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#26 2014-05-07 02:36:11

Agnishom
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From: The Complex Plane
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Re: Euler's Method Tutorials

When you solve an equation you find the values of the variable that make the equation true. When you solve a DE you find the functions that make the DE true.

Given f' and f(x) for some x, euler's method gives us the value of f(y) for some y. But that is not solving the DE since it is not finding f


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#27 2014-05-07 02:38:31

Agnishom
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Re: Euler's Method Tutorials

Do you understand what we have done so far concerning the numerical solution of a DE by Euler's method?

I have. But I would be grateful if you would write down the recurrence formula


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#28 2014-05-07 02:38:42

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

Numerically solving is the correct phrase. You always have to remember the context of the discussion to understand English. When I use solve here it has a different meaning than solve in an analytical discussion.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#29 2014-05-07 02:42:00

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
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Re: Euler's Method Tutorials

I asked you what is 'solving'. You said:

When you solve an equation you find the values of the variable that make the equation true. When you solve a DE you find the functions that make the DE true.


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#30 2014-05-07 02:43:07

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

That is for using analytical methods. Getting an exact answer. Numerically solving I assumed you knew.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#31 2014-05-07 02:47:36

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
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Re: Euler's Method Tutorials

I get it. Thank You


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#32 2014-05-07 02:51:40

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

The numerical methods use algorithms to get the answer without solving the DE. This is extremely useful because only a few DE's can be solved in terms of elementary functions. Or sometimes the answer is too complicated.

Want to do another one?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#33 2014-05-07 03:04:59

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Euler's Method Tutorials

Yes smile

But what is an elementary function?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#34 2014-05-07 03:09:23

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

Wikipedia wrote:

In mathematics, an elementary function is a function of one variable built from a finite number of exponentials, logarithms, constants, and nth roots through composition and combinations using the four elementary operations (+ – × ÷). By allowing these functions (and constants) to be complex numbers, trigonometric functions and their inverses become included in the elementary functions (see trigonometric functions and complex exponentials).


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#35 2014-05-07 03:13:51

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
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Re: Euler's Method Tutorials

okay


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#36 2014-05-07 03:17:11

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

For instance:

Which is in terms of elementary functions and which is not?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#37 2014-05-07 03:24:04

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
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Re: Euler's Method Tutorials

What is Si?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#38 2014-05-07 03:25:55

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

It is a function that is defined like this:


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#39 2014-05-07 03:28:25

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
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Re: Euler's Method Tutorials

The bumpkins invented it?


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#40 2014-05-07 03:38:25

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

No, it was so useful they defined and gave it a name.

But which is which?


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#41 2014-05-07 03:49:42

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
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Re: Euler's Method Tutorials

The one with the Si does not look like elementary


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#42 2014-05-07 03:50:48

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

That is correct. It is an integral which is not an elementary function. The other one being a linear combination of sines and cosines is.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#43 2014-05-07 04:22:00

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
Website

Re: Euler's Method Tutorials

But it is also an integral


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#44 2014-05-07 04:34:34

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

There are no integrals on the RHS. That is in elementary form by the definition.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#45 2014-05-07 04:35:08

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
Website

Re: Euler's Method Tutorials

up


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#46 2014-05-07 04:49:48

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

y(0) = 1

What is y(1)? Compute using Euler's.


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#47 2014-05-07 15:13:13

ElainaVW
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Registered: 2013-04-29
Posts: 291

Re: Euler's Method Tutorials

Hello:

Last edited by ElainaVW (2014-05-07 15:13:32)

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#48 2014-05-07 15:14:09

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials

Hi;


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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#49 2014-05-07 17:37:14

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 16,873
Website

Re: Euler's Method Tutorials

3.15483

Last edited by Agnishom (2014-05-07 18:17:01)


'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'
'Humanity is still kept intact. It remains within.' -Alokananda

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#50 2014-05-07 21:28:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 86,776

Re: Euler's Method Tutorials


In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.

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