Friday, July 27, 2007

BOD..I mean BIDMAS!

The page that wouldn't fully load for me yesterday, has blessed me with it's insight! (It's the 'Common Undergraduate Errors' one).

In school I was taught 'BODMAS' - Brackets O.. Division, Multiplication, Addition, Subtraction. (I can't remember what the O was).

Hence, if I may copy something from that site, I used to interpret -3^2 as (-3)^2, which resulted in the wrong answer. I remember this very well since in my case the number had been -2 (I think) and it had been an integration question at college. I've just managed to locate the question and it was:

\displaystyle\int^2_0 xe^{-x^2}dx

I'll tell you something embarrassing- just know I tried doing the question on paper and my mind was blank. The first thought to zoom into and out of my head had been, 'integration by parts'! Don't worry, a good bang against the wall soon sorted me out. (In my defence the chapter after this one was on integration by parts....)

I might as well attempt it here in the way I did a year or so ago. I can't do substitutions in my head (since integration stinks!), so we do it the long way. I don't really know how the write this out 'nicely' so here goes.

We use the substitution u=-x^2.

\begin{array}{ccc} u & = &-x^2\\*[1ex] \displaystyle\frac{du}{dx} & = & -2x\\*[1ex] dx & = & \displaystyle\frac{du}{-2x}\\ \end{array}

Now this is the place when I made my silly mistake- changing the limits. I did,
\\\text{When }x=2, u=(-2)^2=4 \text{ and when }x=0, u=0.

Oops- the mistake has been made. (It's meant to be -4). I don't think I ever realised my mistake at that time and had just regarded the answer in the back of the book to be wrong. (The answer in the back of the book was \frac{1}{2}(e^4-1). Please tell me that it is wrong! Since having done it again, hopefully properly, I get \frac{1}{2}(1-e^{-4}). I think the book might be wrong, since it says the answer is about 26 which doesn't sound right.

However the point is, that I think nowadays in schools they are thankfully taught BIDMAS, rather than BODMAS. (I=indices). I'm not sure how I feel... frustrated maybe that I didn't know this before, although it seems to be a must know thing. I probably had come across it, but this convention wasn't drilled into me. I do recall asking my normal maths teacher (since that question had been driving me nuts) about this, but she'd concluded that the book must be wrong. I then asked my further maths teacher, but I think I had been embarrassed at the nature of the question and instead had stupidly just asked him whether -2 squared was 4, which it is. (Did get a weird look for that).

The question after all says -1(x^2), which I'd overlooked. Ah well, hopefully I won't be making that mistake again! BIDMAS all the way. (BTW what did the O stand for?) I'm not sure whether this is taught in primary schools, but words like indices should be made known to students at an early age.


I might as well mention a small (and unrelated to BIDMAS) thing now and expand on it later. A friend of mine has been reading a book and supposedly 'successful' people are those who are committed to achieving certain goals. They know what they want to accomplish. If you ask this kind of person what they hope to achieve, they'll give you a well thought out and concise answer. Whereas those who are not committed to anything but 'earning loads of cash' may not be as successful. Success is a result of commitment more than luck. I've asked to borrow this book, but I'm writing this since Andrew Wiles popped into my head when I was talking to my friend. He was totally focused on achieving something and he did. It's all about our attitude and approach to things that matters after all. Maybe I should take heed? (I'll be back with more after reading that book!)

9 comments:

beans said...

Having read further, BO = bracketed operations.

egm said...

The O is OF. as in half OF 3. Remember this from way back when I was taught BODMAS in school.

beans said...

Ah, I see. The words of and over had gone through my head, but I couldn't settle for any. The of didn't make sense before but when you put it that way I understand!

(Oh and welcome back- hope you had fun! :D)

Jake said...

I don't think it will stand for 'of' as 'of' in that sense just means multiplication

e.g. half 'of' 3 just means half multiplied by three.

I would assume that the 'o' stood for order, as in exponentiation as that fits in with BIDMAS.

beans said...

I think order makes the most sense since that does fit in with BIDMAS. Hmmm, I'd never actually heard of the O being order before! So BODMAS is fine, as long as the O is made clear I suppose.

Anonymous said...

O = Order
another word for order is "power"

ie 2^2=4
2 to the order of 2 is 4
2 to the power of 2 is 4

brackets, power, devision, multi, add, sub.

yet BPDMAS just doesnt have that same ring to it =)

Беанс said...

I am sure we could think of a saying with the P there! ;)

Like SOHCAHTOA is remembered by: Silly Old Harry Caught A Herring ....

Anonymous said...

hey lots of info there and y plus o in BODMAS stands for Of! so u can put that in

jas said...

hey O means of or on