.........
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#106 2011-11-09 23:36:39
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Naturual Logarithms
The Taylor series is very useful in all branches but especially in numerical mathematics. One nice fact about it is that when you find it for a particular function it is unique. In other words if a function has a Taylor series expansion there is one and only one.
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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