User:Kinglag/sandbox

Math Tex

Some Stuff about bases to practice TeX

$n_{m}b^{m}+\cdots +n_{1}b^{1}+n_{0}b^{0}+\cdots$

• b, is the base
• m, is the place magnitude
• n, is the multiplier its range is $0\geq n\geq b-1$

Examples

• In base 10, one thousand two hundred thirty four and 5 tenths: $1\times 10^{3}+2\times 10^{2}+3\times 10^{1}+4\times 10^{0}+5\times 10^{-1}$
• In base 2, one sixtyfour one eight and one twoth $1\times 2^{6}+1\times 2^{2}+1\times 2^{-}1$

Coding Your Own Random Base Adder (Object Oriented, Integers Only)

1. Classes that will be needed:
2. A number class (Number) that represents your random base number, whose members are:
   1. A simple class that won't need accessors it will contain an integer datatype whose range is equal to or greater than the desired base. (Integer)
   2. A data structure in the form of a double linked list. (ArrayList)
   3. A boolean that is the sign.
3. Operators can be contained in the number class or in a separate operator class that uses two number parameters and static methods.

Stated another way: Number has a ArrayList of type Integer and boolean.

Each Integer in the ArrayList is the n in the above formula. Each Integer's index in the ArrayList is its magnitude.

To add two numbers start at the lowest magnitude (0) and add them. Compare the sum to the base and if the sum is greater than the base set carry to 1. Then add the next greatest magnitude and the previous magnitude's carry, repeat until the highest magnitude is reached. If there is a carry add one to the next greatest magnitude of number of the sum.

Example:

1. $19+29$
2. $9+9=18$
3. ??8, carry the 1
4. $1+2+1=4$ 1 from 19 + 2 from 29 + carry
5. 48

Example 1

From Field Mathematics for Electromagnetics, Photonics and Material Science by Dr. Bernard Maxum. Equation: 5.3-10: $\oint _{S_{o}}{\overline {D}}\cdot {\overline {da}}=\lim _{\Delta v_{i}\to 0}\sum _{i}{\begin{matrix}\underbrace {\left({\frac {\oint _{S_{o}}{\overline {D}}\cdot {\overline {da}}}{\Delta v_{i}}}\right)} \\\nabla \cdot {\overline {D}}\end{matrix}}\Delta v_{i}$

Example 2

${\bar {A}},{\dot {A}},{\ddot {A}}$ ${\overline {A}}$

Example 3

$k={1 \over 4\pi \epsilon _{0}}={1 \over 144\pi ^{2}10^{-9}}$

$E=k{q \over r^{2}}$

${\bar {r}}=r{\hat {u}}_{r}+z{\hat {u}}_{z}$

${\bar {r}}'=z'{\hat {u}}_{z}$

${\overline {R}}={\overline {r}}-{\overline {r}}'$

${\hat {u}}_{R}={{\overline {R}} \over R}$

$R={\sqrt {r^{2}+\left(z-z'\right)^{2}}}$

$d{\overline {E}}=k\rho _{L}{dz' \over R^{2}}{\hat {u}}_{z}$

${\bar {E}}=k\rho _{L}\int _{-a}^{a}{{r{\hat {u}}_{r}+\left(z-z'\right){\hat {u}}_{z}} \over {\left(r^{2}+\left(z-z'\right)^{2}\right)^{\frac {3}{2}}}}\,dz'$

$E_{r}=k\rho _{L}\int _{-a}^{a}{{r} \over {\left(r^{2}+\left(z-z'\right)^{2}\right)^{\frac {3}{2}}}}\,dz'$

$E_{z}=k\rho _{L}\int _{-a}^{a}{{\left(z-z'\right)} \over {\left(r^{2}+\left(z-z'\right)^{2}\right)^{\frac {3}{2}}}}\,dz'$

Example 4

• 2x^2 - 5x - 12 / x^2 + 3x - 10 * x^2 + 4x + 3 / x^2 - 3x + 2

${\left({{2x^{2}-5x-12} \over {x^{2}+3x-10}}\right)}{\left({\frac {x^{2}+4x+3}{x^{2}-3x+2}}\right)}$

Statistics

Vocabulary

• data: raw observations of a particular question.
• statistics: collecting, simplfying, describing, and infering data.
• population: a whole group.
• sample: a part of a whole group.
• parameter: a description of data based on a population.
• statistic: a description of data based on a sample.
• ranked: data grouped in ascending or descending order.
• resistant measure: A measure of data that is not influenced by extreme data values.

Formula

Range

H: High data value
L: Low data value
R: Range
$R=H-L$

Arithmetic Average (Mean, Average)

• Population

x: data value
i: index of a data value
N: the count of data values of a population.
$\mu {}={\frac {\Sigma _{i}{x_{i}}}{N}}$

• Sample

μ: Arithmetic average of a population.
n: the Count of data vaules of a sample.
${\bar {x}}$: Arithmetic average of a sample.
${\bar {x}}={\frac {\Sigma _{i}{x_{i}}}{n}}$

Note: there is no numeric difference in these formulas.

Median

${\tilde {x}}$: Median 

N: the count of data values of a population.
$i={\frac {N+1}{2}}$

n: the Count of data vaules of a sample.
$i={\frac {n+1}{2}}$

${\tilde {x}}=x_{i}$
If i is not a whole number average the two nearest values.

Note: there is no numeric difference in these formulas.

Standard Deviation and Variance

• Population

$\sigma ^{2}$: Population variance
$\sigma$: Population deviation
$\sigma ^{2}*Sample<math>s^{2}$: sample variance
$s$: sample deviation

Table

Practice of wikicode tables. Help:Table#Other_table_syntax

Multiplication Table

1	2	3
2	4	6
3	6	9

Coordinate Table

Upper Left is the origin

0,0	1,0	2,0
0,1	1,1	2,1
0,2	1,2	2,2