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/sci/ - Science & Math

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3215962 No.3215962 [Reply] [Original]

What are series used for? Why is it important to know if they converge (absolutely or not) or diverge?

Why do we learn about them in calculus II? Is there some significance for placing it there?

I'm told series are used in computer science and other fields. Any applications?

>> No.3215978

Rational numbers: able to be represented as the quotient of two nonzero integers.

Irrational numbers: able to be represented as the sum of a series of rational numbers.

>> No.3215981

>What are series used for?
What are functions used for? A series is a concept that is spread all over math, it's hard to say what it's used for exactly. You can view a series as the analogon of an integral for discrete functions, but that reeeeally doesn't do it justice.
>Why is it important to know if they converge
Why is it important to know that <span class="math">\pi[/spoiler] is positive? Convergence behaviour is one of the, if not *the*, most important property of a series.

>Any applications?
You bet.

>> No.3215991

Finite series are a big deal in comp sci.
Infinite series are a big deal in physics.
Both are everywhere in classical and modern mathematics.

>> No.3216089

And what would those applications be?

>> No.3216096

>>3216089
That's like asking what the application of numbers would be.

>> No.3216099
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3216099

>>3216089

They are used fucking everywhere in Electrical Engineering. Fourier transforms make your computer possible.

>> No.3216111

>>3216096

OK and why would you ignore that question .. it's legit .. To you maybe trivial , but still legit ..

Can you answer this one with few concrete examples ?

>> No.3216118

>>3216111

Are you blind?
Look at the post above yours.

>> No.3216119

>>3216089
An easy example would be the computational complexity of an algorithm. Finite series are used here.
Another example would be in differential equations where infinite series are truncated at a certain point to yield a close enough approximation to a solution.

>> No.3216132

>>3216111
- Taylor series allow you to approximate functions around a certain point, which is heavily used in physics.
- Fourier series approximate functions by sines. Also heavily used.
- Many functions can be defined as some power series, for example <span class="math">\exp[/spoiler] and <span class="math">_pF_q[/spoiler].

>> No.3216136

anybody that tells you there's an application in anything you learn in calculus is lying to you

even the best of engineers avoid calculus as much as possible and do everything in their power to keep design arithmetic based

the only people who need higher level math are faggy math majors who are useless, and phsyciscians in the lab who are only slightly less useless

>> No.3216146

>>3216089
Most often, for calculating approximate numerical results which are not integers. For example, I want to multiply <span class="math">\sqrt{2}[/spoiler] by <span class="math">\pi[/spoiler]. I approximate <span class="math">\sqrt{2}[/spoiler] by the truncated series

1.4142135623730950488016887242097

and <span class="math">\pi[/spoiler] by the truncated series

3.1415926535897932384626433832795

which, multiplied together give me

4.44288293815836624701588099006069565609527138763000160783171115

or

44428829381583662470158809900607

where I truncate the terms where I don't have accuracy. You may be familiar with this technique.

>> No.3216149
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3216149

>>3216136
>Thinks airplanes can be built with long division and the plus button on a calculator

>> No.3216157
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3216157

check this shizzle out: using the MAGIC of geometric series you can show that the area of this object is finite but the length of its perimeter is infinite. Also the curve is nowhere differentiable since it's "all corners"

>> No.3216158

>>3216149
No, long division involves a series representation of real numbers, so that's not allowed either.

>> No.3216162

>>3216158
Only rationals then. Glad we could resolve the contradiction.

>> No.3216175

>>3216146
CORDIC methods

>> No.3216176

Thanks /sci/. That was more of what I was looking for.

I was just wondering why it seems to be randomly stuck in calculus II of all places but now I see why.

>>3216157

Interesting...is this related to Gabriel's horn?

>> No.3216207

>>3216176
only if you give it the same colouring paradox: i can take a marker and try to trace out the koch curve but i'll never be able to, yet i can colour in its area thus tracing its perimeter. Both this and the paradox of colouring gabriel's funnel is resolved in the same way.