A centered difference matrix is the difference between the preceding and following entries in x. I hope that's correct.
So it follows that your 3D centered difference matrix,
x1 is the difference between x2 - 0
x2 is the difference between x3 - x1
However
x3 is NOT the difference between 0 -...
A difference matrix takes the entries of a vector and computes the differences between the entries like
[x1 - 0 ] = difference from 0 and x1: 1 step
[x2 - x1] = difference from x2 and x1: 1 step
[x3 - x2] = difference from x3 and x2: 1 step
assuming we had a vector x in Ax = b
So why now when...
LOL Okay. I got the answer. Welp it seems like they way you derive the matrix you have to say consistent, otherwise you fall in a a trap.
https://en.wikipedia.org/wiki/Active_and_passive_transformation#/media/File:PassiveActive.JPG
Staring at this image for a bit and making sense of this...
Alright. I was looking into a 2D rotation matrix and there are two equations: one is through the transformation of the component of p (always with respect to x,y), x,y into x',y' and the other is through the transformation of the unit vectors i,j into i',j'.
In a sense 1 is passive the other is...
These are the notations of quaternions that i have seen:
q = s + v
q = (s, v)
q = s + ai + bj + ck
where s, a, b, & c are members of the reals
but why not use the notation of:
q = (s, a, b, c)
isn't it the same as the 2nd notation except it is clearer? So why does it take a quaternion to be...
So how would you bound a complex equation between a δ?
Because when you are doing ε δ proofs you often work with linear functions.
And when you get a quadratic, you simplify into linear functions and bound one of them.
for example:
lim f(x) = x2 - 25 = 0
x -> 5
0 < |x - 5| < δ →...
3 + 7i < 5
Is that a valid statement?
Would that be taking the magnitude of 3 + 7i and comparing that to the magnitude of 5?
Or would it be as simple as subtracting and -2 + 7i < 0
But then what does that mean, for a complex number (-2 + 7i) to be less than zero?
Homework Statement
Find the equation of the asymptotes.
On the interval -pi < x < pi
Homework Equations
tan(2 sin x)
The Attempt at a Solution
sin(2 sin x)/cos( 2 sin x)
Set cos( 2 sin x) = 0
2 sin x = arccos(0) = pi/2
2 sin x = arccos(0) = -pi/2
x = +-(arcsin pi/4)...
Alright I've been giving it a go. And so far so good. I tried the brute force method and it worked like a charm. I then tried the basic symmetrical law of creating 3 equations, then adding them up to, again, brute force into the symmetrical form desired-- it's just great! I'm learning a lot...
Its makes so much sense. Thanks to both you guys. But I have one more question. How would someone know the equation is symmetrical? Is there a dead giveaway, or do you just have to try it and see if it works out?
Original Equation
(Q1+Q2-Q3)2 = 4Q1Q2
Recomposed
(Q1+Q2+Q3)2 = 2(Q12 + Q22 + Q32)
Q's stand for quadrances or the area or a square built on the segment that is the square root of the Q.
http://www.parabola.unsw.edu.au/vol43_no1/img145.png
Q1 is (A1 to A2)2
Q2 is (A2 to A3)2
Q3 is...