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I Notation help

  1. Sep 20, 2016 #1
    Is there some standardized math text with "proper universal notation" I could read for calculus?

    In one of my courses, $$\int\frac{dx}{x}$$ had a red mark through it, with a note that said "impossible" or something. I earned a zero on the question due to the above. In another instance $$\int(x^{-2}v)'dx$$ had a red-mark that said it was equal to zero and said terrible. In the same question ##v'=yy'## during a substitution had a mark that just said terrible. I got two points for the question, even though the answer matched others who had gotten full credit so I'm assuming I was just marked down for notation.

    What's wrong with the above? Maybe this instructor just hates prime notation....
  2. jcsd
  3. Sep 21, 2016 #2


    Staff: Mentor

    I would ask your instructor about it. It may not be notation but perhaps Something more fundamental.

    In the first, your teacher may not have liked you dividing the ##dx## by ##x## and would have preferred that you wrote ##(1/x) dx## instead. It doesn't make sense to divide ##dx##as it's not a value but a kind of placeholder that indicates what variable to integrate over.

    In the second, I'd say the prime In the integral means that ##f(x)' dx## integrates to ##f(x)##. If that not what you meant then you can see your teachers concern.
    Last edited: Sep 21, 2016
  4. Sep 21, 2016 #3


    Staff: Mentor

    What you show above is an indefinite integral. Was the integral that the instructor marked a definite integral?
    Again, was the actual integral a definite integral?
    What do v' and y' mean here? Prime notation doesn't show which variable the derivative is taken with respect to.
  5. Sep 21, 2016 #4


    Staff: Mentor

    I don't think this is very likely. ##\int \frac{dx}{x}## is a wellknown integral that is often written this way.
  6. Sep 21, 2016 #5
    No. It was just a simple separable differential equation.. $$\frac{dy}{dx}=\frac{1}{x}$$ $$\int{dy}=\int \frac{dx}{x}$$ $$y=ln|x| + C$$

    It was just me writing out of a substitution for a Bernoulli Equation.. $$xy\frac{dy}{dx}+x^2-y^2=0$$ $$\frac{dy}{dx}-yx^{-1}=-xy^{-1}$$ so I had ##v=y^2##, ##v'=2yy'## so I guess v' would be ##\frac{dv}{dx}## and y' is ##\frac{dy}{dx}## then I multiplied, found integrating factor, and subbed out to get to $$\int(vx^{-2})'dx=\int\frac{-2dx}{x}$$ $$vx^{-2}=-2ln|x|+C$$

    Yeah, we've wrote it that way in earlier courses, no one seemed to mind. Physics professor always puts the differential in the expression... but she's a physics teacher, and probably doesn't care as much if it is wrong. The instructor was trying to show how it was wrong in the very next class, but I didn't really follow the "proof" that well.
    Last edited: Sep 21, 2016
  7. Sep 21, 2016 #6


    Staff: Mentor

    I don't see anything wrong with this, speaking as a former college math teacher of 18 years. I would ask the instructor why it was marked off.
    You have a sign error in the 2nd equation.
  8. Sep 21, 2016 #7
    Whoops, fixed it.

    Okay, but he seemed adamant that it was "wrong" notation. Terrible, terrible notation, garbage notation notes give that kind of vibe. Just a bit worried, have an exam in that class soon. Most of my quiz scores are abysmal due to notation I guess. To be fair, some it's certainty because I made errors like the above, missing a sign..etc. The problems are long, so I'm working on being more careful. Was kind of hoping there was some kind of one stop shop for "proper notation."
  9. Sep 21, 2016 #8


    Staff: Mentor

    What you have here -- ##\int(vx^{-2})'dx=\int\frac{2dx}{x}## isn't very good. An improvement would be ##\int d(vx^{-2})=\int\frac{2dx}{x}##

    If your instructor is dinging you for ##\int \frac{dx} x##, s/he is being pedantic, IMO.
  10. Sep 21, 2016 #9
    Got it.

    Just worried about what other notation 'mistakes' I'm not aware of.

    Thanks though, appreciate all the comments and time you've spent replying.
  11. Sep 21, 2016 #10


    User Avatar
    Science Advisor
    Gold Member

    For your first question I believe he was looking for [itex] \int \frac{dy}{dx}dx=\int \frac{dx}{x}[/itex]. Writing [itex]\int dy[/itex] should not be used, until you are taking a differential equations course.
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