<p>At the end of the day, you’re the student and he’s the professor. If you didn’t answer it the way the course taught you, and he wanted you to, he can give you whatever grade he wants. I’m guessing the problem was not unlike other problems you’ve seen in that class, and that those didn’t require all of the work you did, so it’s only reasonable to assume you should have been prepared to do it the way he wanted you to. </p>
<p>Tests in these classes are achievement tests. The point is to demonstrate that you learned whatever the course is teaching you, not that you can do it a completely different and convoluted way. Anyway, if your answer was expressed with hyperbolic trig, I’d say you didn’t simplify it and marking you off for that is justifiable. </p>
<p>If I was the professor, I wouldn’t have marked you off for it, but that’s his call. Suck it up and move on.</p>
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<p>I doubt it. I’d argue that all you demonstrated was that you can’t factor a simple polynomial.</p>
<p>OP-I’m assuming your answer must be an additive string of cosh and sinh where various terms cancel out.Actually my hat is off to you. That 1/4 in the denominator would have really thrown me for a loop. I guess that’s one benefit of a young brain. I would trade a few exam points for that.</p>
<p>which is what I got. I don’t have to solve this type of problem regularly. The linear algebra took me a little longer than when I had to do this sort of thing more regularly, while as a grad student, about 20 years ago.</p>
<p>As a general comment, we don’t know the whole story here. We only know one side; we have heard nothing from the professor or his staff. We don’t know the details of original problem statement on the exam. Also, we don’t know what sorts of expectations have been set, e.g. were labs or problem sets on similar topics assigned earlier that required answers to be given in a particular way?</p>
<p>I believe I would have had more problems arriving at an answer involving exponentials by completing the square also. However, I think the professor was a bit harsh giving zero credit. Also, I think he should have been open, at least, to a discussion of why zero credit was given. If @eurekameh just showed up during the professor’s regular office hours and didn’t insist that the professor change his mind, I don’t see that as harassment.</p>
<p>If the class the OP is taking is an EE class then hyperbolic function is probably not the desired solution because it does not help to understand the behavior of the circuit.</p>
<p>Laplace transform was part my EE class during my sophomore year. I don’t remember much now. My prof. did not give much time when he gave the tests. We could not afford to have a long solution if the solution was simple because we would not be able to finish the tests. My worst mistake was misreading the numbers on the questions (for example plugging 5 instead of 3 as given). This completely messed up my solutions.</p>
<p>I am not a math person…but I am wondering if maybe the professor had been teaching a certain method that is useful in engineering contexts…and that on the exam he wanted and expected to see students able to use THAT method because they would be needing to use it in engineering contexts? Sort of like being proficient in both Latin and Spanish, and a professor wanting to see a translation in the colloquial Spanish rather than a tortured translation derived from the knowledge of Latin?</p>
<p>The OP over-engineered a simple solution. If a student has studied Laplace transform then he/she should be familiar with both factorization and square completion because both forms are useful for taking inverse Laplace transform.</p>
<p>The expression (s^2 + 5s + 6)(s + 1) is in a product form. The OP failed to perform a simple test to determine if (s^2 + 5s + 6) can be factored further so that the entire expression can be decomposed into a sum a of fractions.
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<p>You can go on and say cosine can be expressed as an infinite sum:</p>
<p>cos(t) = 1 - t^2/2! + t^4/4! - t^6/6! + … </p>
<p>This is very useful in numerical analysis and computer software algorithm. However, it’s not useful to describe a simple alternating voltage or current so that people can visualize the waveform.</p>
<p>What was the professor trying to determine? Factoring ability? Not sure why, given we’re doing Laplace transforms, but, if so, give the student s^3 + 6s^2 + 11s + 6. Just testing ability to invert? Give them (s+1)(s+2)(s+3). The in-between form of the function is misleading. The OP may have missed a simple observation, but showed some creativity AND showed s/he could invert. Good job. </p>
<p>Clearly reasonable people can disagree. I disagree with giving the student zero points. I disagree with the “oh well, too bad, it’s the professor’s call, deal with it”. And I disagree with how the problem was presented.</p>
<p>How is the in between form misleading? It makes the problem trivial. And in a path of sequential devices the trransfer function will oftren be given as the producr of multiple transfder function, say for examole sequentisl filters.with different charateristics.</p>
<p>I still think a mathematically correct answer should not receivezero though.</p>
<p>In case anyone is wondering what class this is, it’s Dynamic Systems.</p>
<p>People seem to think that the way I did it was completely different from the way the professor wanted me to do it. It isn’t. The method is called ‘partial fraction expansion,’ but the way I completed the square and everything is the way you should do it when you have complex roots. The problem did not have complex roots, and I could simply have factored the polynomial and avoided this situation altogether. But the fact that I missed this factorization following the fact that I have demonstrated my knowledge of what to do when overlooking it shows something about my ability to recover from it. People make mistakes all the time (in this case, my overlooking of the factorization), but the professor is giving me zero points on the problem because I “could not” factor a simple polynomial although I recovered from it by using yet another method to solve it. It is ridiculous to have points taken off, let alone 20 points, for not realizing to factor a polynomial when what I did is also correct.</p>
<p>I have also been hearing a lot about this problem being trivial, and it is. I have done many more solving equations using the Laplace Transform back in my Differential Equations class, and I did just fine. So when I looked at the solutions before I got my test back, I was shocked at how trivial it was and wondered how I could have overlooked the factorization, but I didn’t worry because I knew the way I did it was still mathematically sound. Then I got my test back, and I was completely shocked at how it turned out.</p>
<p>Yes OP I was actually taking issue with the poster who said rthe problem was confusing. I’m sure you don’t think it was confusing. You likely are kicking yourself as well as the prof. Basically you missed a simple factorization that 99 times out of 100 you would have seen. We’ve all done these rhings abd caused ourselves heaaches. That’s why I also disagree with the zero points.</p>
<p>BTW when I say we’ve all done these things most of us don’t recover so adeptly and end up with a mathematically correct answer.so good for you on that.</p>
<p>This really sounds like the prof didn’t recognize what you did, thought you were way off, and gave a zero. Any prof could make the same mistake, especially when grading exams in a hurry. But in this case they should admit their mistake. </p>
<p>Eurekameh, unfortunately grades do matter. But at least you know what you’re doing, whether or not your grade reflects it.</p>
<p>^ He already spoke to his prof so if the prof didn’t recogniize what he did initially, OP should have been able to communicate it when he met with him. I highly doubt that is what happened.</p>
<p>I don’t think he/she should have lost 20 pts either, but since OP already spoke to prof there is not much else to be done, unless OP goes over his head, which would be very risky and probaby not worth it.</p>
I think that would be a little diffiicult. But I am curious about some things-
Was your entire answer composed of sinh and cosh or did you have any isolated exponential term?
Did you have to make any change in variables to solve this?
How many tems in your partial fraction expansion? I’m assuming to wind up with hyperbolic functions you must have had terms with an (s^2)-(a^2) in the denominator. Was the a=1/2? </p>
<p>I’m trying to figure out how you did it myself.*** Your answers would let me know if I’m on the right rack or anywhere in the vicinity. I know I must be missing something here. I do absolutely nothing remotely mathematical at work anymore.</p>
<p>*** Let me qualify this. I’m actually too lazy to sit down and try to grind out and replicate what you did, therefore I just want to know qualitatively so I can see if I’m anywhere close in my thinking.</p>
<p>I hope I can post links like this on here. There was one isolated exponential term because of the s+1 term in the denominator. I did not do any change of variables. There were three terms. The coefficients were A = -3/2, B = -5/2, and C = 3/2.</p>
<p>Yep, that’s the right answer. I assume you showed how you got the constants because that’s the main part of the PFE. The rest is just copying out of a table.
But that’s about how I imagined it.
Impressive work around though.</p>
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