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

C++ Streams
C++ Streams Write to File #include <iostream>#include <fstream>using namespace std; int main () { ofstream myfile ("example.txt"); if (myfile.is_open()) { myfile << "This is a line.\n"; myfile << "This is another line.\n"; myfile.close(); } else cout << "Unable to open file"; return 0; } Read file token by token #include <iostream>#include <fstream>#include <string>using namespace std; int main () { ifstream myfile ("example.txt"); if (myfile.is_open()) { while (myfile >> temp) { cout << temp << ' '; } myfile.
0001/01/01 · Notes
Centripetalacceleration
Centripetalacceleration $$\vec{a} = -\frac{v^2}{r} \hat{r}$$
0001/01/01 · Notes
Centripetalkraft
Centripetalkraft Kraften ind mod midten af en cirkel under Jævn Cirkelbevægelse $$F_{c} = m \cdot \frac{v^2}{r} $$
0001/01/01 · Notes
Change of Variables
Change of Variables Used to get of non-constant boundaries of integrals. We define a function to map another, more convenient, space to the original space: $$ \int_{g(D)} f(x,y) = \int_D f(g(u,v)) \cdot ||J|| $$ $f(x,y)$: The original function $g(x,y)$: The function in the more convenient space ($g$ must be injective) $||J||$: The absolute value of the determinant of the jacobian of $g(u, v)$ at the point $(u,v)$ Explaination What is Jacobian?
0001/01/01 · Notes
Chebyshev Filter
Chebyshev Lektion 1 - Filterfunktioner.pdf>page=28 Høj forstærking ved lav orden 2dB
0001/01/01 · Notes
Circles
Circles A unit circle scaled by $a$ in the $x$-direction and by $b$ in the $y$ direction. $$\frac{x^{2}}{a} + \frac{y^{2}}{b} = 1$$
0001/01/01 · Notes
Cirklens Ligning
Cirklens Ligning $$\sqrt{(x-x_0)^2 + (y-y_0)^2} = r$$ alternativ: $$(x-x_0)^2 + (y-y_0)^2 = r^2$$ Variabler: $C = (x_0,y_0)$, cirklens centrum $P = (x,y)$, punkt på cirklen $r = |\vec{CP}|$, cirklens radius Tangenter på cirklen Order of operations Find $\vec{CP}$ ved at sætte et tal ind på $x$’s plads i ligningen. Bemærk at der nok kommer to $y$-værdier ud, så må man bare vælge den rigtige. Vi kan nu sætte hat på $\vec{CP}$ for at finde tangentens retningsvektor og lave parameterfremstilling eller bruge $\vec{CP}$ som normalvektor og opstille linjens ligning for tangenten.
0001/01/01 · Notes
Classes in C++
Classes in C++ class MyClass { public: MyClass(); private:
0001/01/01 · Notes
Classification of Second order PDEs
Classification of Second order PDEs $$Au_{xx} + Bu_{xy} + C_{yy} + Du_{x} + Eu_{y} + Fu = G$$ Linear: $A$, $B$, $C$, $D$, $E$ and $F$ are only a function of $x$ and $y$ (and not $u$). In a linear PDE the sum of two solutions is also a solution. Quasi-linear: $A$, $B$, $C$, $D$, $E$ and $F$ may be functions of $x$, $y$, $u$, $u_{x}$ and $u_{y}$. **Fully Non-linear**: $A$, $B$, $C$, $D$, $E$ and $F$ may be functions of $x$, $y$, $u$, $u_{x}$, $u_{xx}$, $u_{xy}$ and $u_{yy}$.
0001/01/01 · Notes
Coulumbs konstant
Coulumbs konstant $$k_c=8.9876 \cdot 10^9 \ \frac{\text{N} \cdot \text{m}^2}{\text{C}^2}$$
0001/01/01 · Notes