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Math Math MATH!

  1. Jul 15, 2004 #1
    I was thinking of a career in engineering, but now that i think of it , not anymore, i love physics, i can do physics with no problems, but math....thats a different story, i dont know wut the hell is wrong with me, i'v had a calculus test on Limits yesterday and i studied the night before four about 5 hours (reading over notes, mostly practicing lots of problems), and then i get 70% on the test.... this is really getting on my nerves and im thinking of dropping the course, we are now doing derivatives and im doing that fine, but today my teacher introduced the chain rule, and now my head is about to explode from trying to figure that out. I do lots of problems so i can be ready for my tests. My teacher puts questions similar to the ones she assigns for homework, but puts about 3 questions that are really hard, and she makes those questions worth more than all of the other questiosn put togther... its not like i cant do them, but they confuse me because i'v been practicing something and something like that comes in and messes me up...

    Is there anything i can do to better help me prepare for math tests, or is math just not for me.... i mean i like math, and i love physics, im good at physics, but i suck at math...how would this effect my choice of career in engineering...

    Thanks in advance.
     
  2. jcsd
  3. Jul 15, 2004 #2

    chroot

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    Gold Member

    Sounds like you need a patient tutor. Pay one if you have to.

    - Warren
     
  4. Jul 15, 2004 #3

    BobG

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    If you can do physics problems, then I assume you can do unit conversions, right? The chain rule isn't really much more than doing unit conversions. Item A changes by a certain amount in response to a change in B, except you don't want your answer in terms of B. So you have to have to multiply your first answer by the rate that B changes in response to C - the term you want your answer in. And so on, sometimes, just like unit conversions can be several steps.

    For example:

    You want to find out how fast your radius is changing in meters per second along an elliptical orbit. Unfortunately, you have to find out how much the radius changes per degree first (the derivative of your radius with respect to angle). Then you need to find out how fast your angle is changing in degrees per second or radians per second (the derivative of your angle with respect to time). When you multiply them together, you have meters/degree times degrees/second. Since degrees are on both the top and bottom, they cancel out, leaving you with meters/second.
     
  5. Jul 16, 2004 #4

    Gza

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    It's actually pretty unusual to be good at physics without being good at math. Thats like saying you are terrible at dribbling and shooting, but you are a good basketball player. I suggest you strengthen your algebra skills, since that's what i'm beginning to suspect your troubles stem from, since calculus in itself is not very difficult; in fact that reminds me of a quote I heard about someone claiming he could teach a fifth grader calculus, but its really the algebra that would kill them.
     
  6. Jul 16, 2004 #5
    I agree with the tutor suggestion. If you're taking classes at a college, you should check to see if they offer free tutoring. If so, give it a shot. The worst that happens is that you waste a little time. It might really help.
     
  7. Jul 16, 2004 #6
    I tutor and I hear your complaints at the beginning of every semester. The chain rule takes time and practice to master. Once you do it a zillion times it will come second nature. Just practice that's the only thing I'd recommend. Do all the problems in your book. If you still have trouble go to a library and grab a calc book and start doing the problems. Eventually a little light will come on or a bell will ring and from that point on you'll apply the chain rule without a probelm (and without realizing it).

    You can applly the chain rule from the outermost function inward or the innermost function outward. I recommend the latter because it follows the rules you apply from algebra anyway.

    example:
    [tex]
    f(x)=\sqrt{x^2+9}
    [/tex]

    In this case if you where to substitute a valu in for x then solve it where would you begin? You replace the x with said value, square it and add 9 so why not start there with your derivative?

    [tex]
    \begin{equation}
    (x^2+9)\frac{d}{dx}=2x\ dx
    \end{equation}
    [/tex]

    Now if this were algebra again and you had a number under the radical what would you do? You find the root of coarse do the same thing with the chain rule here:

    [tex]
    \sqrt{\ }\frac{d}{dx}=\frac{1}{2}(\ )^{-\frac{1}{2}}\ dx
    [/tex]

    Now all you have to do is combine the two

    [tex]
    \sqrt{(x^2+9)}\frac{d}{dx}=2x\frac{1}{2}(\ )^{-\frac{1}{2}}\ dx
    [/tex]

    and stick the original inner equation(1) into the void and simplify.

    [tex]
    \sqrt{(x^2+9)}\frac{d}{dx}=x(x^2+9)^{-\frac{1}{2}}\ dx
    [/tex]

    The chain rule will come as second nature. Also, don't sweat limits either. You need to understand what is going on with a limit because that concept eventually builds into the concept of a derivative but you'll eventually learn this theorem called L'Hopitals rule which will make finding limits much easier--in fact if you find it in your text you could use it on your final to "verify" your answer when doing limits the conventional way.

    Well, good luck and may the [itex] \lim_{\Delta x \rightarrow 0} \frac{f(x+\delta x)-f(x)}{\Delta x} [/itex] be with you.
     
    Last edited: Jul 16, 2004
  8. Jul 19, 2004 #7
    thx faust and everyone else for advice and help...i think you are right, my problem is with the algebra, i have reviewed my tests, and my biggest source of error is the algebra, i understand the concepts well, and now how to apply them, i just have to learn to apply them right. Any suggestions to help me in my "weak" algebra skills?
     
  9. Jul 19, 2004 #8
    Resist the temptation to do algebra in your head. Always write down every step no matter how easy or insignificant. You're less likely to mess up and when you do you can usually spot it. Make you negative signs big and pronounced. Not distributing a negative is a big offender. If you spot a mistake don't try and squeeze a correction in (ie write a negative near the top of a number because you forgot it). Erase or put a light line through the error and start writing in another location. Keep your work neat and organixed. I still do this:

    Code (Text):

    (x-2)(x-4)=

    x^2-4x
       -2x +8 = x^2-6x+8

     
    keep your work neat and organized. Make the radian/degree equivilents second nature. When someone says 30 degrees you should immediatly say
    [tex]
    \frac{\pi}{6},\sin{\frac{\pi}{6}}=\frac{1}{2},\cos{\frac{\pi}{6}}=\frac{\sqrt{3}}{2},\tan{\frac{\pi}{6}}=\frac{\sqrt{3}}{3}
    [/tex]

    Verify the solution to every function which involves a quotient is a valid solution. I've seen this a lot where people will determin the domain of a function write said domain down but never verify the soultions are in the domain.

    Basically, write everything down, and be very neat about what you do.

    Here: something to comb through http://archives.math.utk.edu/visual.calculus/

    Good luck.
     
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