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

Laplace's Equation
Laplace’s Equation The Heat Equation where $u_{t} = 0$. $$\nabla^{2} u = 0$$
0001/01/01 · Notes
Laplaces lov
Laplaces lov $$F=B \cdot I \cdot L \arrows $$ Vi holder L konstant, mens vi ændre på I $$F=B \cdot L \cdot I$$
0001/01/01 · Notes
Laplacian Operator
Laplacian Operator “How much of a minimum is this (> $x$> ,> $y$> )?" - Khan Academy $$\nabla = \left[i \frac{\partial}{\partial x} + j \frac{\partial}{\partial y} + k \frac{\partial}{\partial z}\right]$$ An operator that takes in a function and returns another function. $$\Delta f = \nabla^{2}f = \nabla \bullet \nabla \bullet f = \mathbf{div}(\mathbf{grad}\ f)$$ 2 Dimensions $$\nabla = >\begin{bmatrix} >\frac{\partial}{\partial x} \ >\frac{\partial}{\partial y} \ >\end{bmatrix} >$$ 3 Dimensions $$\nabla = >\begin{matrix} >\frac{\partial}{\partial x} \ >\frac{\partial}{\partial y} \ >\frac{\partial}{\partial z} \ >\end{matrix} >$$ Explaination See Gradient
0001/01/01 · Notes
Law of Cosines
Law of Cosines $$a^{2} = b^{2} + c^{2} - 2bc \cos(A)$$ $$b^{2} = a^{2} + c^{2} - 2ac \cos(B)$$ $$c^{2} = a^{2} + b^{2} - 2ab \cos(C)$$ also $$\frac{a}{\sin A} = \frac{b}{\sin{B}} = \frac{c}{\sin C}$$
0001/01/01 · Notes
Ledere og Isolatorer
Ledere og Isolatorer Ledere Elektroner flyder frit mellem protonerne, der ofte (som i et metal) sidder i et gitter. Isolatorer Elektronerne er bundet til hvert sit proton Halvledere
0001/01/01 · Notes
Libraries in C++
Libraries in C++ Locations Headerfiles should be stored in /usr/include Library files (.so) should be stored in /usr/lib64 (on Fedora) Relevant Flags -I{dir} add header file directory. -l{library} Search for a compiled library file (.so) -L{dir} add .so directory
0001/01/01 · Notes
Ligninssystemer Uden Løsninger
Ligninssystemer Uden Løsninger Når koefficient-delen og højresiden af den udvidede matrix har forskellig rang, så har ligningssystemet ingen løsninger. $$\rang(A) \neq \rang(\tilde{A}) \arrow \text{Ingen løsninger!}$$ Eksempel $$ \begin{cases} 3x_{1} + 2 x_{2} + x_{3} &= 3 \ 6x_{1} + 3x_{2} + 3x_{3} &= 0 \ 6x_{1} + 2x_{2} + 4x_{3} &= 6 \end{cases} \arrow \left( \begin{array}{ccc|c} 3 & 2 & 1 & 3 \ 0 & -1 & 1 & -6 \ 0 & -2 & 2 & 0 \ \end{array} \right) \sim \left( \begin{array}{ccc|c} 3 & 2 & 1 & 3 \ 0 & -1 & 1 & -6 \ 0 & 0 & 0 & 12 \ \end{array} \right) \s \text{VRØVL!
0001/01/01 · Notes
Linarisering
Linarisering En linearisering er tangenten i et punkt $$L(x) = f(a)+f'(a) \cdot (x-a)$$ $a$: $x$-værdien i punktet . Vi bruger denne tangent i stedet for den komplicerede funktion, til at estimere funktionen (bedst omkring punktet). Dette er et førstegrads Taylorpolynomium Eksempel Bestem en approksimativ værdi at $\sqrt{26}$ vha. linarisering af $f(x) = \sqrt{x}$ omkring $x=25$. $$f'(x) = \frac{1}{2\sqrt{x}}$$ $$f'(25) = \frac{1}{10}$$ $$f(25)=5$$ Sætter ind i formlen $$L(x)=f(25)+f'(25)(a-25)=5+ \frac{1}{10} (x-25)$$ $$L(26)=5+\frac{1}{10} (26-25)=5+ \frac{1}{10}=5.
0001/01/01 · Notes
Line Coding
Line Coding Schemes Also check out this helpful site. Ways to convert digital data to an analog signal in a “good way”, making it easy for the receiver to interpret the signal. The receiver must be able to convert the received signal in a relative way, as absolute voltages may not be preserved. Unipolar NRZ (NON-RETURN-TO-ZERO) Problems A lot of power to send one bit Synchronisation has to be perfect Baseline Wandering: Many ones will shift the running average (baseline for the reciever) Polar NRZ-L(=level) and NRZ-I(=invert) Fixes the baseline wandering of >Unipolar NRZ (NON-RETURN-TO-ZERO).
0001/01/01 · Notes
Line Integrals
Line Integrals Integrate a three-dimensional function along a curve. $$ \int_{t=a}^{t=b}f(x(t),y(t)) \mathrm{dS} $$ $$ \mathrm{dS} = \sqrt{ \left(\frac{\partial x}{\partial t}\right)^{2}+ \left(\frac{\partial y}{\partial t}\right)^2 } \mathrm{dt} $$ Examples lektion6.pdf>page=4 lektion6.pdf>page=5 With Conservative Fields Let $C$ be a smooth curve parameterized by $\vec{r}(t)$ from $\vec{r}(a) = A$ to $\vec{r}(b) = B$ for continuous $\mathbf{F} = \nabla f$ ($\mathbf{F}$ is conservative). $$ \oint_{C} \mathbf{F} \cdot d\vec{r} = f(B) - f(A) $$
0001/01/01 · Notes