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MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Separation of Variables

Just finished off this Diff Eq page: Separation of Variables

It would be really nice if everyone could check it for mistakes before I make it live on the website.

Comments and suggestions welcome too.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Separation of Variables

Hi MIF

The page is awesome! I can't find anything wrong or missing.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

Re: Separation of Variables

Hi MathsIsFun,

The page on Variables Separable is excellent!

The illustrations, graphs and examples are remarkable.

The Pierre François Verhulst population growth rate is relevant and worth mentioning, as you stated.

Last edited by Jai Ganesh (2014-06-15 13:26:44)

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: Separation of Variables

hi MathsIsFun

Well done.  An excellent page.  Just one point.  I hope I'm right about this.

You start with

Separation of Variables is a special method to solve some Differential Equations

Then you have an example of a DE.  Then you follow with

It only works for First Order (with only a first derivative like above) Differential Equations.

Now the 'It' refers to 'Separation of Variables', but, unless I'm very much mistaken, the example is an example of a DE., not a Separation DE.

That could confuse some readers, as an example that cannot be done by this method comes in the middle of two sentences that are linked by the use of 'It'.

Suggestion:

(1)  Choose another example, where Separation can be used.

or

(2) Start by suggesting users jump to Differential equations (http://www.mathsisfun.com/calculus/differential-equations.html) to learn what a DE. is before returning to learn about this method.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Separation of Variables

Hi MIF;

Nice page as always. My concern is at the top.

It only works for First Order (with only a first derivative like above) Differential Equations.

I think I have seen it done on second order and higher and on partial DE's too. At least for some of the simpler ones.

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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.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Separation of Variables

Are you sure? It doesn't seem possible without reducing it to a First Order DE.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Separation of Variables

No, I am not sure. I have just seen some pdf's where it was used on a partial DE and another where they claimed to have used it on a coupled system of second ordered DE's. I can not get it to work on even a simple second order like

so maybe I just am mistaken. But are not the first 2 reasons enough to drop the line "It only works for First Order (with only a first derivative like above) Differential Equations?"

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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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Separation of Variables

Have made changes to the page Separation of Variables

Is it looking better now? Did I miss any of your points in the rewrite?

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

Jai Ganesh

Administrator

Registered: 2005-06-28

Posts: 48,425

Re: Separation of Variables

Hi MathsIsFun,

The page on Separation of Variables looks remarkable!

I don't think any further improvement is required.

Great job, MathsIsFun!

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It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Separation of Variables

Hi MIF;

Can you number or letter the examples then we can refer to them easier?

For

can we not also consider the negative of your answer a solution too?

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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.

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,713

Re: Separation of Variables

Makes sense to me, I will put ±, thanks.

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"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

ShivamS

Member

Registered: 2011-02-07

Posts: 3,648

Re: Separation of Variables

Looks pretty good!

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 24,996

Website

Re: Separation of Variables

Nice page.

Now, how do I use this to get the time-independent equation?

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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.