# laplace transform thingies

Discussion in 'Homework Help' started by S_lannan, Apr 5, 2008.

1. ### S_lannan Thread Starter Active Member

Jun 20, 2007
247
2
any basic texts on what the hell they are / do / are used for in EE??

i'm going to uni next year and would like to get a head start on a few university topics studied in electronics engineering.

cheers

2. ### hgmjr Moderator

Jan 28, 2005
9,030
218
Try here at Wikipedia.

hgmjr

3. ### hgmjr Moderator

Jan 28, 2005
9,030
218
And here also.

hgmjr

4. ### S_lannan Thread Starter Active Member

Jun 20, 2007
247
2
well.

looks like i got a bit of work ahead of me, the mathematics used are completely alien to me.

5. ### Dave Retired Moderator

Nov 17, 2003
6,960
163
Laplace Transforms are widely used in control systems analysis and analysing analog circuits (some of the analog experts here will tell you how prevalent the techniques are from a practical perspective - I'm not sure).

The fundamental bilateral equation is: http://upload.wikimedia.org/math/b/d/b/bdb9d6ca4bbf485387d7a13749c9863a.png - All Laplacian identities are derived from this equation.

For any time-based function f(t) you can (attempt!) to derive the Laplacian representation of the equation. What the Laplace transform does is maps the time-domain function f(t) to the s-plane, where the functions are frequency-based. If you have done Fourier analysis then Laplace transforms are almost identical however where the s-parameter is a complex number with real and imaginary part, in Fourier analysis s is completely imaginary.

6. ### Dave Retired Moderator

Nov 17, 2003
6,960
163
You will cover Laplace Transforms as part of a Signal and Systems course. The mathematical constucts should be taught in 2nd semester maths, but if you are curious look at "Signals and Systems" by Oppenheim (and some other bloke, I can't remember his name).

Sedra and Smith will show you how Laplace Transforms are used in understanding practical electronic circuits.

Dave

7. ### colsandurz New Member

Apr 7, 2008
2
0
Try
Oppenheim & Wilsky
or
B.P. Lathi
I can't remember the titles, but they're both pretty generic titles. As far as the contents are concerned they're both very similar, they're just organized differently(ie one separates discrete and continuous time and the other doesn't). Also, learn differential equations first, because you won't understand any the material in these books if you don't know any differential equations.

8. ### Dave Retired Moderator

Nov 17, 2003
6,960
163
Yes, Wilsky is the other author who writes "Signals and Systems". Couldn't remember his name. Thanks.

Dave

9. ### S_lannan Thread Starter Active Member

Jun 20, 2007
247
2
ok cheers guys.

first off my calculus is in great need of revision... that will be the first stop

10. ### scubasteve_911 Senior Member

Dec 27, 2007
1,202
1
Basically, the laplace transform helps you solve differential equations! It turns a difficult calculus question into a more of an algebraic equation via the transform.

You'll definitely learn the algebra tricks that you need to apply to inverse the transform, such as partial fraction expansion, completing squares, factoring so that you can use existing laplace transform pairs, etc.

Steve

11. ### Dave Retired Moderator

Nov 17, 2003
6,960
163
How could we have missed that one!

$\frac{dy}{dx}$$\rightarrow$$sY(s)$

$\frac{d^{2}y}{dx^{2}}$$\rightarrow$$s^{2}Y(s)$

And so on...

Dave

12. ### scubasteve_911 Senior Member

Dec 27, 2007
1,202
1
hehe, It is a lot better than trying to do friggin silly 'sturm louisville' based solutions
Hands down to Laplace for making my life so much easier

Steve

13. ### Dave Retired Moderator

Nov 17, 2003
6,960
163
Not just a bit easier, but much easier - multi-order differential equations to multiplication and division - very nice

Mind you, we'd just bang it into Matlab or Octave these days!

Dave