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

Tretrinsraketten
Tretrinsraketten En metode til at differentiere funktioner i hånden der gør brug af definitionen af en differentieret funktion. I dette eksempel vil jeg bruge funktionen $f(x) = 3x^2$ Trin 1 find $f(x_0 + h) - f(x_0)$ $$f(x_0 + h) - f(x_0) = 3 (x_0+h)^2-3x_0^2 = 3 \cdot (h^2 + 2 \cdot h \cdot x_0 + x_0^2)-3x_0^2 = 3 \cdot h^2 + 6 \cdot h \cdot x_0 + \bcancel{3 \cdot x_0^2} - \bcancel{3 \cdot x_0^2}$$
0001/01/01 · Notes
Tri-State Buffer
Tri-State Buffer See slides Lesson 3.pdf>page=24 A way to connect different signals to one wire. If signals were connected directly together, it may result in short. The Tri-State buffer prevents this. An enable signal can make the output completely disconnected from the input. Tri-State meaning $\text{HIGH}$, $\text{LOW}$ or $\text{HI-Z}$ (high impedance/disconnected).
0001/01/01 · Notes
Trigonometri
Trigonometri see also: Law of Cosines. Cosinus og Sinus $$\sin(\theta) = \frac{\text{Modstående}}{\text{Hypotenusen}}$$ $$\cos(\theta) = \frac{\text{Hoslæggende}}{\text{Hypotenusen}}$$ $$\tan(\theta)= \frac{\text{Modstående}}{\text{Hoslæggende}} = \frac{\sin(\theta)}{\cos{(\theta)}}$$ And arctan $$a = \arctan\left(\frac{\sin(a)}{\cos(a)}\right) \pm n\pi, \s n \in \Z$$ Or use atan2 for full $360\degree$ resolution! $$a = \text{arctan2}\left(\frac{\sin(a)}{\cos(a)}\right) \pm n \cdot 2\pi, \s n \in \Z$$ Flere Relationer $$\sin(\theta) = \sin(\pi - \theta)$$ $$\cos(\theta) = \sin\left(\theta + \frac{\pi}{2}\right)$$ $$\cos(\theta) = \cos(-\theta)$$ $$\sin(-\theta) = -\sin(\theta)$$ Den med Tangens $$\tan^{-1}(x)= \int\frac{1}{1+x^2}dx$$
0001/01/01 · Notes
Triple Integrals
Triple Integrals Find the bounds in the $xy$-plane
0001/01/01 · Notes
Tyngdeaccelerationen
Tyngdeaccelerationen $$g = 9.815 \frac{m}{s^2} $$
0001/01/01 · Notes
Tyngdekraften
Tyngdekraften $$F_g = m \cdot g$$ $F_g$ : Tyngdekraften. $m$ : Massen. $g$ :Tyngdeaccelerationen
0001/01/01 · Notes
Typer Henfald
Typer Henfald Skemaer er fra formelsamlingen Det Periodiske System $\alpha$-henfald $$\atom{A}{Z}{X} \rightarrow \atom{A-4}{Z-2}{Y} + \atom{4}{2}{He}$$ For moderkerne udsender en heliumkerne, som består af 2 protoner og 2 neutroner, så datterkernen får 4 færre nukleoner. 2 lavere ladningstal. Herved er nukleontallet, ladningen og leptontallet bevaret. Energi og impuls er også bevaret, men dette kan ikke ses i vores reaktionsskema. $\beta^-$-henfald $$\atom{A}{Z}{X} \rightarrow \atom{A}{Z + 1}{Y} + \atom{0}{-1}{e} + \overline{\text{v}_e}$$ En neutron fra moderkernen omdannes til en proton, en elektron og en antineutrino.
0001/01/01 · Notes
Types of Microcontrolers
Types of Microcontrolers General Purpose Microprocessors Standard choice for prototyping. FPGA You can rewire the entire circuits yourself. Application Specific Integrated Cirtuits (ASIC) Static wireing Good for mass production.
0001/01/01 · Notes
UART Protocol
UART Protocol See Lesson 9.pdf>page=23 Data is sent with the LSB first. Common Baud Rates Frequency (Hz) 4800 9600 19200 115200 1000000 To set the baud rate for AVR use this formula to set the UBRRL register. $$\text{UBRRL} = \frac{F_{osc}}{16 \cdot baudrate} -1 $$ Parity If enabled: adds one extra bit at the end of the message.
0001/01/01 · Notes
Uegenlige Integraler
Uegenlige Integraler “Undgå det punkt hvor funktionsværdien er problematisk” - Henrik Typer af uegenlige integtaler $$\int_{a}^{b} f(x) dx$$ Type 1 $$a=-\infty \s \text{eller} \s b = \infty$$ Løsning Lav grænser, integrer, og sæt ind i funktionen. $$\int_{a}^{\infty}f(x)dx \arrow \lim_{R\to \infty}\left(\int_{a}^{R}f(x) dx\right)$$ Type 2 $$\lim_{x\to a \lor b}(f(x))= \infty$$ *Løsning* $$\int_{a}^{b}f(x)dx \arrow \lim_{x\to a\lor b}\left(\int_{a}^{b}f(x)dx \right)$$ Uegenlige Integraler - Video
0001/01/01 · Notes