Math Is Fun Forum

gourish

Member

Registered: 2013-05-28

Posts: 153

Taylor series

hi i am interested in learning Taylor series but i still haven't come across integration to a good depth can i still learn it and can anybody help me learn it because i didn't get any good sites to learn it from....

P.S. i don't even know when is the Taylor series used... i am just curious to learn about it

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"The man was just too bored so he invented maths for fun"
-some wise guy

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Taylor series

http://www.mathsisfun.com/algebra/taylor-series.html

How can calculators find the sines and cosines for all reals? It is done through the taylor series. This is one example of an usage.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: Taylor series

can i apply it to find the sum of sines where the angles are in Arithmetic progression? i mean i don't even know how to find the sum of such series by any method.... so the Taylor series can be helpful (if it can be used..)

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"The man was just too bored so he invented maths for fun"
-some wise guy

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Taylor series

I do not think you can apply it to find the sum of sines in an AP. You can post your problem however.

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: Taylor series

i posted my problem on the forum please help me find the answer for it.... it's bugging me from a long time...

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"The man was just too bored so he invented maths for fun"
-some wise guy

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

The Taylor series is the ultimate in osculating polynomials. Now who can say I ain't got no jargon in me?

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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.

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: Taylor series

osculating polynomials? can you elaborate please

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"The man was just too bored so he invented maths for fun"
-some wise guy

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

The osculating polynomials to quote Scheid not only match a given function at the specified value but also match the derivatives of the function at the specified points.

The Taylor polynomial for a given x0 is required to match the function and its first n derivatives. It is an osculating polynomial.

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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.

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Taylor series

I've found a nice video tutorial on it.

Why do you want to bite the newbie?

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'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

Bite? That is what an osculating polynomial is. Most people studying math only want the definition and the theorem, sometimes maybe the derivation.

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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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Taylor series

We don't here about osculating polynomials until graduate courses.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

They are rarely covered even in numerical analysis.

---

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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Taylor series

I recall them coming up in a talk with a professor some time back and he mentioned they cover it in some graduate level course. I don't remember the details though.

A very good tutorial for Taylor Series is http://tutorial.math.lamar.edu/Classes/ … eries.aspx
or http://www.sosmath.com/calculus/tayser/ … ser01.html or http://www.math.hmc.edu/calculus/tutorials/taylors_thm/

Last edited by ShivamS (2014-05-28 07:49:21)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

One typical use is the problem of the railroad track.

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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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Taylor series

That does not involve that polynomial?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

I am not following you.

---

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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Taylor series

One typical use is the problem of the railroad track.

Use of what?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

The osculating polynomials.

---

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.

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Taylor series

That does not involve that polynomial?

I am not sure you can't use it to make the problem simpler, but you can solve it without that.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

Because the train must not derail on the curves the fit must not only take into account the collocation points it must fit the points of the first derivative too. this requires an osculating polynomial. All this is  comes from the Scheid book.

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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.

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: Taylor series

well i need the Taylor series only for basic applications....

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"The man was just too bored so he invented maths for fun"
-some wise guy

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

The Taylor series is the backbone of numerical analysis and indeed all numerics. You can derive Newton;s method, Euler's, Runge Kutta and many others. Basically all it does is replace a function at a specific point with a big osculating polynomial. Why is this advantageous/ because since the time of newton we know everything about polynomials. The desire to replace all other functions with them is strong.

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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.

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: Taylor series

well... is there a function which cannot be expressed in the form of polynomials...

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"The man was just too bored so he invented maths for fun"
-some wise guy

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Taylor series

There may be! I have never encountered one yet.

You probably like polynomials. Think of power series as "generalized" polynomials. Since (almost) all functions you encounter have a Taylor series, all functions can be thought of as "generalized" polynomials!

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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.

gourish

Member

Registered: 2013-05-28

Posts: 153

Re: Taylor series

well i am stuck with my post on sum of sines with angles in A.P. i still didn't get to prove it can you help me on that?

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"The man was just too bored so he invented maths for fun"
-some wise guy