Further reading

•  Expression

Further reading

•  Order of operations

Cartesian coordinates

Polar coordinates

Real number coordination

A point in XY co ordinate can be presented as (${\displaystyle X,Y}$) and (${\displaystyle R,\theta }$) in R θ co ordinate

A , (${\displaystyle X,Y}$) , (${\displaystyle R,\theta }$)

Scalar maths	Vector Maths
${\displaystyle R\angle \theta ={\sqrt {X^{2}+Y^{2}}}\angle Tan^{-1}{\frac {Y}{X}}}$ ${\displaystyle R={\sqrt {X^{2}+Y^{2}}}}$ ${\displaystyle \theta =\angle Tan^{-1}{\frac {Y}{X}}}$	${\displaystyle X(\theta )=RCos\theta }$ ${\displaystyle Y(\theta )=RSin\theta }$ ${\displaystyle R(\theta )=X(\theta )+Y(\theta )=R(Cos\theta +Sin\theta )}$ ${\displaystyle \nabla \cdot R(\theta )=X(\theta )=RCos\theta }$ ${\displaystyle \nabla \times R(\theta )=Y(\theta )=RSin\theta }$

Complex number coordination

${\displaystyle Z.(X,jY),(Z,\theta )}$ ${\displaystyle Z^{*}.(X,-jY),(R,-\theta )}$	${\displaystyle X(\theta )=ZCos\theta }$ ${\displaystyle jY(\theta )=jZSin\theta }$ ${\displaystyle -jY(\theta )=-jZSin\theta }$ ${\displaystyle Z\angle \theta ={\sqrt {X^{2}+Y^{2}}}\angle Tan^{-1}{\frac {Y}{X}}}$ ${\displaystyle Z\angle -\theta ={\sqrt {X^{2}+Y^{2}}}\angle -Tan^{-1}{\frac {Y}{X}}}$ ${\displaystyle Z={\sqrt {X^{2}+Y^{2}}}}$ ${\displaystyle \theta =\angle Tan^{-1}{\frac {Y}{X}}}$	${\displaystyle Z(\theta )=X(\theta )+jY(\theta )=Z(Cos\theta +jSin\theta )}$ ${\displaystyle \nabla \cdot Z(\theta )=X(\theta )=ZCos\theta }$ ${\displaystyle \nabla \times Z(\theta )=jY(\theta )=jZSin\theta }$ ${\displaystyle Z^{*}(\theta )=X(\theta )-jY(\theta )=Z(Cos\theta -jSin\theta )}$ ${\displaystyle \nabla \cdot Z(\theta )=X(\theta )=Z^{*}Cos\theta }$ ${\displaystyle \nabla \times Z(\theta )=-jY(\theta )=jZ^{*}Sin\theta }$ ${\displaystyle Cos\theta ={\frac {Z(\theta )+Z^{*}(\theta )}{2}}}$ ${\displaystyle Sin\theta ={\frac {Z(\theta )-Z^{*}(\theta )}{2j}}}$ ${\displaystyle -Sin\theta ={\frac {Z^{*}(\theta )-Z^{(}\theta )}{2j}}}$

Definition

Functions are an arithmetical expression which relates 2 variables. Functions are usually denoted as

${\displaystyle f(x)=y}$

meaning for any value of ${\displaystyle x}$ there is a corresponding value ${\displaystyle y=f(x)}$ where

${\displaystyle x}$ - independent variable.

${\displaystyle y}$ - dependent variable.

${\displaystyle f(x)}$ - function of ${\displaystyle x}$.

Graphs of functions

${\displaystyle f(x)=x}$

x	-2	-1	0	1	2
f(x)	-2	-1	0	1	2

Straight line passing through origin point (0,0) with slope equals 1

${\displaystyle f(x)=2x}$

x	-2	-1	0	1	2
f(x)	-4	-2	0	2	4

Straight line passing through origin point (0,0) with slope equals 2

${\displaystyle f(x)=2x+3}$

x	-2	-1	0	1	2
f(x)	-1	1	3	5	7

Straight line with slope equals 2 has x intercept (-3/2,0) and y intercept (0,3)

Types of functions

• Polynomial Function
• Arithmetic Function/Trigonometric Functions
• Arithmetic Function/Exponential Functions
• Logarithmic Functions

Operations on function

• Arithmetic Operation/Limit
• Arithmetic Operation/Rate of change
• Arithmetic Operation/Differentiation
• Arithmetic Operation/Integration

Further reading

•  Function

Examples

Equation . ${\displaystyle 2x+5=9}$

Root . ${\displaystyle x={\frac {9-5}{2}}={\frac {4}{2}}=2}$

${\displaystyle x=2}$ is the root of the equation ${\displaystyle 2x+5=9}$ since substitution the value of x in the equation we have ${\displaystyle 2(2)+5=9}$

Types of equations

• Polynomial Equation
• Differential Equation
• Partial Differential Equation
• Linear equation
• System of linear equations

Further reading

•  Equation