Hi MrAl:
What you did is the double-sided Laplace Transforms, so I think to know what is right, we should make clear what is meant in the original post (one sided LT or double sided LT).

Hi there,

Thanks for the reply.

Yes, that is the double sided LT, and yes, there is some question to all this for various reasons. What i did was i posed the question about this function for example:
K1*(t+a)^9+K2*(t+a)^8+K3*(t+a)^7+...
and ask, what is the LT for that function?
Now given the two sided LT this is a reasonable question, but given the one sided LT this is a silly question because as soon as we see the (t+a) we would realize we have a function that doesnt work so there would be nothing to really do here, so that would make a question with (t+a) in it more reasonable if it was the two sided LT.
Is this absolutely positively certain? Well, it would be better to see other questions in the book and also what section in the book this came from. If they only talked about the one sided LT then it would be harder to say that the result we say is right is really right, but if they talked about both the one sided and the two sided or just the two sided, then it would make more sense to assume that it was correct.
We are working with a limited amount of information that we usually have when we have the whole book or actually know what course it came out of. This means we have to make educated guesses until more information rolls in.

One of the determining factors overall would be is there a practical use for the result in real life, in some application. I think there is but i dont want to have to search it out completely. For example, i think the result could be transformed into the discrete domain and therefore make a filter that could be implemented on a digital computer. Someone could try this i guess, or come up with another example.

 

Hello all, I think I'm getting confused now. Please may I know what is one sided LT and double sided LT accompanied with a small example for each. (forgive me if this seems like a silly question but I started studying Laplace from Saturday)

thank you

Hi,

As WBahn pointed out, the difference is in the lower integration for the two integrals.

There is actually only one transform, and that is what is called the "two sided LT", and this is an integral with kernel e^(-s*t) and with limits of integration that span from minus infinity (-inf) to plus infinity (+inf). Thus we are integrating the kernel times the time function of interest from -inf to +inf. This can be split up into two integrals:
1. The integral from -inf to 0, and
2. The integral from 0 to +inf.

Since many of the time functions we encounter run from t=0 and on, the integration from -inf to 0 is always zero, so there is no reason to integrate over that time period. When the function requires that t<0 though, then we have to use both integrals, and the two taken together is called the two sided LT because we integrate on both sides of zero.
One of the main points here is that time usually starts at some known time instant, like t=0, but time never ends. So we usually have to know the start time t0, and that determines what integral we have to use, and we integrate up to +inf.

 

The one sided transform has a lower integration limit of t=0- (i.e., an infinitesimal amount of time before t=0 so that impulse events at t=0 can be included, which are usually used to take care of initial conditions, which is a way of saying that they deal with the net effect of everything for all time prior to t=0). The two sided transform has a lower limit of negative infinity. The problem with the two sided transform is that the exponential in the transform integral blows up as t get more negative, so the transform integral itself is less likely to converge.

Hi,

Yes the conditions for existence look pretty simple, but then the question of the total result (not the integral itself) which here comes out to an expression in the form:
F(s)=A*e^(B*s)/s^3

It looks bad when s is real, but when s is complex it looks like this is bounded for bounded real part. For example, with s=j*w the limit as the frequency goes to infinity is zero for both real and imaginary parts.
We could look at this more.

 

Thank you Sir, I do understand now. Much appreciation.

I am going to take some pictures from the textbook and will post it up. I just starting studying Laplace over the weekend. I have no guidance from any lecturer since its distant learning. We are given the sections that we have to study for the final examination in 2-3 months time.
So for Laplace these are the sections that are covered as per my tutorial letter. I can use the prescribed text book or any text book that contain these topics.

Chapter 3
Laplace transforms
UNIT 1: Definitions and properties
UNIT 2: Solutions to differential equations
UNIT 3: Applications
UNIT 4: Step and impulse functions
UNIT 5: State-space equations

and also (page 341; Problems 1 – 5 Duffy) examples to attempt from the textbook

thank you.

 

Thank you Sir, I do understand now. Much appreciation.

I am going to take some pictures from the textbook and will post it up. I just starting studying Laplace over the weekend. I have no guidance from any lecturer since its distant learning. We are given the sections that we have to study for the final examination in 2-3 months time.
So for Laplace these are the sections that are covered as per my tutorial letter. I can use the prescribed text book or any text book that contain these topics.

Chapter 3
Laplace transforms
UNIT 1: Definitions and properties
UNIT 2: Solutions to differential equations
UNIT 3: Applications
UNIT 4: Step and impulse functions
UNIT 5: State-space equations

and also (page 341; Problems 1 – 5 Duffy) examples to attempt from the textbook

thank you.

Hi,

It might help to show us the definitions they must show in UNIT 1. That could narrow it down right away. It may also help to see some applications from UNIT 3.
UNIT 5 would show some really amazing applications of the LT, and that would be cool to see too although maybe not as helpful to this particular question.

 

Hi Sir. Definitely. Thats why I just go over the text book and work through the examples. The university does cater for special lectures but I also work and its very expensive. But what fustrates me is the textbook does not give full working for the questions. One day I desire to write a textbook and full model answers to help people.

 

Hi Sir. Definitely. Thats why I just go over the text book and work through the examples. The university does cater for special lectures but I also work and its very expensive. But what fustrates me is the textbook does not give full working for the questions. One day I desire to write a textbook and full model answers to help people.

Sadly, if you do write that textbook it probably won't sell well. Most people want textbooks that DON'T explain things in detail, but rather just give them formulas and recipes to memorize.

 

Seriously wow. I thought most students have similar mindsets. Not that I'm lazy and want to be spoon fed. It's just that trying to learn a whole new concept from scratch can be a little overwhelming. Especially with no guidance from a lecturer. That's why i have a lot of respect for lecturers.

 

Seriously wow. I thought most students have similar mindsets. Not that I'm lazy and want to be spoon fed. It's just that trying to learn a whole new concept from scratch can be a little overwhelming. Especially with no guidance from a lecturer. That's why i have a lot of respect for lecturers.

Yeah... I thought that most students wanted to actually learn things, too, at one time. And it's actually too broad a brush even with the caveat of "most students" just wanting a bunch of mindless formulas and recipes. There are some fields where the reverse is very much the case. Physics students, for example, seem to very strongly want to know the why of things and so most physics texts, particularly upper level physics texts, spend a lot of time developing the foundations for the material presented. Lower level physics texts used to, as well (somewhat guilt by association), but I've seen quite a few more recent introductory physics texts (which means that MOST of the students taking those classes are NOT physics majors) that have backed off the fundamentals in favor of much more rote memorization of formulas and techniques. It was a real culture shock to me when I went from a physics undergrad to an engineering grad program and was smacked in the face by how few engineering majors really cared about why things work. Certainly there were some who did (and more than just "a few"), but no where near a majority. Even though I had taken many, many engineering courses as an undergrad and had seen examples of this attitude, I hadn't realized that they were the norm rather than the exception.

 

Yeah... I thought that most students wanted to actually learn things, too, at one time. And it's actually too broad a brush even with the caveat of "most students" just wanting a bunch of mindless formulas and recipes. There are some fields where the reverse is very much the case. Physics students, for example, seem to very strongly want to know the why of things and so most physics texts, particularly upper level physics texts, spend a lot of time developing the foundations for the material presented. Lower level physics texts used to, as well (somewhat guilt by association), but I've seen quite a few more recent introductory physics texts (which means that MOST of the students taking those classes are NOT physics majors) that have backed off the fundamentals in favor of much more rote memorization of formulas and techniques. It was a real culture shock to me when I went from a physics undergrad to an engineering grad program and was smacked in the face by how few engineering majors really cared about why things work. Certainly there were some who did (and more than just "a few"), but no where near a majority. Even though I had taken many, many engineering courses as an undergrad and had seen examples of this attitude, I hadn't realized that they were the norm rather than the exception.

Hi Sir. Interesting to know this. Because I see many friends who attend university tend to just want to pass and forget the work thereafter. So then what's the point of studying when it is all about getting the degree and forgetting the work there after??? In one way or the other I am guilty of this like in school I just wanted to pass those dreaded theory subjects.

 

Hi Sir. Interesting to know this. Because I see many friends who attend university tend to just want to pass and forget the work thereafter. So then what's the point of studying when it is all about getting the degree and forgetting the work there after??? In one way or the other I am guilty of this like in school I just wanted to pass those dreaded theory subjects.

Even people that really want to learn as much as they can tend to have at least some areas that they just aren't sufficiently motivated enough to put in the effort to really learn as much as they can. For lots of people it's those "dreaded theory subjects", which tend to come back and haunt them. Even for people that love the theory, there usually comes a point where the theory just gets too abstract for them. This is commonly the case in math classes when it comes time to learn about when something actually has a solution and when a solution, even if the approach appears to yield an answer, is invalid because it simply doesn't exist because some integral doesn't converge absolutely (or whatever). We often get by just fine when we ignore those things because, in the real world for real problems, the solutions almost always do exist (in a mathematical sense). But not always -- and so the solution that the math yields ends up bearing no resemblance to the way the system actually behaves. But that isn't because the math is wrong -- the math didn't yield a solution that was wrong, the math didn't yield a solution period. It was simply we that failed to take proper not of that fact.

 

Even people that really want to learn as much as they can tend to have at least some areas that they just aren't sufficiently motivated enough to put in the effort to really learn as much as they can. For lots of people it's those "dreaded theory subjects", which tend to come back and haunt them. Even for people that love the theory, there usually comes a point where the theory just gets too abstract for them. This is commonly the case in math classes when it comes time to learn about when something actually has a solution and when a solution, even if the approach appears to yield an answer, is invalid because it simply doesn't exist because some integral doesn't converge absolutely (or whatever). We often get by just fine when we ignore those things because, in the real world for real problems, the solutions almost always do exist (in a mathematical sense). But not always -- and so the solution that the math yields ends up bearing no resemblance to the way the system actually behaves. But that isn't because the math is wrong -- the math didn't yield a solution that was wrong, the math didn't yield a solution period. It was simply we that failed to take proper not of that fact.

Hi Sir. I can desern you are very wise and have years of experience to back it. I hope to continue to be motivated and not loose focus.
I have a Z transform question that seems to be annoying me as I am currently studying Z transforms as we speak. It's about impluse response.

 

Hi Sir. I can desern you are very wise and have years of experience to back it. I hope to continue to be motivated and not loose focus.
I have a Z transform question that seems to be annoying me as I am currently studying Z transforms as we speak. It's about impluse response.

Thanks -- and more than a small amount of what I have learned from those many years has come as a result of making the mistakes that I am now able to caution people about. The notion of needing to be aware of whether a solution exists is a case in point. When I was first learning that stuff I was interested by the existence criteria, but I didn't really see it as being important passed being of intellectual curiosity. So I'm still weak on a lot of that stuff, even though I HAVE seen real world instances (not many) in which solutions that don't exist have been blindly implemented (only to completely fail).

 

Hi Sir. Definitely. Thats why I just go over the text book and work through the examples. The university does cater for special lectures but I also work and its very expensive. But what fustrates me is the textbook does not give full working for the questions. One day I desire to write a textbook and full model answers to help people.

Most text books come with a separate answer book so you have to purchase them. The authors need to make extra income from those answer books.

 

Hi Josh007, true.

 

Most text books come with a separate answer book so you have to purchase them. The authors need to make extra income from those answer books.

Usually the author's solution manual is NOT for sale to students, but rather is available free of charge to instructors.

 

Usually the author's solution manual is NOT for sale to students, but rather is available free of charge to instructors.

Its makes sense because I went to one of the university book stores and asked them about the solution manual for the Circuit analysis book and they told me I need to be working for the university to be able to order it from USA and then can purchase it from them.

 

Its makes sense because I went to one of the university book stores and asked them about the solution manual for the Circuit analysis book and they told me I need to be working for the university to be able to order it from USA and then can purchase it from them.

Hi,

If you can get to the University that uses that book then you might find it in their bookstore. That's where i found mine back when. They may not always publish one though.
Another source is on Amazon or similar. They sell solutions editions for some books. They may or may not have the one you want though so it's hit or miss.

 

Hi,

If you can get to the University that uses that book then you might find it in their bookstore. That's where i found mine back when. They may not always publish one though.
Another source is on Amazon or similar. They sell solutions editions for some books. They may or may not have the one you want though so it's hit or miss.

thanks Sir, I will look on Amazon. I hope to find those that I need or next year.