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Nov
18
revised Using Runge-Kutta-Fehlberg 4-5 for higher dimension systems
added 1137 characters in body
Nov
17
revised Using Runge-Kutta-Fehlberg 4-5 for higher dimension systems
added 1015 characters in body
Nov
17
revised Using Runge-Kutta-Fehlberg 4-5 for higher dimension systems
added 23 characters in body
Nov
17
comment Using Runge-Kutta-Fehlberg 4-5 for higher dimension systems
Thanks. Do you know of a reference which contains RK45 in 2 and 3 dimension spaces?
Nov
17
revised Using Runge-Kutta-Fehlberg 4-5 for higher dimension systems
added 58 characters in body
Nov
17
asked Using Runge-Kutta-Fehlberg 4-5 for higher dimension systems
Nov
13
comment Show $\frac {1}{2\pi i}\int_\gamma\frac {f'(z)}{f(z)}$ is sum of poles and zeroes times their order
Could $\int \frac{f'}{f} = \log f$ be of help here ?
Nov
11
comment How to solve the Integral $\int_{-\infty}^\infty [\tanh(\frac{x+a/2}{b})-\tanh(\frac{x-a/2}{b})]e^{ikx} dx$?
Also, perhaps Fourier transform or some integral transform method?
Nov
11
comment How to solve the Integral $\int_{-\infty}^\infty [\tanh(\frac{x+a/2}{b})-\tanh(\frac{x-a/2}{b})]e^{ikx} dx$?
Maybe differentiate wrt to $a $. Just a thought to try...
Nov
7
revised Not every holomorphic function $f$ can be written as $f(z)=e^{g(z)}$
edited body
Nov
6
accepted How to write down, think about, and evaluate a simple Lebesgue integral
Nov
4
asked How to write down, think about, and evaluate a simple Lebesgue integral
Nov
3
comment What does it mean for two functions to be orthogonal?
I've been expecting that comment. I can mentally grasp the idea of orthogonality in higher dimensions. Visualisation is tricky of course. I think my original confusion was in accepting functions as vectors, but once i intuitively pictured these functions as infinitely many component values along the x axis i can by extension mentally accept orthogonality of function vectors too. It's all a bit mental and vague, but helps to grasp the maths.
Nov
3
accepted What does it mean for two functions to be orthogonal?
Nov
3
comment What does it mean for two functions to be orthogonal?
@Thomas Andrews so one interpretation is that two orthogonal functions have zero linear relationship.
Nov
3
revised What does it mean for two functions to be orthogonal?
added 111 characters in body
Nov
3
comment What does it mean for two functions to be orthogonal?
Thanks, nice property to point out. Although, I was hoping to avoid referring back to the inner product (the integral - which is related to the area). I was thinking more of properties of $f$ and $g$ which didn't rely on the inner product. Much like perpendicularity can be viewed geometrically without referring back to the scalar product. If that makes sense.
Nov
3
revised What does it mean for two functions to be orthogonal?
deleted 138 characters in body
Nov
3
comment What is the geometric meaning of the inner product of two functions?
So when we compute the "angle" between two functions, $\cos\theta=\frac{\langle f,g\rangle}{\|f\|\|g\|}$, we don't really know what "angle" means any more ?
Nov
3
asked What does it mean for two functions to be orthogonal?