Math question - Discrepancy in answer

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P

PurdueRy

Lifer
Nov 12, 2004
13,837
4
0
So I am helping out my roommate with his diffEQ hw and they are taking laplace transforms. This problem has me seriously confused as the answer IMO is easy however, the book did it in a different way, that I find no error in. Matlab agrees with me...however, as I said, I can't find an error in the books work:

Laplace transform of t^2-2t+2

I would use the linearity property and take each transform individually resulting in

2/s^3-2/s^2+2/s

Which is what matlab gives also.

However, the book proceeds as follows:

(t-1)^2 + 1

(e^-s)*(2/(s^3))+1/s)

(e^-s)(s^2+2)/s^3

All I am looking for are why are these answers are different. I see no way that they would give near the same answer if you were to actually use them. Anyone see anything I am missing?

 
J

jagec

Lifer
Apr 30, 2004
24,442
6
81
You saw what happened in the plane thread, and you expect consensus on a much more complex problem?

I can't say why the book does it that way, but I would have done it the way you did, and indeed I get the same answer. Note that it's been a while since I did them.
 
P

PurdueRy

Lifer
Nov 12, 2004
13,837
4
0
Originally posted by: jagec
You saw what happened in the plane thread, and you expect consensus on a much more complex problem?

I can't say why the book does it that way, but I would have done it the way you did, and indeed I get the same answer. Note that it's been a while since I did them.
Click to expand...

LOL, I think the title may scare away those who don't understand.

BTW, congreats on the lifer title...whether you wanted it or not. ;)
 
J

jagec

Lifer
Apr 30, 2004
24,442
6
81
Originally posted by: PurdueRy
BTW, congreats on the lifer title...whether you wanted it or not. ;)
Click to expand...

I feel like there should be a ceremony involved, like welding the door to my room shut, or chaining myself to my keyboard :(

That said, I finally got hired, so maybe the postcount won't rise as dramatically now :)
 
P

PurdueRy

Lifer
Nov 12, 2004
13,837
4
0
Originally posted by: jagec
Originally posted by: PurdueRy
BTW, congreats on the lifer title...whether you wanted it or not. ;)
Click to expand...

I feel like there should be a ceremony involved, like welding the door to my room shut, or chaining myself to my keyboard :(

That said, I finally got hired, so maybe the postcount won't rise as dramatically now :)
Click to expand...

depends if people stop posting

"OMG Wat i5 s000000 t0ugh...TEH PLANE ha5 n0 airflowz n0 liftorz!!!! /THREADz!!!one111"
 
M

Mday

Lifer
Oct 14, 1999
18,647
1
81
Originally posted by: PurdueRy
So I am helping out my roommate with his diffEQ hw and they are taking laplace transforms. This problem has me seriously confused as the answer IMO is easy however, the book did it in a different way, that I find no error in. Matlab agrees with me...however, as I said, I can't find an error in the books work:

Laplace transform of t^2-2t+2

I would use the linearity property and take each transform individually resulting in

2/s^3-2/s^2+2/s

Which is what matlab gives also.

However, the book proceeds as follows:

(t-1)^2 + 1

(e^-s)*(2/(s^3))+1/s)

(e^-s)(s^2+2)/s^3

All I am looking for are why are these answers are different. I see no way that they would give near the same answer if you were to actually use them. Anyone see anything I am missing?
Click to expand...

The book is wrong. It completed the square properly in t, but completely hosed the transform. And, doing each term independently as you did is the way this problem should have been done. Although, I would have simplified the result.
 
P

PurdueRy

Lifer
Nov 12, 2004
13,837
4
0
Originally posted by: Mday
Originally posted by: PurdueRy
So I am helping out my roommate with his diffEQ hw and they are taking laplace transforms. This problem has me seriously confused as the answer IMO is easy however, the book did it in a different way, that I find no error in. Matlab agrees with me...however, as I said, I can't find an error in the books work:

Laplace transform of t^2-2t+2

I would use the linearity property and take each transform individually resulting in

2/s^3-2/s^2+2/s

Which is what matlab gives also.

However, the book proceeds as follows:

(t-1)^2 + 1

(e^-s)*(2/(s^3))+1/s)

(e^-s)(s^2+2)/s^3

All I am looking for are why are these answers are different. I see no way that they would give near the same answer if you were to actually use them. Anyone see anything I am missing?
Click to expand...

The book is wrong. It completed the square properly in t, but completely hosed the transform. And, doing each term independently as you did is the way this problem should have been done. Although, I would have simplified the result.
Click to expand...

Yes, after talking with my EE friend at UofM we came to the conclusion that the time shift property also involves the heaviside function with the same shift...since this isn't the case here...they violated that property.

Thanks :)
 
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