Recent content by Septimra

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 -...

its not for a particular application, just for better understanding of centered difference matrices

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...

Hehe alright, thanks. Looking back at it, I was being pretty dense.

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 you cannot bound an equation with imaginary parts? What you are saying is that to do that wouldn't even make sense.

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?

Haha whilst formulating my response... I saw the light! Thank you so much! Great way to start the day, and good one to ya!

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...