Applied mathematics

From Wikiversity
Jump to navigation Jump to search

Function[edit]

Function's Graphs[edit]

Linear function
Parabolic function

Mathematical Operation on Functions[edit]

Differentiation[edit]

Integration[edit]

Transformations[edit]

Transformations Laplace transform Fourier transform

Partial Differentiation[edit]

Vector
Scalar
Unit vector

Laplace notation

Scalar operation
Vector operation

Solving equations[edit]

Polynomial equations[edit]

Equation Equation equation's root
1st ordered polynomial
2nd ordered polynomial

Differential equations[edit]

Electric circuit Equation Function s ω
Decay equation of series RL and RC circuit Gives decay function

Oscillation Wave of seires LC circuit
Gives wave function


Simultaneous equations[edit]

Equation Equation equation's root
Linear equation of 2 variables
Linear equation of n variables

Coordination[edit]

Real Number Coordination[edit]

A point in XY co ordinate can be presented as () and () in R θ co ordinate

A , () , ()
Scalar maths Vector Maths






Complex Number Coordination[edit]

A point in XY co ordinate can be presented as (X,Y) and (Z,θ) in Z θ co ordinate























Vector[edit]

Real coordination[edit]

For any vector in real coordination
The horizontal component vector
The vertical component vector

Complex coordination[edit]

Vector in complex coordination Horizontal Vector Component Vertical Vector Component
For any vector in complex coordination
For any conjugate vector in complex coordination

Motion Formulas[edit]

Types of motion
Uniform Horizontal Linear Motion
Uniform Vertical Linear Motion
Non Uniform Linear Motion
Non Linear Motion
Complete Circle's Motion
Circle's Arc
Wave
Momentum

Oscillation Formulas[edit]

Oscillation Wave Equation Wave function Angular speed Time constant
Spring's Up and Down Motion
Spring's Side to Side Motion
Series RLC at equilibrium
Series RLC at resonsnce
Series LC at equilibrium
Series LC at resonsnce
Electromagnetic oscillation

Momentum Formulas[edit]

Momentum Mass Speed Moment Work
Mometum of a mass in motion
Mometum of a relativistic mass in motion
Mometum of a massless quanta in motion

Electricity Formulas[edit]

Electriciy can be generated from the following sources

Electrolysis Galvanic cell labeled.svg DC
Electrochemical Cell DC
Photon Electricity Photoelectric effect.svg DC
Electromagnetic Induction AC

Electric Conductor[edit]

Matter that interacts with electricity are divided into three types Conductor, Semi Conductor, and Non Conductor

  • Conductor . All matter allow current to flow easily like Metal Ferrite, Copper
  • Semi Conductor . All matter does not allow current to flow easily like Semi Conductor Silicon, Germanium
  • Non Conductor . All matter does not allow current to flow like Rubber

Resistor[edit]

Resistor is a electric component thats exhibit resistance to the current flow . Resistance has a symbol R measured in ohm unit Ω .

Resistor is made from straight wire line conductor

DC Response


AC Response


Capacitor[edit]

DC response' AC response











Inductor[edit]

DC Reponse[edit]

Inductance . Inductance has a symbol L measured in Henry unit H

Magnetic Intensity . Measurement of magnetic strength

Current

AC Response[edit]

Voltage .

Current .

Reactance . Resistance to the AC current flow

In frequency domain
In phasor domain

Impedance . Resistance to the AC current flow

In frequency domain


In phasor domain

Time Constant

Power . Power of the capacitor

Straight line conductor[edit]

Ohms law voltage source.svg
Entities Symbol Mathematical Formula Unit
Voltage Volt . v
Current Ampere . a
Resistance Ohom . Ω
Conductance 1/Ω
Power provided Watt . W
Power loss as Heat dissipated W
Power transmitted W
Magnetic field

Electromagneticism Formulas[edit]

Entities Symbol Mathematical Formula Unit
North pole N
+
South pole S
-
Magnetic field direction -->
N --> S
Magnetic field
Potential difference
Volt . v
Induced magnetic field
Volt . v
Induced potential difference
Volt . v
Magnetic force
Newton . N
Magnetization field
Magnetization equations



Magnetic oscillation equation



Magnetic wave equation

Magnetic wave function



Magnetic wave radiation




Photon Formulas[edit]

Photon[edit]

Photon, Massless Quanta's energy of electromagnetic radiation

Photons are found in 2 states

Radiant photon at threshold frequency
Non - Radiant photon at frequency greater than threshold frequency

Photon can only be found in 1 out of 2 states at a time . Hence, Heiseinberg's uncertainty principle

Quanta[edit]

Quanta . Massless quantity

Process Wave Particle Duality

Wave like .
Particle like .