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#11601 2013-06-27 19:10:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Suppose you had the integral

So now we let:

We have

and

Adding these two equations yields:

Thus,

#11602 2013-06-27 19:24:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

Hi;

Yes, that is a very nice idea.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#11603 2013-06-27 19:27:42

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Unfortunately it doesn't seem to work nearly as often as one would like!

#11604 2013-06-27 19:33:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

It is a trick and as such you use it when you can.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11605 2013-06-27 19:40:56

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

That's the thing when you learn a new trick... you want to use it on everything but really it will only work on a few problems.

#11606 2013-06-27 19:47:45

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

I think it was Alan Turing along with Alonzo Church that proved a long time ago that for an infinite number of problems you will require an infinite number of methods.

My favorite trick involved an integral and a recurrence. Not so difficult but when I first so it I was amazed.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11607 2013-06-27 20:37:09

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

What trick is that?

#11608 2013-06-27 21:02:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

Supposing you want to evaluate this integral:

you might first embed it into a whole family of integrals called y.

you could now work it like this.

Factor:

Now you have solved for the family y in terms of a useful recurrence relation.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11609 2013-06-27 21:20:27

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

That is impressive. A question like that came up in my STEP III exam -- except we had a trig version.

#11610 2013-06-27 21:29:10

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

When I first saw it I loved it and tried to find more of them. But they are few and far between.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11611 2013-06-28 08:33:50

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Do you use a CAS for almost every integration problem you encounter?

#11612 2013-06-28 10:40:27

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

If I am doing an integration problem where there is something I need to learn how to do then I do it by hand no matter how long it takes. If someone is asking a question I will do it by hand for them and then use the CAS to check.

But if I am doing another type of problem and an integral or a sum or a limit crops up as a small part of the problem I do not let it take my concentration off the bigger problem. If you get caught up in the small details you can lose sight of what you originally were working on. I always use a CAS there.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11613 2013-06-28 21:11:19

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I understand what you mean. And there are also lots of problems that CAS's give odd-looking answers for, and many integrals that they cannot do (yet can be done on paper). A lot of integrals in STEP were like that.

#11614 2013-06-28 21:18:28

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

CAS's give odd-looking answers for, and many integrals that they cannot do

A CAS does not mean you shut your brain off. Sometimes you have to help him along. With practice you will find that the number of integrals, sums, DE's , limits and simplifications you can do will increase by a factor of 10.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11615 2013-07-02 20:03:23

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

I was just looking at my UCL course and it appears that you can't go down the computational route without sacrificing the pure maths route... I can either fit into one category or the other!

#11616 2013-07-02 21:34:55

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

Who ever said you needed UCL to teach you computational math or any other type. They are mostly just good for supplying you with credentials and reputation. Like all the other things in life you will have to teach yourself.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11617 2013-07-02 21:41:58

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

OK, but the problem is that if I do not take some computational modules then I won't be allowed to take other ones the next year (they claim I would not have the pre-requisite knowledge).

I like to self-teach, but often when I do that, there are lots of holes in my knowledge.

#11618 2013-07-02 21:47:46

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

They are a product of self understanding. If you are forced down that road and that just might be the case you will have the satisfaction of knowing you are unique. If a hundred of them come out of some university they may not be fragmented but they are also bereft of imagination. All one hundred will be mirror images, all exactly alike.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11619 2013-07-03 23:35:26

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Yes, I do not want to be like that. But, hopefully my passion will never dwindle.

#11620 2013-07-04 00:21:38

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

Then if they will not teach then you will still find a way to learn.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11621 2013-07-04 01:47:59

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Hopefully the quality of teaching won't affect it too much.

#11622 2013-07-04 01:51:43

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

If you can decide what you most likely want to be then choose the one that fits that best.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11623 2013-07-04 01:56:23

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

What do you mean? You mean, as a career?

#11624 2013-07-04 01:58:37

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,759

Re: Linear Interpolation FP1 Formula

Not necessarily, although that would certainly be a way to decide. Even as a lifelong hobby.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

Offline

#11625 2013-07-04 02:19:12

zetafunc.
Guest

Re: Linear Interpolation FP1 Formula

Seems like life is just flying by...

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