Please help with PDE in polar coordinates.

For Polar coordinates, and ,

, then

as

You can now put in , you'll get and

Let's just use an example where ##\theta =60^o##, so to every unit change of , will change for 2 unit. So

The same reasoning, . So using this example, which does not agree with the example I gave.

I am missing something, please help.

Re: Please help with PDE in polar coordinates.

I am puzzled as to what your question is . Your title refers to a "PDE in polar coordinates" but there is no PDE, just relations between Cartesian Coordinates and Polar Coordinates. In any case, from , so , not . Similarly, .

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**HallsofIvy** I am puzzled as to what your question is . Your title refers to a "PDE in polar coordinates" but there is no PDE, just relations between Cartesian Coordinates and Polar Coordinates. In any case, from

,

so

, not

. Similarly,

.

Thanks for the reply, but according to the derivation shown in my first post,

This is verified by more than one book.

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**Alan0354** For Polar coordinates,

and

,

, then

as

You can now put in

, you'll get

and

Let's just use an example where ##\theta =60^o##, so to every unit change of

,

will change for 2 unit. So

The same reasoning,

. So using this example,

which does not agree with the example I gave.

I am missing something, please help.

if . If , then , so .

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**SlipEternal**

Thanks for the reply. This is just so confusing.

So what is correct?

Re: Please help with PDE in polar coordinates.

Just a thought...are we to assume that you have a DEq that is being integrated over a region? And that you are trying to convert that region from rectangular coordinates to polar coordinates? In that case x and y are independent (except on the boundaries) and thus .

It might help to post the entire problem.

-Dan

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**topsquark** Just a thought...are we to assume that you have a DEq that is being integrated over a region? And that you are trying to convert that region from rectangular coordinates to polar coordinates? In that case x and y are independent (except on the boundaries) and thus

.

It might help to post the entire problem.

-Dan

Thanks for the reply. This is the complete question. I just find this that I cannot explain. It is just simple Polar coordinates and I listed the derivation according to more than one sources in the first post. Then I just use an example to show a different result that I cannot explain.

As you can see from the derivation, if as I showed my work. But that does not explain the example I gave when .

And the plot even thickens when SlipEternal showed that

Thanks

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**Alan0354** Thanks for the reply. This is the complete question. I just find this that I cannot explain. It is just simple Polar coordinates and I listed the derivation according to more than one sources in the first post. Then I just use an example to show a different result that I cannot explain.

As you can see from the derivation,

if

as I showed my work. But that does not explain the example I gave when

.

And the plot even thickens when SlipEternal showed that

Thanks

Well, that's why I'm curious. First about the DEq tag in your thread title. Why is that there if you don't have a DEq you are working with? And your comment that you found that "verified by more than one book" leads me to believe you are converting a domain in xy to a domain in . At the very least you don't seem to be converting an equation (differential or otherwise) in this thread.

This whole question is just confusing!

-Dan

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**topsquark** Well, that's why I'm curious. First about the DEq tag in your thread title. Why is that there if you don't have a DEq you are working with? And your comment that you found that

"verified by more than one book" leads me to believe you are converting a domain in xy to a domain in

. At the very least you don't seem to be converting an equation (differential or otherwise) in this thread.

This whole question is just confusing!

-Dan

I might have use the wrong tittle, but my question is still valid. I triple checked my post before I posted it. Maybe, you can change it to a better tittle for me.

Thanks

Re: Please help with PDE in polar coordinates.

Now I am officially lost!!! I since posted this question in two different math forums, people there both asked and clarified, then no response!!!

I have one book and at least one article derived the equations like in my first post, but obviously the example I gave does not agree with the first post and I triple checked my example. I don't think I did anything wrong.......apparently I have not get any suggestion otherwise from three forums!!! I am pretty sure I am missing something as the book I used is a text book used in San Jose State and I studied through 7 chapters and yet to find a single mistake until the question here.

Anyone has anything to say?

From my example,

And this answer makes a lot more sense.

Thanks

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**Alan0354** Now I am officially lost!!! I since posted this question in two different math forums, people there both asked and clarified, then no response!!!

I have one book and at least one article derived the equations like in my first post, but obviously the example I gave does not agree with the first post and I triple checked my example. I don't think I did anything wrong.......apparently I have not get any suggestion otherwise from three forums!!! I am pretty sure I am missing something as the book I used is a text book used in San Jose State and I studied through 7 chapters and yet to find a single mistake until the question here.

Anyone has anything to say?

From my example,

And this answer makes a lot more sense.

Thanks

The reason no one has a suggestion for you is because you are not asking any valid questions. If , then . But, if , then .

Also, as HallsofIvy showed, , so setting those two equal, we get , so only if where is an integer. Hence, only if .

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**SlipEternal** The reason no one has a suggestion for you is because you are not asking any valid questions. If

, then

. But, if

, then

.

Also, as HallsofIvy showed,

, so setting those two equal, we get

, so

only if

where

is an integer. Hence,

only if

.

But I posted in post #5 proof for polar coordinates.

On top of that, you showed , which I agree with you. But the proof in post #5 say otherwise, so what am I missing?

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**Alan0354** But I posted in post #5 proof

for polar coordinates.

On top of that, you showed

, which I agree with you. But the proof in post #5 say otherwise, so what am I missing?

In post 5, you assumed , which means you were already assuming . You never proved it.

Re: Please help with PDE in polar coordinates.

Quote:

Originally Posted by

**SlipEternal** In post 5, you assumed

, which means you were already assuming

. You never proved it.

Oops, I wrote that upside down. I meant you assumed

Re: Please help with PDE in polar coordinates.