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Deriving equations am I just dumb?

  1. Nov 5, 2006 #1
    I'm in third year undergraduate physics, and more and more I'm seeing problems in homework and assignments that say "Prove that" and "Show that", basically just deriving equations.

    There's just one problem, I can't do it for the life of me. I had a thermodynamics test recently, and despite understanding the material and how all the equations work, I failed the test because the questions were proofs.

    I look at problems like this and all I see is a million different possible things to do with the equation, but none of them seem to lead me to the desired solution. Then when I see the solution afterwards, I realize how stupid I was and how simple the problem really is, which will probably be exactly what happens with the test I wrote.

    Studying also seems impossible as well, because even if I practice a proof, there's an entirely different kind that will be asked of me on a test.

    Is there any special way to get good at these derivations or am I just doomed to failure even though I understand the concepts?
  2. jcsd
  3. Nov 5, 2006 #2


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    Exercise, exercise and exercise.

    And, of course, one should think about the proofs, i.e. have in mind the point of your proof, as the assumptions and basic equations which you are using to construct a proof.
  4. Nov 5, 2006 #3


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    Also, know how to work backwards. You know what you're trying to prove, so see what steps you can take from that to get to what you're assuming to be true. With any luck, the steps are all reversible (if they're not, you should be able to find a work around), and you can just put the reverse of what you found down for your proof
  5. Nov 5, 2006 #4

    Claude Bile

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    This indicates to me that you are having difficulty interpreting the mathematical constraints given to you by the question.

    I suggest you practice proofs, even though they wont be the ones you will be tested on, at least you will be practising interpreting the physical constraints of the problem into mathematical ones. I think once you master this, proofs will become 'bread-and-butter' questions you should almost always get right.

  6. Nov 5, 2006 #5


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    As you're studying the derivations in your textbooks and lecture notes, don't just follow along from one step to the next, nodding and thinking, "Yeah, that step looks OK." Try to figure out the strategy that the derivation is following. That is, ask yourself, "Why might I have done it this way if I were doing it myself? What's the motivation behind these steps?" Good lecturers and textbooks try to explain this as they go along, but many textbooks, especially, don't do a good job of it or even attempt to do it at all.

    Also, fill in missing steps as you go along. That is, the ones where the textbook says, "It is easy to show..." or something like that.
  7. Nov 5, 2006 #6
    One thing that has helped me with proofs in math is to have some basic types of problems and their proofs in mind. That way when I see a different problem, I can relate it to one I already know. Even if it's not exactly alike, it can give a starting place.
  8. Nov 5, 2006 #7
    Grab a text book, when a proof shows up instead of reading it, close the text book and try to prove it yourself. If you get seriously stuck, read one line only and try again. Repeat the process til you got the proof down pact.
  9. Nov 5, 2006 #8
    Always read your texts with a paper and pencil in hand. Work through the text, don't just read it. As someone else suggested, try to do some of the derivations yourself with the book closed.

    Also, do lots of problems. The 2 volume _A Guide to Physics Problems_ might be helpful.
  10. Nov 5, 2006 #9
    Thanks for all the tips guys, I'll try doing this next I read my text.
  11. Nov 7, 2006 #10


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    Dearly Missed

    Another tip:
    Always write down a list of the assumptions given.
    This focuses your mind onto precisely those mathematical constraints that exist in the problem, and tells you "what type" of problem you are working with.
  12. Jun 6, 2011 #11
    I have to say, i have exactly the same problem. I'm only in the first year of university, however, despite being fascinated by the idea of deriving things from first principle, i feel like i just don't know where to start?

    Could anyone recommend some good material that could help me on my way?
    I'm not shy of getting stuck in, just need a good place to start. It seems every time i ask my lecturer's about this sort of thing they are puzzled as to what I'm actually asking, one person even told me there's no need to derive things... i personally don't see how this could be true and even if it is, still want to know how.

    Any key tips would be greatly appreciated.


  13. Jun 7, 2011 #12
    There are some proofs, particularly in thermodynamics, which are very hard to have any intuition for. In that case it becomes a matter of being familiar enough with all the equations that you can notice if a bit of an expression looks like part of another equation that you know.

    I always have to do every step when I read my notes or textbooks, even if it is simple algebra or calculus. If I don't, after a few lines I feel like I have no idea what is going on, even if the steps are explained comprehensibly. I can see how some people would think this is a waste of time, but I think doing that has helped me a lot, because familiarity with the equations is really key.
  14. Jun 7, 2011 #13


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    It would be expected that if you went into some area professionally, that you would be able to produce whole proofs and condense them down anyway that is required to solve problems or even teach classes, but I think expecting students to do that in a week is probably a bit too much.

    However understanding the reasons why you go from assumptions to final proof is in my view very very important. If you don't know these reasons, you need to get that resolved. If you get stuck transforming some statement into something else that is needed to get the final result, I can understand that, and if you know why the hell you are doing it in the first place, it's basically a transformation problem that deals with math and not a conceptual problem that deals with the specific subject and its application (engineering, physics, and so on).

    Things involved in math like transforming, decomposing and so on, are hard (even for mathematicians!). Sometimes there are tricks that just so shrewd you would think you are stupid for not picking them up (like multiplying both sides by some variable for instance), but you have to keep in perspective that science is something that has been contributed to by many many thousands of people, and no one "super genius" created all the proofs that you see that are polished in the minimal form that you get presented to you.

    Posters here have emphasized great points about assumptions, and I echo them as well. If you know why you are going from A to B, you will probably with some extra effort be able to fill in the gaps (including if that means consulting with your lecturer). If you have no idea why you are going from A to B, then you need to sort that out ASAP.
  15. Jun 7, 2011 #14
    I agree with this. Once I got better at math and was better able to "read" the math--that is, once I was able to see an equation and intuit what it meant, not just how to use it--my "proof" skills much improved.
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