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Tips for memorizing equations

InteractiveMind
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Last Modified: 2011-09-20
This isn't necessarily a math/science question itself, but I figured that if anyone could help on this, it would be you lot !

I've got a huge number of equations, identities, et al., that I need to learn — within a considerably short period of time as well..

I've found that some of these equations just stick; I read them once or twice, and they're in there for good (or, at least until after the exams :)).

But others, (particularly the trig and trig-calculus stuff) are not setting as firmly as I'd like them to (if at all).


I'm sure you've all faced this problem before... what has helped you?

Mneumonics (spelt correctly?) ? Simply applying the equations as often as you can ? Something else ? .. Something original ?  :)

Help !

Thanks.
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CERTIFIED EXPERT
Top Expert 2009
Commented:
Just understanding the equations, or at least seeing the logic of them. That has always been what helps me best to learn ...

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CERTIFIED EXPERT
Top Expert 2009

Commented:
A simple example to explain what i mean.

Ohm's law :

  I = V / R

When you know what voltage, current and resistance are (conceptually), then you can easily derive that raising the voltage will generate more current, while raising the resistance will limit the current. Hence the above formula - and you'll never forget it again :)
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Top Expert 2009

Commented:
regarding trigonometry : a lot of the equations can be generated from the others ... so, basically, you just have to learn
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Top Expert 2009

Commented:
continued :

so, basically, you just have to learn a few, and the others can be derived from them ...
Knowing how to derive them is the important thing.  

When I revised for exams I would progressively condense the whole year's notes for each subject down to one A4 sheet. By the time I'd iterated through the notes three or four times in this manner, weeding out stuff I knew that I wouldn't forget, I was left with the awkward formulae which were the starting points for derivation, together with a description of what needed to be done (multiply this bit out, etc.).  It certainly doesn't harm going through the derivation in the exam, there should be some slack to enable it to be done - if a step goes amiss you are arguably more likely to score points for your effort, as opposed to simply writing a formula down wrong from memory.  If you are doing stuff like Laplace or Fourier Transforms you should expect to be given the relevant tables in the exam.
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Top Expert 2009

Commented:
>> condense the whole year's notes for each subject down to one A4 sheet
same "tactic" here :)

>> It certainly doesn't harm going through the derivation in the exam
Agreed ... it refreshes the context for you, which will make it easier to apply the equation.
Infinity's ohms law there has jogged my mind about something.  

Quite often you can double-check the validity of your formulae simply by sticking the units in and knowing for instance that a kilogram metre per second squared is in fact the same thing as Newtons.  Knowing how units are derived from each other will get you out of some tight spots sometimes.
Top Expert 2006

Author

Commented:
Thanks guys; I certainly have found it easier to recall things if I am able to actually derive them.

However, we've not been shown how many of these identities have been derived; so this is not entirely applicable :(


But I suppose that half of the identities that we've been given are just shortcuts... for example, we're given both of these:

   ~  d/dx[ e^f(x) ] = f'(x).e^f(x), and
   ~  d/dx[ e^(ax+b) ] = ae^(ax+b)

But the second one is clearly a simplification for when f(x) is linear... so it's not really necessary that I learn it..


So, I shall try and condense my "notes for each subject down to one A4 sheet" as well, and see where that gets me  :)


Any other ideas are more than welcome! Anything really strange that has seemed to help any of you? (such as... erm.. i don't know... <random>reading upside down?</random> :\ ).
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Top Expert 2009

Commented:
  ~  d/dx[ e^f(x) ] = f'(x).e^f(x), and
   ~  d/dx[ e^(ax+b) ] = ae^(ax+b)

even "worse" :

d/dx[ e^f(x) ] = f'(x) . e^f(x)

is derived from this more general formulae :

d/dx[ a^x ] = ln a . a^x              (a > 0)

or :

d/dx[ e^f(x) ] = ln e . e^f(x) . d(f(x))/dx = f'(x) . e^f(x)
Harisha M GEngineer
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Commented:
Hi, as Infinity08 and moorhouselondon have said, you need to know how to derive them..

For ex, you know chain rule.. d[f(x)]/dx = d[f(x)]/df  . d[f]/dx

So, easily you can derive any derivative...

 d/dx[ e^f(x) ] = d[e^y]/dy  .  dy/dx  = e^y . dy/dx = e^f(x) . df(x)/dx

Never remember the "shortcut" equations ! They are the ones, which make you suffer in the exams if you forget them !

And remember that you need to *work hard* and probably harder, and solve as many problems as you can, in each category, to master mathematics ... as ozo does !


Here is my personal experience: In my textbook (3 year before) there was a problem... and here is an extract:

"d[3^(4^(5^(e^(1/sin x))))]/dx = 3^(4^(5^(e^(1/sin x)))) . log 3. 4^(5^(e^(1/sin x))) . log 4 . 5^(e^(1/sin x)) . log 5 . e^(1/sin x) / sqrt(1-x²)

Note that we have not given details regarding the use of chain rule in the above problem. After some practice it should be possible to write down the derivatives in one step! ..."


There were 185 exercise problems, and I solved each of them and realised that the above statement was true :)

"Practice makes man perfect !"

---
Harish
The more you do, the more you learn. Do a lot of exercises, repeat them again and again until it is secured in your mind. Explaining to your colleagues what you have learnt also helps.
CERTIFIED EXPERT
Commented:
Flash cards are a well tested method of learing many equations, words, and arithmetic operations..
Get yourself a pack of 3 X 5 cards or near size.
Write the name of the equation on one side and the equation on the other. Carry them with you and look at them at the odd moment.

on one side     on other side
tan(a)               sin(a)/cos(a)
sin(2a)             2 sin(a) cos(a)
quadratic formula    etc


Thus you can not waste the few min waiting for something
To remember a lot of the calculus stuff, I just remembered it as words.

Chain Rule:
THe derivative of the outside times the derivative of the inside

Product Rule:
The derviative of the first times the second plus the first times the derivative of the second

Quotient Rule:
The top Times the derivative of the bottom minus the bottom times the derivative of the top all over the bottom squared.


Try to explain all these formulas to your self in words, sometimes it helps.

Brian
Top Expert 2006

Author

Commented:
Thanks all, I shall give this stuff a go. :)
CaptainCyrilFounder, Software Engineer, Data Scientist

Commented:
Resistors stripe colors in order:
Black
Brown
Red
Orange
Yellow
Green
Blue
Violet
Grey
White

Make a story
Bad Boys Raped Our Young Girls But Violet Gave Willingly (Bad Version)
Bad Boys Raced Our Young Girls Behind Valley Garden Walls (Good Version)

On some formulas I try to make a sentence by taking the first letter or the letters from the equation. Most of the trig formulas can be easily derived. If it's hard to memorize, create a story on the letters and the operations.

In Physics you have to know how to derive each formula most of the time so I don't think there is a problem there.

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