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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

'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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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,728

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,728

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.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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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'

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,728

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.**

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okay

'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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.****If it ain't broke, fix it until it is.**

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What is Si?

'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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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It is a function that is defined like this:

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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The bumpkins invented it?

'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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.****If it ain't broke, fix it until it is.**

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The one with the Si does not look like elementary

'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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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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.**

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But it is also an integral

'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****Administrator**- 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.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
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y(0) = 1

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

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**ElainaVW****Member**- Registered: 2013-04-29
- Posts: 508

Hello:

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

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,728

Hi;

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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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****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 103,728

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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