Members Raskolnikovs axe Posted November 4, 2010 Members Share Posted November 4, 2010 I'm trying to compute the inverse Laplace transform of the function F(s)=arctan(1/s) and I'm kind of stuck. I've gotten this far and I think I'm on the right track but don't know where to go next. I'm using the convention that the inverse transform of F(s) = f(t) . I suspect it's obvious but the curriculum here put me in differential equations before multivariable calculus so I don't really know how to deal with the right side of my last equation. Any ideas? Help would be greatly appreciated! Link to comment Share on other sites More sharing options...
Members jhamnett Posted November 4, 2010 Members Share Posted November 4, 2010 It's sin(t)/t Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 i have to show all the steps - can you give me any details? Link to comment Share on other sites More sharing options...
Members Blakemore Effects Posted November 4, 2010 Members Share Posted November 4, 2010 Sorry. Wish I could help, but I have Diff EQ next semester. If it helps though, I really don't want to take it now after looking at that. Link to comment Share on other sites More sharing options...
Members jhamnett Posted November 4, 2010 Members Share Posted November 4, 2010 i have to show all the steps - can you give me any details? Most of the time you just use the Laplace transform charts... that's what I've used a bunch in math classes in the past. They didn't give you any? Damnnnnnnnnn. Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 No, I've got charts and I can google stuff to get the answer no problem, but my diff eq teacher is hardcore and doesn't allow any use of table for transforms or integration, so we have to basically prove it all every time. My answer came out to sin(t)/t though, so it's all good! thanks. Link to comment Share on other sites More sharing options...
Members lolque? Posted November 4, 2010 Members Share Posted November 4, 2010 Sorry. Wish I could help, but I have Diff EQ next semester. If it helps though, I really don't want to take it now after looking at that. This Link to comment Share on other sites More sharing options...
Members jhamnett Posted November 4, 2010 Members Share Posted November 4, 2010 Your RHS integral is also applying the Laplace transform to a function in s, you need to change it to this: ... I also have no idea why you're differentiating at the end either... Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 i was trying something another student told me to, which turned out to be the wrong way to go. here's what I went with: This is actually what I originally tried to do, but I made a stupid differentiation error right off the bat that screwed me up. As soon as I noticed that, it was pretty easy. Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 Sorry. Wish I could help, but I have Diff EQ next semester. If it helps though, I really don't want to take it now after looking at that. I have to say it's taking a lot of work, but if you make sure to understand the underlying concepts instead of just learning the methods by rote you will be OK. That applies to any math class, really, but I found it especially true here. It's also very interesting. I'm about a month away from finishing it and so far I've actually found it a slight bit easier than Calc II. I think multivariable calc will be easy after this. Link to comment Share on other sites More sharing options...
Members Blakemore Effects Posted November 4, 2010 Members Share Posted November 4, 2010 I have to say it's taking a lot of work, but if you make sure to understand the underlying concepts instead of just learning the methods by rote you will be OK. That applies to any math class, really, but I found it especially true here. It's also very interesting. I'm about a month away from finishing it and so far I've actually found it a slight bit easier than Calc II. I think multivariable calc will be easy after this. Funny you should mention that. I was just getting pissed that my Probability teacher is making us derive all the formulas for our test on this chapter of the book instead of just letting us use them without knowing where they came from. Good to hear you think it's easier than Calc II though. Calculus has just always made sense to me for some reason. Calc just seems to come naturally, which is part of why I was excited to take Diff EQ was that I heard it was basically like a continuation of Calc. I'd rather take calculus over any sort of geometry class any day. Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 Funny you should mention that. I was just getting pissed that my Probability teacher is making us derive all the formulas for our test on this chapter of the book instead of just letting us use them without knowing where they came from. Good to hear you think it's easier than Calc II though. Calculus has just always made sense to me for some reason. Calc just seems to come naturally, which is part of why I was excited to take Diff EQ was that I heard it was basically like a continuation of Calc. I'd rather take calculus over any sort of geometry class any day. You'll probably be just fine. All you do is learn methods to solve equations involving derivatives - you're solving for a function, not a variable, based on a relationship of said function's derivatives. So if you thoroughly understand the concepts of integration and differentiation you shouldn't have much trouble. I think the people who struggle with this are the ones who didn't make it through calc very easily either. That'd be like trying to do algebra without being totally solid in your arithmetic. Link to comment Share on other sites More sharing options...
Members Dr.Pain-MD Posted November 4, 2010 Members Share Posted November 4, 2010 I suspect it's obvious but the curriculum here put me in differential equations before multivariable calculus so I don't really know how to deal with the right side of my last equation. You don't need any multivariable calc to solve that since there is only one variable, t. Your complex number s is treated as a constant. Ah, the joys of being an EE student, huh? Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 You don't need any multivariable calc to solve that since there is only one variable, t. Your complex number s is treated as a constant. Ah, the joys of being an EE student, huh? Nailed it, EE. Yeah, I now realize I don't need the multivariable - i was just trying that cause a friend said to take the derivative with respect to s of the transform integral in t, which was wrong. EE is a lot of work but in a semester or two i'm gonna start taking some realllly awesome classes so it's totally worth it. Link to comment Share on other sites More sharing options...
Members Dr.Pain-MD Posted November 4, 2010 Members Share Posted November 4, 2010 Nailed it, EE. Yeah, I now realize I don't need it. EE is a lot of work but in a semester or two i'm gonna start taking some realllly awesome classes so it's totally worth it. I know because you've posted it here before and I'm in the same boat. I'm in my third year and while it's "awesome", it's also really not that awesome at the same time. I'm only really interested in a limited number of topics, but I have to do a bunch of stuff I couldn't care less about like software-oriented programming and that sucks big time (even though I get to specialize in my last year). Tomorrow is my birthday, but I'll be stuck at school until 8PM writing a quiz for my systems and controls class. {censored}in' A. Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 What are you aiming to do with your degree? At the program I'm in you have a very wide selection of courses to choose from your junior and senior year so you can really pick what you will specialize in. I'm doing an EE major with a minor in computer engineering, so I'll probably have more programming classes, but there's also some acoustics & audio classes in the EE dept that i'll be taking which I'm really looking forward to. I'm trying to tailor my knowledge to work on guitar & recording gear, analog or digital, and be able to program the digital stuff. Link to comment Share on other sites More sharing options...
Members Dr.Pain-MD Posted November 4, 2010 Members Share Posted November 4, 2010 Well, I'd love to do something in the audio industry, but I don't want to move around too much and that most likely won't be happening so that will stay a hobby. My uni gives you pretty much all of your senior year(s) to pick and choose your own tech electives from a big list, so there is a lot of choice. I'll probably be doing all the power and power electronics courses and I'm hoping to get some kind of hardware job after school, not too fussed about the exact area at the moment. Link to comment Share on other sites More sharing options...
Members Dr. Goldenglove Posted November 4, 2010 Members Share Posted November 4, 2010 Maths Though I don't have the slightest idea what you're talking about here. I do study differential equations, though. Link to comment Share on other sites More sharing options...
Members Dr.Pain-MD Posted November 4, 2010 Members Share Posted November 4, 2010 Link to comment Share on other sites More sharing options...
Members Raskolnikovs axe Posted November 4, 2010 Author Members Share Posted November 4, 2010 Link to comment Share on other sites More sharing options...
Members christianatl Posted November 4, 2010 Members Share Posted November 4, 2010 Magnets. Link to comment Share on other sites More sharing options...
Members humancertainty Posted November 4, 2010 Members Share Posted November 4, 2010 Magnets. To it. I was beat'd. Link to comment Share on other sites More sharing options...
Phil O'Keefe Posted November 5, 2010 Share Posted November 5, 2010 :phil: Link to comment Share on other sites More sharing options...
Members christianatl Posted November 5, 2010 Members Share Posted November 5, 2010 Link to comment Share on other sites More sharing options...
Members Dr.Pain-MD Posted November 5, 2010 Members Share Posted November 5, 2010 Magnets.Fun to joke about with juggalos, but absolutely no fun to learn about. Link to comment Share on other sites More sharing options...
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