OpenLLM-France/wikimedia huggingface dataset:
# Queen's Pawn Opening
## 3.c4
## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. Nf3 d5 3.c4
| | 3 | 4 |
| Slav Defense | ... c6 | Nc3 | to 1...d5 2.c4 c6 3.Nf3 Nf6 |
| Queen's Gambit Declined | ... e6 | Nc3 | to 2.c4 e6 3.Nf3 d5 |
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# Queen's Pawn Opening
### 2...e6

A typical black move in Queen's Pawn Openings, 2...e6 allows black to develop the f8 bishop, after which castling will be possible.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. d4 Nf6 2. Nf3 e6
| 3 |
| c4 ... | = to 2. c4 e6 3. Nf3 |
| Bg5 ... | = |
| g3 ... | = |
| e3 d5 | = |
| Bf4 ... | = |
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# London System Indian Setup with a Early 2. Nf3

The London System has evolved significantly since its showcase in the 1922 London tournament. A prominent shift in modern play is the preference for 2.Bf4 instead of the traditional 2.Nf3. Both sides have seen strategic advancements in the London System.
The move order with 2. Nf3 before 3. Bf4 in the London System can be seen as a more flexible way to reach the London System and has its specific advantages and drawbacks.
For a general introduction to the London System, take a closer look at 1. d4 d5 2. Bf4

### Advantages:

* Flexibility: By playing 2. Nf3 first, White keeps more options open. This can be particularly useful if Black opts for setups that may not be best met with the traditional London System. For instance, White can divert into other openings or setups based on Black's moves.
* Control over e5: Central control, particularly over the e5 and e4 squares, is vital in the London System. The move 2. Nf3 immediately prevents any potential pawn break with ...e5 by Black.
* Avoiding Immediate Pressure: Certain move orders by Black might put immediate pressure on the d4 pawn (like ...c5 and ...Qb6 setups). The knight on f3 provides additional support to the d4 pawn.

### Drawbacks:

* Delaying the London System's Set-up: The very essence of the London System is rapid and harmonious development, particularly the dark-squared bishop. By playing 2. Nf3 first, White is essentially delaying the typical London setup. By shifting the knight from f3 to d4, White diminishes their hold on the e5 square.
* When White plays 2.Nf3, it can prompt Black to opt for 2...c5 because the subsequent 3.Bf4 can be met by 3...cxd4 4.Nxd4 Nd7.
* Allowing Black's Equalizing Attempts: Black might employ certain systems that challenge White's center more directly before White can establish the typical London System setup.
* Potential Transpositions: The move 2. Nf3 allows various transpositions into other openings, which could be a disadvantage if the White player is specifically aiming to play the London System and avoid other lines.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. d4 Nf6 2. Nf3 e6 3. Bf4
| | 3 | 4 | 5 | 6 |
| London System Main Line with c5 | Bf4 d5 | e3 c5 | c3 Nc6 | Nd2 | = |
| London System Transposition Main Line with c5 | ... c5 | e3 d5 | | | |
| Queen's Indian London System Setup | ... b6 | c4 | | | = |
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## References

* Sedice, Shaun (2022). The London System – Play the Opening as White & Black. chessable.com.
* Nunn's Chess Openings. 1999. John Nunn (Editor), Graham Burgess, John Emms, Joe Gallagher. ISBN 1-8574-4221-0.
* Modern Chess Openings: MCO-14. 1999. Nick de Firmian, Walter Korn. ISBN 0-8129-3084-3.
# Torre Attack
### 3.Bg5
## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation.
1. d4 Nf6 2.Nf3 e6 3.Bg5
| 3 | 4 |
| Bg5 c5 | e3 |
| ... h6 | Bh4 |
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## References

* Nunn's Chess Openings. 1999. John Nunn (Editor), Graham Burgess, John Emms, Joe Gallagher. ISBN 1-8574-4221-0.
* Modern Chess Openings: MCO-14. 1999. Nick de Firmian, Walter Korn. ISBN 0-8129-3084-3.
* This Chess related article is a stub. Please assist Wikibooks by expanding it.
# Torre Attack

e3 continues white's plan for a kingside assault, with the bishop on d3 and knight on e5 as targets. Black has failed to disrupt white, and needs to play carefully now.
At this point, perhaps c5 is the best response, although white already has a solid advantage.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. Nf3 d5 3. Bg5 e6
* 4
* Be7
* c5
* Nbd7
* h6
* c6
* b6
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## References

* Kasparov, Garry, & Keene, Raymond 1989 Batsford chess openings 2. ISBN 0-8050-3409-9.
# Queen's Pawn Opening

This is the beginning of the Colle ==3.e3==

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. Nf3 d5 3.e3
| | 3 | 4 |
| Queen's Pawn Game | ... e6 | c4 | to 2...e6 3.e3 d5 |
| Queen's Pawn Game | ... c5 | c4 | |
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# Chess Opening Theory/1. d4/1...Nf6/2. Nf3/2...d5/3. e3/3...c5
## 3...c5

* This Chess related article is a stub. Please assist Wikibooks by expanding it.

## Theory table

For explanation of theory tables, see theory table and for notation, see algebraic notation. .
1. d4 Nf6 2. Nf3 d5 3.e3 c5
* 4
* c3
* c4
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# Engineering Tables/Properties of Integrals

Table of Properties of Integrals :
| | Rule | Conditions |
| 1 | $\int a\,dx=ax$ | |
| 2 Homogeneity | $\int af(x)\,dx=a\int f(x)\,dx$ | |
| 3 Distributivity | $\int {\left(f\pm g\pm h\pm \cdots \right)\,dx}=\int f\,dx\pm \int g\,dx\pm \int h\,dx\pm \cdots$ | |
| 4 Integration by Parts | $\int _{a}^{b}fg'\,dx={\biglfg{\bigr ]}_{a}^{b}-\int _{a}^{b}gf'\,dx$ | |
| 4 General Integration by Parts | $\int f^{(n)}g\,dx=f^{(n-1)}g'-f^{(n-2)}g''+\dots +(-1)^{n}\int fg^{(n)}\,dx$ | |
| 5 | $\int f(ax)\,dx={\frac {1}{a}}\int f(x)\,dx$ | |
| 6 Substitution Rule | $\int g\{f(x)\}\,dx=\int g(u){\frac {dx}{du}}\,du=\int {\frac {g(u)}{f'(x)}}\,du$ | $u=f(x)\,$ |
| 7 | $\int x^{n}\,dx={\frac {x^{n+1}}{n+1}}$ | $n\neq -1\,$ |
| 8 | $\int {\frac {1}{x}}\,dx=\ln |x|$ | |
| 9 | $\int e^{x}\,dx=e^{x}$ | |
| 10 | $\int a^{x}\,dx={\frac {a^{x}}{\ln |a|}}$ | $a\neq 1$ |
| Notes: | f, g, h are functions of x a, n are constants. The constant of integration, C has been omitted from this table. It should be included in the working of the equation if applicable. | f, g, h are functions of x a, n are constants. The constant of integration, C has been omitted from this table. It should be included in the working of the equation if applicable. |
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# Engineering Tables/Table of Integrals

This is a small summary of the identities found Here.
| | Integral | Value |
| 1 | $\int c\,dx$ | $cx+C$ |
| 2 | $\int x^{n}\,dx$ | ${\frac {x^{n+1}}{n+1}}+C$ for $n\neq -1$ |
| 3 | $\int {\frac {1}{x}}\,dx$ | $\ln {\left|x\right|}+C$ |
| 4 | $\int {1 \over {a^{2}+x^{2}}}\,dx$ | ${1 \over a}\arctan {x \over a}+C$ |
| 5 | $\int {1 \over {\sqrt {a^{2}-x^{2}}}}\,dx$ | $\arcsin {x \over a}+C$ |
| 6 | $\int {-1 \over {\sqrt {a^{2}-x^{2}}}}\,dx$ | $\arccos {x \over a}+C$ |
| 7 | $\int {1 \over x{\sqrt {x^{2}-a^{2}}}}\,dx$ | ${1 \over a}\operatorname {arcsec} {|x| \over a}+C$ |
| 8 | $\int \ln {x}\,dx$ | $x\ln {x}-x+C$ |
| 9 | $\int \log _{b}{x}\,dx$ | $x\log _{b}{x}-x\log _{b}{e}+C$ |
| 10 | $\int e^{x}\,dx$ | $e^{x}+C$ |
| 11 | $\int a^{x}\,dx$ | ${\frac {a^{x}}{\ln {a}}}+C$ |
| 12 | $\int \sin {x}\,dx$ | $-\cos {x}+C$ |
| 13 | $\int \cos {x}\,dx$ | $\sin {x}+C$ |
| 14 | $\int \tan {x}\,dx$ | $-\ln {\left|\cos {x}\right|}+C$ |
| 15 | $\int \cot {x}\,dx$ | $\ln {\left|\sin {x}\right|}+C$ |
| 16 | $\int \sec {x}\,dx$ | $\ln {\left|\sec {x}+\tan {x}\right|}+C$ |
| 17 | $\int \csc {x}\,dx$ | $-\ln {\left|\csc {x}+\cot {x}\right|}+C$ |
| 18 | $\int \sec ^{2}x\,dx$ | $\tan x+C$ |
| 19 | $\int \csc ^{2}x\,dx$ | $-\cot x+C$ |
| 20 | $\int \sec {x}\,\tan {x}\,dx$ | $\sec {x}+C$ |
| 21 | $\int \csc {x}\,\cot {x}\,dx$ | $-\csc {x}+C$ |
| 22 | $\int \sin ^{2}x\,dx$ | ${\frac {1}{2}}(x-\sin x\cos x)+C$ |
| 23 | $\int \cos ^{2}x\,dx$ | ${\frac {1}{2}}(x+\sin x\cos x)+C$ |
| 24 | $\int \sin ^{n}x\,dx$ | $-{\frac {\sin ^{n-1}{x}\cos {x}}{n}}+{\frac {n-1}{n}}\int \sin ^{n-2}{x}\,dx$ |
| 25 | $\int \cos ^{n}x\,dx$ | $-{\frac {\cos ^{n-1}{x}\sin {x}}{n}}+{\frac {n-1}{n}}\int \cos ^{n-2}{x}\,dx$ |
| 26 | $\int \arctan {x}\,dx$ | $x\,\arctan {x}-{\frac {1}{2}}\ln {\left|1+x^{2}\right|}+C$ |
| 27 | $\int \sinh x\,dx$ | $\cosh x+C$ |
| 28 | $\int \cosh x\,dx$ | $\sinh x+C$ |
| 29 | $\int \tanh x\,dx$ | $\ln \left|\cosh x\right|+C$ |
| 30 | $\int \operatorname {csch} \,x\,dx$ | $\ln \left|\tanh {x \over 2}\right|+C$ |
| 31 | $\int {\mbox{sech}}\,x\,dx$ | $\arctan(\sinh x)+C$ |
| 32 | $\int \coth x\,dx$ | $\ln \left|\sinh x\right|+C$ |
# Engineering Tables/Properties of Derivatives

| | Derivative | Conditions |
| 1 | ${\frac {d}{dx}}c=0$ | |
| 2 | ${\frac {d}{dx}}(cx)=c$ | |
| 3 Elementary Power Rule | ${\frac {d}{dx}}(x^{n})=nx^{n-1}$ | |
| 4 Sum Rule | ${\frac {d}{dx}}\left(f\pm g\pm h\pm \cdots \right)={\frac {df}{dx}}\pm {\frac {dg}{dx}}\pm {\frac {dh}{dx}}\pm \cdots$ | |
| 5 Constant Multiple Rule | ${\frac {d}{dx}}(cf)=c{\frac {df}{dx}}$ | |
| 6 Product Rule | ${\frac {d}{dx}}(fg)=f{\frac {dg}{dx}}+g{\frac {df}{dx}}$ | |
| 6 Product Rule (Extended) | ${\frac {d}{dx}}(fgh)=fg{\frac {dh}{dx}}+fh{\frac {dg}{dx}}+gh{\frac {df}{dx}}$ | |
| 7 Quotient Rule | ${\frac {d}{dx}}\left({\frac {f}{g}}\right)={\frac {g{\frac {df}{dx}}-f{\frac {dg}{dx}}}{g^{2}}}$ | $g\neq 0\,$ |
| 8 Chain Rule | ${\frac {df}{dx}}={\frac {df}{dg}}\cdot {\frac {dg}{dx}}$ | |
| 9 | ${\frac {d}{dx}}\left(f^{n}\right)=nf^{n-1}{\frac {df}{dx}}$ | |
| 10 Reciprocal Rule | ${\frac {d}{dx}}\left({\frac {1}{f}}\right)=-{\frac {1}{f^{2}}}{\frac {df}{dx}}$ | $f\neq 0\,$ |
| 11 Functional Power Rule | ${\frac {d}{dx}}\left(f^{g}\right)={\frac {d}{dx}}\left(e^{g\ln f}\right)=f^{g}\left({\frac {g}{f}}\cdot {\frac {df}{dx}}+{\frac {dg}{dx}}\ln f\right)$ | $f>0\,$ |
| 12 Logarithm Rule | ${\frac {df}{dx}}=f{\frac {d}{dx}}\left(\ln f\right)$ | $f>0\,$ |
| 13 Inverse Function Rule | ${\frac {df}{dx}}={\frac {1}{\frac {dx}{df}}}$ | ${\frac {dx}{df}}\neq 0\,$ |
| Notes: | f, g, h are functions of x c, n are constants. | f, g, h are functions of x c, n are constants. |
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# Engineering Tables/Normal Distribution/Tail Function Graph

The tail function is the area under the normal distribution N(0,1) between x and +∞:
       ${\mbox{T}}(x)=\int \limits _{x}^{\infty }{{1 \over {\sqrt {2\pi }}}\exp \left({-{{y^{2}} \over 2}}\right)dy}$
For x > 6.5, the tail function can be approximated as:
       ${\mbox{T}}(x)={1 \over {x{\sqrt {2\pi }}}}\exp \left({-{{x^{2}} \over 2}}\right)$
# Engineering Tables/Table of Derivatives

Table of Derivatives :
| ${d \over dx}c=0$ |
| ${d \over dx}x=1$ |
| ${d \over dx}cx=c$ |
| ${d \over dx}|x|={x \over |x|}=\operatorname {sgn} x,\qquad x\neq 0$ |
| ${d \over dx}x^{c}=cx^{c-1}$ | where both x$^c$ and cx$^{c−1}$ are defined. |
| ${d \over dx}\left({1 \over x}\right)={d \over dx}\left(x^{-1}\right)=-x^{-2}=-{1 \over x^{2}}$ |
| ${d \over dx}\left({1 \over x^{c}}\right)={d \over dx}\left(x^{-c}\right)=-{c \over x^{c+1}}$ |
| ${d \over dx}{\sqrt {x}}={d \over dx}x^{1 \over 2}={1 \over 2}x^{-{1 \over 2}}={1 \over 2{\sqrt {x}}}$ | x > 0 |
| ${d \over dx}c^{x}={c^{x}\ln c}$ | c > 0 |
| ${d \over dx}e^{x}=e^{x}$ |
| ${d \over dx}\log _{c}x={1 \over x\ln c}$ | c > 0, c ≠ 1 |
| ${d \over dx}\ln x={1 \over x}$ |
| ${d \over dx}\sin x=\cos x$ |
| ${d \over dx}\cos x=-\sin x$ |
| ${d \over dx}\tan x=\sec ^{2}x$ |
| ${d \over dx}\sec x=\tan x\sec x$ |
| ${d \over dx}\cot x=-\csc ^{2}x$ |
| ${d \over dx}\csc x=-\csc x\cot x$ |
| ${d \over dx}\arcsin x={1 \over {\sqrt {1-x^{2}}}}$ |
| ${d \over dx}\arccos x={-1 \over {\sqrt {1-x^{2}}}}$ |
| ${d \over dx}\arctan x={1 \over 1+x^{2}}$ |
| ${d \over dx}\operatorname {arcsec} x={1 \over |x|{\sqrt {x^{2}-1}}}$ |
| ${d \over dx}\operatorname {arccot} x={-1 \over 1+x^{2}}$ |
| ${d \over dx}\operatorname {arccsc} x={-1 \over |x|{\sqrt {x^{2}-1}}}$ |
| ${d \over dx}\sinh x=\cosh x$ |
| ${d \over dx}\cosh x=\sinh x$ |
| ${d \over dx}\tanh x=\operatorname {sech} ^{2}x$ |
| ${d \over dx}\operatorname {sech} x=-\tanh x\operatorname {sech} x$ |
| ${d \over dx}\operatorname {coth} x=-\operatorname {csch} ^{2}x$ |
| ${d \over dx}\operatorname {csch} x=-\operatorname {coth} x\operatorname {csch} x$ |
| ${d \over dx}\operatorname {arsinh} x={1 \over {\sqrt {x^{2}+1}}}$ |
| ${d \over dx}\operatorname {arcosh} x={1 \over {\sqrt {x^{2}-1}}}$ |
| ${d \over dx}\operatorname {artanh} x={1 \over 1-x^{2}}$ |
| ${d \over dx}\operatorname {arsech} x={1 \over x{\sqrt {1-x^{2}}}}$ |
| ${d \over dx}\operatorname {arcoth} x={1 \over 1-x^{2}}$ |
| ${d \over dx}\operatorname {arcsch} x={-1 \over |x|{\sqrt {1+x^{2}}}}$ |
# Circuit Theory/Parallel Resistance
## Parallel Resistance

Resistors in parallel share the same voltage. They split the current up. Giving the current multiple paths to follow means that the overall resistance decreases.
    $R_{\mathrm {total} }={\frac {1}{{\frac {1}{R_{1}}}+{\frac {1}{R_{2}}}+\cdots +{\frac {1}{R_{n}}}}}={\frac {1}{\sum {\frac {1}{R_{i}}}}}$
The above equation is often called the "one over -- one over" equation.

## Parallel Impedance

A group of parallel branches split up the current, but share the same voltage. The parallel branches connect the same two nodes.
The impedance of parallel branches can be combined into one impedance.
Consider these parallel branches: one with a resistor, another with a capacitor and a third with an inductor.
Now drive them with a voltage source:
    $V_{s}=10*cos(22400t+30^{\circ })$
    $V_{s}=10*e^{-5000t}cos(22400t+30^{\circ })$
There is just one current, $V$.

## symbolic derivation

The terminal equations are:
    $\mathbb {V} _{s}=\mathbb {I} _{r}*R$
    $\mathbb {V} _{s}=\mathbb {I} _{L}*j\omega L$ or $\mathbb {V} _{s}=\mathbb {I} _{L}*sL$
    $\mathbb {I} _{c}=\mathbb {V} _{s}*j\omega C$ or $\mathbb {I} _{c}=\mathbb {V} _{s}*sC$
There are no loop equations and the junction equation is:
    $\mathbb {I} _{r}+\mathbb {I} _{L}+\mathbb {I} _{c}-\mathbb {I} _{s}=0$
Solving the terminal equation for currents, substituting and dividing both sides by $\mathbb {V} _{s}$ yields:
    ${\frac {\mathbb {I} _{s}}{\mathbb {V} _{s}}}={\frac {1}{R}}+{\frac {1}{j\omega L}}+j\omega C$
    ${\frac {\mathbb {I} _{s}}{\mathbb {V} _{s}}}={\frac {1}{R}}+{\frac {1}{sL}}+sC$
In terms of impedance, if:
    ${\frac {1}{Z}}={\frac {1}{R}}+{\frac {1}{j\omega L}}+j\omega C$
    ${\frac {1}{Z}}={\frac {1}{R}}+{\frac {1}{sL}}+sC$
Then:
    ${\frac {\mathbb {I} _{s}}{\mathbb {V} _{s}}}={\frac {1}{Z}}$
In general, impedances add in series like resistors do in the time domain:
    ${\frac {1}{Z}}=\sum {\frac {1}{R_{i}}}+\sum {\frac {1}{j\omega L_{i}}}+\sum j\omega C_{i}$
    ${\frac {1}{Z}}=\sum {\frac {1}{R_{i}}}+\sum {\frac {1}{sL_{i}}}+\sum sC_{i}$
or
    $Z={\frac {1}{\sum {\frac {1}{R_{i}}}+\sum {\frac {1}{j\omega L_{i}}}+\sum j\omega C_{i}}}$
    $Z={\frac {1}{\sum {\frac {1}{R_{i}}}+\sum {\frac {1}{sL_{i}}}+\sum sC_{i}}}$

## numeric example

    $Z=99.9938-0.7857i=99.9969\angle -0.0079(-0.4502^{\circ })$
    $Z=186.85-837.07i=857.6701\angle -1.3512(-77.4170^{\circ })$
So the exact same components hooked in series are dominated by the inductor (large reactance of the inductor overshadows the smaller reactance of the capacitor), but when the same components are hooked in parallel, the small er capacitive reactance dominates.

## notes

What is the point of all this? The goal is to start with simple circuits, explore them with words and symbols, find the patterns and generalize, establish and name concepts and then wait for their application. What are we waiting for? Selecting channels on a TV/Radio/Wifi, ZigBee, RFID, Cellphones, Blue Tooth and sending data over these channels as well as to hard drives and SD cards, monitors and hubs, designing antennas, ....
# Circuit Theory/Phasor Theorems
## Circuit Theorems

Phasors would be absolutely useless if they didn't make the analysis of a circuit easier. Luckily for us, all our old circuit analysis tools work with values in the phasor domain. Here is a quick list of tools that we have already discussed, that continue to work with phasors:
* Ohm's Law
* Kirchoff's Laws
* Superposition
* Thevenin and Norton Sources
* Maximum Power Transfer
This page will describe how to use some of the tools we discussed for DC circuits in an AC circuit using phasors.

## Ohm's Law

Ohm's law, as we have already seen, becomes the following equation when in the phasor domain:
    $\mathbb {V} =\mathbb {Z} \mathbb {I}$
Separating this out, we get:
    $M_{V}\angle \phi _{V}=(M_{Z}\times M_{I})\angle (\phi _{Z}+\phi _{I})$
Where we can clearly see the magnitude and phase relationships between the current, the impedance, and the voltage phasors.

## Kirchoff's Laws

Kirchoff's laws still hold true in phasors, with no alterations.

### Kirchoff's Current Law

Kirchoff's current law states that the amount of current entering a particular node must equal the amount of current leaving that node. Notice that KCL never specifies what form the current must be in: any type of current works, and KCL always holds true.
[KCL With Phasors]
    $\sum _{n}\mathbb {I} _{n}=0$

### Kirchoff's Voltage Law

KVL states: The sum of the voltages around a closed loop must always equal zero. Again, the form of the voltage forcing function is never considered: KVL holds true for any input function.
[KVL With Phasors]
    $\sum _{n}\mathbb {V} _{n}=0$

## Superposition

Superposition may be applied to a circuit if all the sources have the same frequency. However, superposition must be used as the only possible method to solve a circuit with sources that have different frequencies. The important part to remember is that impedance values in a circuit are based on the frequency. Different reactive elements react to different frequencies differently. Therefore, the circuit must be solved once for every source frequency. This can be a long process, but it is the only good method to solve these circuits.

## Thevenin and Norton Circuits

Thevenin Circuits and Norton Circuits can be manipulated in a similar manner to their DC counterparts: Using the phasor-domain implementation of Ohm's Law.
    $\mathbb {V} =\mathbb {Z} \mathbb {I}$
It is important to remember that the $\mathbb {Z}$ does not change in the calculations, although the phase and the magnitude of both the current and the voltage sources might change as a result of the calculation.

## Maximum Power Transfer

The maximum power transfer theorem in phasors is slightly different then the theorem for DC circuits. To obtain maximum power transfer from a thevenin source to a load, the internal thevenin impedance ($\mathbb {Z} _{t}$) must be the complex conjugate of the load impedance ($\mathbb {Z} _{l}$):
[Maximum Power Transfer, with Phasors]
    $\mathbb {Z} _{l}=R_{t}-jX_{t}$
# Circuit Theory/Open Puzzles

Sloppy people build circuits with shorts where wires accidentally touch. These people are easy to spot. The circuit looks like a bird's nest.
Opens are harder. Intermittent opens are caused by bad wires, bad connections, bad soldering, warm up/cool down expansion contraction, dust, and physical movement of the circuit. Finding them is difficult. One technique is to push every where in the circuit with a wooden stick to try and re-create an open. Identifying opens is the best thing to practice at the moment.
This circuit has an open between the red and black dots. No current is flowing. The electro motive force (EMF) extends from the battery + terminal through resistors 4 and 5. The EMF from the negative terminal of the battery extends through resistor 6. Thus the voltage drop between the red and black dots is the battery voltage of 1 volt.
Opening a wire can cause dangling resistors. A wire removed between red and green removes resistor 2 from the circuit.
Opening a short can put a resistor back into the circuit. A wire between between green and ground would short resistor 4. Opening this wire puts resistor 4 back into the circuit.
If a wire connected black, green and red, then resistor 4 would be shorted out of the circuit. Resistors 2 and 3 would combine in parallel, and the combination would combine in series with resistor 1.
Two wires have been removed from this circuit. This has left resistors 2,3,7,5 and 8 dangling.
It has made the EMF of red and green, the same as the EMF between resistors 1 and 6.
It has made the EMF of the black and blue the same as the EMF between resistors 6 and 4.
The voltage drop from red to black will be the same voltage drop from green to blue.
Resistors 3,4,5 and 6 are no longer are participating in this circuit.
The EMF of the green, red, yellow, blue points in the circuit is all the same ... that of the positive terminal of the battery.
The EMF of the black is that of the negative terminal of the battery.
The voltage between any pair of green, red, yellow and blue is zero.
The voltage between black and any of the other colors is going to be 1 volt.
# Cluster-Handbook

Welcome! The goal of the wikibook is to outline the basic concepts about computer clusters. This book explains what a cluster is and how to build a simple and clean cluster which provides a great starting point for more complex tasks. In addition, this book contains a guide for task scheduling and other important cluster management features.

## Contents

* Introduction
* Software
* Qlustar
* Cluster Monitoring
* SLURM
* Network
* OSSEC
* Munin
* SnortIDS
* Prelude
* Firestarter
* Torque
* ARM-Cluster (German)

## Bibliography

[BC08] Rory Bray and Daniel Cid. OSSEC Host-Based Intrusion Detection Guide. Syngress Media, 2008.
# Cluster-Handbook/Introduction
## Introduction

The goal of the handbook is to outline the basic concepts about computer clusters. Firstly what exactly a cluster is and how to build a simple and clean cluster which provides a great starting point for more complex tasks. Also the handbook provides a guide for task scheduling and other important cluster management features. For the practical part most of the examples use Qlustar. Qlustar is a all-in-one cluster operating system that is easy to setup, extend and most importantly operate.
A computer cluster consists of a number of computers linked together, generally through local area networks (LANs). All the connected component-computers work closely together and in many ways as a single unit. One of the big advantages of computer clusters over single computers, are that they usually improves the performance greatly, while still being cheaper than single computers of comparable speed and size. Besides that a cluster provides in general larger storage capacity, better data integrity.
Nodes
The term node usually describes one unit (linked computer) in a computer cluster. It represents the basic unit of a cluster. There a different types of notes like head-nodes, compute-, cloud- or storage-nodes. Nodes in a cluster are connected through dedicated internal Ethernet networks. The figure below shows a simple setup of the components building a basic HPC Cluster.