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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

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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'

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

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.****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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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'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

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.****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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I get it. Thank You

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

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.****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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Yes

But what is an elementary function?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

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.****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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okay

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

For instance:

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

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What is Si?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

It is a function that is defined like this:

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The bumpkins invented it?

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

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

But which is which?

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The one with the Si does not look like elementary

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

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.****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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But it is also an integral

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
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There are no integrals on the RHS. That is in elementary form by the definition.

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'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

y(0) = 1

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

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 580

Hello:

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

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

Hi;

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3.15483

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

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****bumpkin**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 108,522

**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.**

**Online**