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

Morgans Law
Morgans Law
0001/01/01 · Notes
Multiplexer
Multiplexer (Selector) A selection line, selects which of the inputs are output. Can be used to simplify large truthtables. 2-to-1 MUX Lesson 3.pdf>page=3 Simplification of cirtuits Truth-table to MUX Digital Multiplexer The input is never directly connected to the output, but is derived from the input. Analog Multiplexer The input is connected directly connected to the output is enabled. This can be implemented with tri-state buffers like on this slide.
0001/01/01 · Notes
Multivariable Math
Multi-variable Math Math involving integration in and over multi-dimensional spaces. A nice Youtube Playlist list from #multivariablemath sort file.name
0001/01/01 · Notes
n-Space
n-Rum Rum af højere dimensionerer. Punkter Points are considered tuples of > real numbers> , rather than physical points in space. $$(x_1, x_2, x_3, \dots, x_n)$$ Længde mellem punkter Dette er to punkter $x$ og $y$. $$L =\sqrt{(y_1 - x_1)^2 + (y_2 - x_2)^2 + \dots + (y_n-x_n)^n}$$ $L$ : Længden mellem punkterne $y_{1\dots n}$ : Det $n$‘te koordinat i $y$-punktet.
0001/01/01 · Notes
NAT
NAT Network Address Translation See slides. Assign a few addresses to a local network, and have a large number of internal addresses. Translation Table A mapping between local and public addresses. These mappings are temporary. NAT routers can have more than one external address. Forwarding Table DIFFERENT FROM TRANSLATION TABLE See slides. Where to send received packets. Address Aggregation Avoid long forwarding tables. Always choose the address with the longest mask address, as it will be physically closer to the router.
0001/01/01 · Notes
Network Layer
Network Layer NAT Routing vs. Switching Routers store a forwarding table and have to look up where to forward a packet based on its label. This is quite slow. Switches store the forwarding table in a list that can be indexed by the label. It is therefore way faster. MPLS (only IPv6) allows for routers that work as a switch when forwarding labeled packets.
0001/01/01 · Notes
Newtons Afkølingslov
Newtons Afkølingslov $$T' = \frac{dT}{dt} = -k \cdot (T-T_{omg})$$ Som kan omskrives til: $$T'(t) = -k \cdot (T(t)-T_{omg})$$ $T$ / $T(t)$ : Temperaturen som funktion af tid. $T_{omg}$ : Temperaturen af omgivelserne. $k$: Proportionalitetskonstanten. Afkølingsloven og differentialligninger Denne model passer på differentialligningen $y'=b-a \cdot y$. (se Linære førsteordensdifferentialligninger>3 Løsningsformel Newtons Afkølingslov) Dette kan vi se hvis vi ganger parantesen ud $$T' = -k \cdot (T-T_{omg}) \arrows T' = -k \cdot T + k \cdot T_{omg} \arrows T' = k \cdot T_{omg} -k \cdot T$$ $T$ : Temperaturen som funktion af tid.
0001/01/01 · Notes
Newtons Love
Newtons Love Newtons 1. lov: Inertiens Lov Inerti er et legemes (noget, der har masse) “modstand” mod at ændre retning. Newtons 1. lov siger, at påvirkes et legeme ikke af en resulterende kraft, vil det enten ligge stille eller blive ved at bevæge sig med konstant hastighed i samme retning. Newtons 2. lov: Kraftloven $$F_{net} = m \cdot a$$ $F_{res}$ : Den resulterende kraft. $m$ : Massen af objektet. $a$ : Accelerationen af objektet.
0001/01/01 · Notes
Niveaukurver
Niveaukurver Eksempel. $f(x,y)=-x^2-y^2+8$ Vi laver nu et plan i $z =-60$. Skæringen mellem disse flader er niveaukurven. Skæringen mellem disse flader, er niveaukurven
0001/01/01 · Notes
Normal form of a PDE
Normal form of a PDE See video. 1. Compare with the standard PDE $$Au_{xx} + Bu_{xy} + C_{yy} + Du_{x} + Eu_{y} + Fu = G$$ Obtain constant values 2. Classify with Discriminant Classify PDE: Discriminant PDE type $B^{2}-4AC>0$ Hyperbolic $B^{2}-4AC=0$ Parabolic $B^{2}-4AC<0$ Elliptic 3. Find Characteristic Equation (normal form) Hyperbolic: $$ \begin{cases} \frac{dy}{dx} &= &-\frac{\xi_y}{\xi_x} &= &\frac{ -B + \sqrt{B^{2} - 4AC} }{ 2A } \ \frac{dy}{dx} &= &-\frac{\eta_y}{\eta_x} &= &\frac{ -B - \sqrt{B^{2} - 4AC} }{ 2A } \end{cases} $$ Parabolic: $$ \frac{dy}{dx} = \frac{B}{2A} $$ Elliptic: $$ \begin{cases} \frac{dy}{dx} &= &\frac{ B + \sqrt{B^{2} - 4AC} }{ 2A } \ \frac{dy}{dx} &= &\frac{ B - \sqrt{B^{2} - 4AC} }{ 2A } \end{cases} $$
0001/01/01 · Notes