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Do you try to calculate each term then combine them together OR plug them all in at once OR...?

thanks

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- Thread starter zmike
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- #1

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Do you try to calculate each term then combine them together OR plug them all in at once OR...?

thanks

- #2

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Combine several large constants 'GM' for example or 'hc' into a more manageable number

Write the results of intermediate steps.

Check the units balance - and that you have the right units

- #3

phyzguy

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do your calculations slowly, use a scrap paper, don't try to do things with your head, check every calculation the moment you finish it, write big numbers and leters, don't smudge and write messy, if you make an error and use a pen cross over the whole thing with an X and do it again.

And always have an estimate in your head about what you expect-if the outcome looks suspicious try it again to see if you where right to worry. I

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- #7

Integral

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- #8

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Redoing the problem is one way to catch mistakes, but that can be time consuming so if you can find a quicker way to check that is better. You wouldn't want, on an exam, to double the time it takes to do each problem.

How to check an answer quickly depends on what type of problem it is. The OP mentioned doing integrals, so a good check would be to differentiate the result and see if you get the original integrand back.

If you're asked to solve an equation for

If you're asked to simplify an expression, then substitute simple values like 0 or 1 into the initial and final expressions, and see if the values agree.

If you're asked to factor a polynomial, see if the roots give zero in the original polynomial.

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- #10

arildno

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Intelligent *compartmentilization* of sub-expressions can also come in handy.

Suppose your original expression contains many sub-expressions, with different values of k, [tex]k*(\lambda-\mu)[/tex].

Here, introducing [tex]A=\lambda-\mu[/tex] reduces your writing burden (of the relevant sub-expressions) with two-thirds, thereby reducing the risk of calculating wrongly.

In order to maximize this beneficial effect, it might be smart to "complexify" your original expression, by adding zeroes and multiplying by ones in creative ways so that a number of such re-definable families of sub-expressions become apparent.

Sometimes, therefore, the best method to attack a complicated expression is to make it, as a first step,*more* complicated (having more terms/factors), rather than desperately, and naively, trying to reduce this complexity head-on.

Suppose your original expression contains many sub-expressions, with different values of k, [tex]k*(\lambda-\mu)[/tex].

Here, introducing [tex]A=\lambda-\mu[/tex] reduces your writing burden (of the relevant sub-expressions) with two-thirds, thereby reducing the risk of calculating wrongly.

In order to maximize this beneficial effect, it might be smart to "complexify" your original expression, by adding zeroes and multiplying by ones in creative ways so that a number of such re-definable families of sub-expressions become apparent.

Sometimes, therefore, the best method to attack a complicated expression is to make it, as a first step,

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- #11

disregardthat

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Don't rely on computers too much. Do every single step by hand, and in time you will become much more efficient and thank yourself for that extra bit of work. Programs such as WolframAlpha are useful but not very healthy if used often, in my opinion. My advice is to carefully analyze and double-check each step as you go. When you get used to this way of working out long calculations you will become efficient at it and rarely do mistakes, and you won't waste much time desperately looking for errors which can prove fatal to your entire computation.

I second Arildno's last advice; introducing new variables to easen up the algebra/arithmetic can be very useful, and I do it often.

I second Arildno's last advice; introducing new variables to easen up the algebra/arithmetic can be very useful, and I do it often.

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