heh, its really more of an on and off thing. Like, woohoo i got this question right, i love e...... damn it. got this wrong, ****** e, i oughta....Originally posted by confuted
In my experience, when you get to Diff. Eq., you and e will grow to hate each other
Once you get to diff eq's, you'll curse e because a problem that could have simply been nice and insoluble suddenly becomes soluble in a rather painful manner.
The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.
to be honest I don't understand much of what this means. About all I can gather is the solution to this equation gives the sqrt of n:You can use Newton-Raphson to find the roots of (well-behaved) functions quickly (such as: x^2 - n, where n is the number to find the square root of).
Basically, it goes as follows:
x[i+1] = x[i] - f(x[i]) / f'(x[i])
x[0] is an initial guess, basically
x^2 - n = 0
but basically the rest of the notations throws me off, i.e what does x[i+1] mean?
>> but basically the rest of the notations throws me off, i.e what does x[i+1] mean?
think of it as an array called x filled with approximations for your answer. the higher up in the indexing you get, the more accurate your answer becomes. so, you use x[0] to get x[1], then you use x[1] to get x[2] and so on, the more times you repeat this, the more accurate your answer becomes.
x[i+1] = x[i] - f(x[i]) / f'(x[i])
the formula says you take your last value for x, and subtract the function at x divided by the derivative of the function at x. note how you need an initial value to start with.
thanks
I really prefer the letter i to the letter e, its much simpiler and requires less thinking.
Sorry 'bout the notation. The x[i] really should be x subscript i, so yeah, basically an array (though you really don't need to store any more than x[i]), so:
x = x - f(x)/f'(x)
should do just fine.
Prime notation is just another way to show derivates (y' is first, y'' is second, y''' is third, and y subscript (n) with paren is the nth derivative).
The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.
when you said y' is first, y'' is second, and y''' is third, you meanPrime notation is just another way to show derivates (y' is first, y'' is second, y''' is third, and y subscript (n) with paren is the nth derivative).
y' = derivative of y
y'' = derivative of y'
and so on?
Isn't that what integrals are or something like that? (working backwards, like trying to find y when you are given y'''''''''''''''''''''''')
EDIT: and you really must speak in lay men's terms because I don't know much of the terminology or notation or anything really because I haven't taken calculus yet
First part, yep.
Second part, yep although you couldn't be that accurate with your example
There are two 'categories' of integrals you'll run into in single variable calculus. The first, if the indefinite integral, also known as the anti-derivative. Basically, given y', recover the function y. The definite integral has limits of integration between which the integral is evaluated. The two are connected using the fundamental theorem of calculus.
As you suggested, given y(n) (nth deriv of y), you could recover y. In actuality though, you'd recover a family of functions (to which y belongs) that all have the same nth derivative.
Then, later on, you run into things like line integrals, surface integrals, multiple integrals, Stieltjes integrals... All fun stuff.
The word rap as it applies to music is the result of a peculiar phonological rule which has stripped the word of its initial voiceless velar stop.
how rude of you to forget sohcahtoa inverse logarithmic reciprocal hot cake integrals!@#$#$#@!Stieltjes integrals
