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

Phasor Representation
Phasor Representation Representation af AC med Komplekse Tal. Her en den imaginære del ikke repræsenteret af $i$. Her er den repræsenteret af $j$. Her kan vi omdanne en bølge til komplekse tal. $$V(t) = V_{1} \cdot \sin(\omega t + \phi) \rightarrow V_1\angle\phi$$ Det kaldes resonans når den *imaginære* del er $0$. Video Differentiering $$V= V_{1}\angle\phi_1 =V_{1}\cdot e^{j(\omega t+\phi_1)}$$ Vi differentierer $$\frac{dV}{dt} = j\omega \cdot V_{1} \cdot e^{j(\omega t+\phi_1)} = j\omega \cdot V$$
0001/01/01 · Notes
Planck konstanten
Planck konstanten $$h = 6.6261 \cdot 10^{-34} \ \text{J} \cdot \text{s}$$
0001/01/01 · Notes
Plane Kredsløb
Plane Kredsløb Networks that can be drawn on a plane without having one element (or conductor) crossing over another are called planar networks. - > Electrical Engineering>
0001/01/01 · Notes
Planer
Planer Dette er sandt i et plan $$\vec{n} \bullet(P-P_0) = 0$$ $\vec{n}$ : Normalvektor til planen. $P_0$ : Et “startpunkt” på planen. $P$ : Et hvilken som helst punkt på planen. Planens Ligning Fra Calculus. $$n \bullet (r-r_0)=0 \arrows A(x-x_0) + B(y-y_0) + C(z-z_0) = 0$$ eller $$Ax + By + Cz + D = 0 \s \text{hvor } D = Ax_0 + By_0 + Cz_0$$ Omskrivning til funktion at to variable $$Ax + By + Cz + D = 0 \arrow z = - \frac{A}{C} x - \frac{B}{C} y - \frac{D}{C}$$ Dette må betyde at funktionen skal være på formen $$z=\alpha x + \beta y + \gamma $$
0001/01/01 · Notes
Pointers
Pointers Holds an address of a variable. The reference operator (&) is used to get a variable’s address in memory. See also smart pointers. Declaration type * name; Example: // Creates a points p that holds the address of var int * p = &var; Warning Pointers should always point to something. Dereference Operator “What is the pointer pointing at?" var = *pointer // Reads the data at the pointer location.
0001/01/01 · Notes
Poissin's Equation
Poissin’s Equation Laplace’s Equation but with forcing $$\nabla^{2} u = f$$ $u$: Unknown function $f$: Forcing function
0001/01/01 · Notes
Polar Coordinates
Polar Coordinates A two dimensional space described $r$ and $\theta$. Coordinates to Polar Coordinates $$ \begin{align} g(r, \theta) &= ( \underbrace{r \cos\theta}x, \underbrace{r \sin\theta}{y} ) \ ||J|| &= r \end{align} $$ $g(r, \theta)$: The mapping from polar space to cartesian space. $||J||$: The absolute value of the jacobian of $g$. $$ \begin{align} x &= r \cdot \cos(\theta) \ y &= r \cdot \sin(\theta) \ \mathrm{dA} &= r\ \mathrm{d\theta}\ \mathrm{dr} \ x^{2}+y^{2} = a^{2} &\Rightarrow a \end{align} $$
0001/01/01 · Notes
Pooling
Pooling A loop constantly checking for changes on a register, port or other input. An interupt is usually preferred. This method halts the processor when reading the interupt. Example while(1) { ADCSRA=0b11000011; //ADC starts conversion while(ADCSRA==0b11000011); //Check if ADC is done PORTB=~ADCH; }
0001/01/01 · Notes
Potensregneregler
Potensregneregler page=7#page=7"
0001/01/01 · Notes
Potentiel Energi
Potentiel Energi $$U = m \cdot g \cdot h$$ $U$ : Den potentielle energi $m$ : Massen. $h$ : Højden over jorden. $g$ : Tyngdeaccelerationen. Arbejde $$\Delta U = -W$$ $\Delta U$ : Ændring i potential energi $W$ : Arbejde Fjeder $$\Delta E_{pot} = kx^2$$ $\Delta E_{pot}$ : Ændring i den oplagrede energi. $k$ : Fjederkonstanten. $x^2$ : Udstrækning af fjederen. Landskaber $$F(x) = - \frac{dU(x)}{dx}$$ $\frac{dU(x)}{dx}$ : Hældningen af den potentielle energi, som funktion af position.
0001/01/01 · Notes