Balder W. Holst

Hello there!

My name is Balder and this is my personal website. Here i write down what i learn to maybe help others some day. For now i will just act like people are reading my articles, and make them for fun.

This website has three main sections:

I write these articles for fun, and even though i try to make sure that they are correct, i am not a perfect human and there are sure to be mistakes. Below is a list of most recent articles in all categories.

Recent Posts

Gnidning
Gnidning Formel $$F_{\text{gnid}} = \mu \cdot F_{N}$$
0001/01/01 · Notes
Gnidningsmordstand gennem Luft
Gnidningsmordstand gennem Luft $$F_{luft} = \frac{1}{2} \cdot c_w \cdot \rho \cdot A \cdot v^2$$ Renolds-tallet (for en kugle) $$F_D= 6\pi \eta rv$$ $$Re = \frac{\rho \cdot v \cdot d}{\eta}$$ $\rho$ = densitet $v$ = hastighed $d$ = diameteren af kuglen $\eta$ = Viskositeten Re Strømningens Art Re < 1 Laminar Re > 2000 Turbulent
0001/01/01 · Notes
Gradient
Gradient See also Laplacian Operator En vektor der peger i $x$-$y$-planet, til den stejlsete side $$\nabla f(x_0,y_0)=\v{f_x'(x_0,y_0)}{f_y'(x_0,y_0)}$$ To get the rate of change ($h$) in a specific direction in a point, you can project the gradient onto the unit vector in the direction ($\hat{\vec v}$). $$h = \hat{\vec v} \bullet \nabla f(x_{0}, y_{0})$$
0001/01/01 · Notes
Gravitation
Gravitation $$F= G \frac{m_1 \cdot m_2}{r^2}$$ $$G = 6.67 \times 10^{-11} m^3kg^{-1}s^{-2}$$ Nær jorden overflade $$F_g= G \frac{Mm}{r^2} = m \cdot g \s\Rightarrow\s g = \frac{GM}{r^2} = 9,83 \s m \cdot s^{-2}$$
0001/01/01 · Notes
gravitationskraft
Gravitationskraft $$F_{gravitation} = G \cdot \frac{m \cdot M}{r^{2}}$$ $G$: Gravitationskonstanten (altid det samme) $m$: Den lille masse $M$: Den store masse $r$: Baneradius
0001/01/01 · Notes
Gray Codes
Gray Codes When a digital system switches its binary output, the bit updates may not happen at the same time. Therefore the gray system was invented. Here only one bit changes at a time
0001/01/01 · Notes
Green's Theorem
Green’s Theorem $$ \oint_{\mathcal{C}} \vec{F}(x,y) \ \mathrm{d\vec{r}} = \int_{a}^{b}\vec{F}(x(t),y(t)) \cdot \vec{r}'(t) \mathrm{dt} = \oint_\mathcal{C} f_{1}(x,y) \mathrm{dx} + f_{2}(x,y) \mathrm{dy} = \iint_{R} \frac{\partial f_{2}}{\partial x} - \frac{\partial f_{1}}{\partial y}\ \mathrm{dA} $$ Curve segments are always integrated counter clockwise. Meaning the bounded region is always in the left. You can go clockwise by simply making the expression negative. Example
0001/01/01 · Notes
Grænser
Grænser $$\lim_{x\rightarrow \infty}\left(f(x)\right) = L$$ L’Hopital-reglen Hvis et udtryk på brøkform, både har en tæller og en nævner der går mod $0$ eller $\pm\infty$, kan denne regel bruges. $$\lim_{x\rightarrow a}(f(x)) = \lim_{x\rightarrow a}(g(x)) = 0$$ $$\lim_{x\rightarrow a}(f(x)) = \lim_{x\rightarrow a}(g(x)) = \pm\infty$$ Hvis et af de ovenstående er sandt, er dette også sandt. $$\lim_{x\rightarrow a}\left( \frac{f(x)}{g(x)} \right) = \lim_{x\rightarrow a}\left( \frac{f'(x)}{g'(x)} \right)$$ L’Hopital-reglen - Video
0001/01/01 · Notes
Halveringtid
Halveringtid $$N = N_0 \cdot (1/2)^{\frac{t}{T_{\frac{1}{2}}}}$$ $N$ er antallet af kerner $t$ er tid $N_0$ er antallet af kerner i starten $T_{\frac{1}{2}}$ er halveringstiden $$A = A_0 \cdot (1/2)^{\frac{t}{T_{\frac{1}{2}}}}$$ $A$ er aktiviteten (henfald pr. tid) $t$ er tid $A_0$ er aktiviteten i starten $T_{\frac{1}{2}}$ er halveringstiden
0001/01/01 · Notes
Hamming Distance
Hamming Distance The number of bit-flips required to change one string of bits to another.
0001/01/01 · Notes