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twesterm on 24 December 2008
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TheLivingShadow said:
twesterm said:

Now, if people are *really* in for some nerd stuff, here are some fun math problems (not high school level):


If F(s) = s3 / (s2 + 9)2, find f(t) using Laplace transforms

Solution

s3 / (s2 + 9)2 = (As + B) / (s2 + 9)2 + (Cs + D) / (s2 + 9)

= (3): A[s / (s2 + 9)2] + B[1 / (s2 + 9)2] + C[ 1/  (s2 + 9)2] + (D / 3)(3 /  (s2 + 9))

Using (1) and (2)...

L-1[s3 / (s2 + 9)2] = A((1 / (2 * 3))t sin (3t)) + B( (1/(2 * 33)) sin (3t)) - ((1 / (2 * 32)) t cost (3t))) + C cost (3t) + (D / 3) sin (3t)

multiply both sides of (3) by (s2 + 9)2 to get

s3 = As + B + (s2 + 0)(Cs + D)

S3: 1 = C,
S2: 0 = D,
S: 0 = A + 9C,
1 = s0: 0 = B + 9D.

A = -9,
B = 0,
C = 1,
D = 0.

(1): L-1[s / (ss + b2)] = (1 / 2b)t sin (bt)

(2): L-1[1 / (s2 + b2)2] = )(1 / (2b3)) sin (bt)) - ((1 / 2b2) / (t cost (bt)))

God I loved DiffEQ.

 

You're right about my problem, good for you!

However I could never answer that now because that is beyond my current knowledge (though not perhaps capabilities). I don't even know who's Laplace...

Also, it seems that you guys have misunderstood me a little. Mathematic problems are not the same as mathematic exercises. Problems make you think, exercises make you practice knowledge. Please try to get some problems if you can.

By the way since you answered that one correctly, here's a harder one for anyone who may want to do it.

There's N which is equal to the product of the first 99 numbers. There's also M which is equal to the product of the reverse of the first 99 numbers. If a number has only one digit, its reverse is the same number. If the digit is of the form ab, its reverse is of the form ba. Calculate the value of

M/N

I shall wait for some answers!

 

Sadly don't have time to think about your problem (or even read the FF thread I made ;_;), though I'm going to take a wild shot in the dark and say it's 1, but I will say this, that thing I posted above is a problem and not just an exercise. 

I skipped A LOT of thinking steps in there and just stuck to the answer.  You have to put a lot of thought in how you go about solving that problem and not just apply a few formulas. You have to move things around just right to get things into a specific type or else it just doesn't work.

So yeah, not really a logic problem but not just an exercise either. 

Usually those types of problems take me about 1-2 pages of work (turning in homework for that class was like turning in a book).

Merry Christmas, I'm off to my parents and then the wife's parents tomorrow ^^