Engineer handbook

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Nuvola apps kcmsystem.svg Subject classification: this is an engineering resource.

Chemistry[edit]

Chemical Element[edit]

Symbol

mZE

States

Solid . Fe, Cu
Liquid . Ex Mg
Gas . Ex He, H

Periodic table

Table of columns and rows that list characteristics of chemical elements

Chemical bonding[edit]

Oxidation[edit]

Fe + O2 --> FeO2
Cu + O2 --> CuO2

Ionic bonding[edit]

H2O --> 2H+ + O-
2H2O --> 4H+ + 2O-2

Chemical Compound[edit]

One or more than one element combines to form chemical compound

Oxygen O + O --> O2
Ozone O + O + O --> O3
Water 2H + O --> H2O

Chemical Reaction[edit]

Chemical interaction of substances to create new substance . mathematically can be expressed in Chemical reaction equation

Substance1 + Substance2 = New Substance

Example

Cu + H2SO4 = CuSO4 + 2H

Physics[edit]

Force[edit]

Force Symbol Mathematical Formula
Opposing Force
Gravity Force
Motion Force
Pressure Force
Elastic Force
Circulation Force
Centripetal Force
Electrostatic Force
Electromotive force
Electromagnetomotive Force
Electromagnetic Force

Motion[edit]

Linear Motion[edit]

O ----> O
Distance
Time
Speed
Accelleration
Force
Work
Energy


O
O
Distance
Time
Speed
Accelleration
Force
Work
Energy
Distance
Time
Speed
Accelleration
Force
Work
Energy

Non Linear Motion[edit]

Distance
Time
Speed
Acceleration
Force
Work
Energy

Circular Motion[edit]

Circle-withsegments.svgUniform circular motion.svgVelocity-acceleration.PNG
Distance
Time
Speed
Acceleration
Angular spped
Frequency
Force
Work
Energy
Distance
Time
Speed
Acceleration
Force
Work
Energy

Momentum[edit]

Characteristics[edit]

Mass
Speed
Moment
Force
Work
Energy

Momentum of a mass[edit]

Speed
Mass
Momentum
Force
Work
Energy

Momentum of a relativistic mass[edit]

Speed
Mass
Momentum
Energy

Momentum of a massless quanta[edit]

Speed
Mass
Energy
Momentum
Wavelength

Momentum of an electric charge in circle[edit]

Equilibrium
Speed
Radius

Momentum of atom's free electron[edit]

Equilibrium
Speed
With
to have

Momentum of a bind electron[edit]

Equilibrium
Speed
Radius
Potential Energy Level n

Wave[edit]

AC electrical sinusoidal wave generator[edit]

An interaction of 2 electromagnets creates an AC electricity that has amplitude varies sinusoidally

Alternator 1.svg

LC sinusoidal wave generator[edit]

Series LC Circuit.svg

Series LC operates at equilibrium satisfy wave equation

that has root of a sinusoidal wave function

FreqWave1.png

Electromagnetic sinusoidal wave generator[edit]

VFPt Solenoid correct2.svg

A coil of N turns operates at equilibrium satisfy wave equation

that has root of a sinusoidal wave function

Onde electromagnetique.svg

Wave Characteristics[edit]

Distance
Time
Speed
Angular speed
Frequency
Sinusoidal wave equation
Sinusoidal wave function

Wave types[edit]

Wave 2 dimensional sinusoidal wave 3 dimensional sinusoidal plane wave
FreqWave1.png Onde electromagnetique.svg
Wave oscillation equation
Wave function




Electricity[edit]

Electricity types[edit]

Electricity types Definition Mathematical Formula Source
DC Electricity Electricity that provides constant voltage over time Electrolysis, Electrochemcial Cell, PhotonVoltaic
AC Electricity Electricity that provides sinusoidal changing voltage over changing time Electromagnetic induction

DC & AC Response[edit]

Characteristics DC AC
Voltage
Current
Resistance
Power provided
Power Loss
Power delivered
Reactance
Impedance
Phase
Characteristics DC AC
Voltage
Charge
Capacitance
Current
Power provided
Reactance


Impedance


Phase
Time Constant
Characteristics DC AC
Magnetic Field Strength
Current
Inductance
Current
Power provided
Reactance


Impedance


Phase
Time Constant
RL Series Open-Closed.svg

RC switch.svg

Modes of Oscillation Oscillation equation Wave Function Angular Speed Oscillation Time Constant Oscilation Constant Decay Constant ' Decay Time Constant
Electric decay current
sinusoidal wave oscillation
RLC series circuit v1.svg
Electric peak current
sinusoidal wave oscillation
RLC series circuit v1.svg





Electric current
sinusoidal wave oscillation
Series LC Circuit.svg

Electric current sinusoidal
standing wave oscillation
Series LC Circuit.svg

Electromagneticism[edit]

Electric charge[edit]

Charge acquired process Electric charge Charge quantity Electric field Magnetic field
Matter + e- - -Q -->E<-- B ↓
Matter - e- + +Q <--E--> B ↑

Electromagnetic force[edit]

Force Electric charge Charge quantity
Electrostatic Force
Electromotive Force
Electromagnetomotive Force
Electromagnetic Force

Electromagnetic Field Intensity[edit]

Configuration Symbol Mathematical Formulas
For any configuration
For straight line conductor Circular B field
For circular loop conductor Circular B field around a point charge
For coil of N circular loops conductor Eleptic B field around the coil

Electromagnetism[edit]

VFPt Solenoid correct2.svg
Electromagnetic field intencity

Induced electromagnetic field intencity

Electromagnetization field intencity

Eletromagnetization




Electromagnetic induction[edit]

VFPt Solenoid correct2.svg
Coil's voltage induction intencity

Turn's induced voltage intencity

Electromagnetic oscillation wave radiation[edit]

VFPt Solenoid correct2.svg
Electromagnetic oscillation




Electromagnetic wave
Onde electromagnetique.svg







Electromagnetic wave radiation





Photon[edit]

Mathematical formula of Photon

Photon exist in 2 states

Radiant Photon
Non Radiant Photon . With f>fo

Photon can only exist in one state at a time . Heiseinberg's uncertainty principle of successfully finding photon

Photon and matter[edit]

Photon and matter interacts to create Heat transfer through 3 phases Heat conduction, Heat convection and Heat radiation

Heat transfer
Heat conduction Matter changes it's temperature while absorb heat energy
Heat convection Matter conducts heat energy to the max at Threshold frequency fo

Heat radiation Matter uses excess energy above maximum absorbing energy to release electron off atom
. When v>0
with f > fo

Causes matter to decay through 3 kinds of decays

Mattter decay Reaction
Alpha decay Ur--> Th - He + Alpha radiation
Beta decay C-->N + Beta radiation
Gamma decay ee) + Gamma radiation

Experienment has shown that , electron of an atom can be freed or binded from absorbing or releasing photon's energy

Atom decay Absorbing photon energy Releasing photon energy
Equilibrium
v
r
n

Quanta[edit]

Mathematical formula of Quanta

Quanta process Wave particle duality meaning

Sometimes it behaves like wave
Sometimes it behaves like particle

Mathematics[edit]

Trigonometry[edit]

Fundamental trigonometry functions[edit]

Right Triangle With Labeled Sides.png
Trignometry Function Sin Cos Tan Cotan Sec Cosec
Definition Opposite side over hypotnuse Adjacent side over hypotnuse Opposite over Adjacent Adjacent over opposite 1 over opposite 1 over adjacent
Mathematical Formula
Graphs Sin.svg Cos.svg Tan.svg Cot.svg Sec.svg Csc.svg
Trigonometry function Laplacian operation Complex operation power of e periodic

Arithmatic mathematic[edit]

Trigonometry functions[edit]

Relation of Pythagorean's right triangle sides are defined as trigonometry functions below

Right Triangle With Labeled Sides.png
Trignometry Function Sin Cos Tan Cotan Sec Cosec
Definition Opposite side over hypotnuse Adjacent side over hypotnuse Opposite over Adjacent Adjacent over opposite 1 over opposite 1 over adjacent
Mathematical Formula
Graphs Sin.svg Cos.svg Tan.svg Cot.svg Sec.svg Csc.svg

Sinusoidal wave equation and wave function[edit]

Sinusoidal wave Wave equation wave function
Electric sinusoidal wave
Electromagnetic wave



Vector[edit]

If there exists a vector R(θ) as a sum of vector x(θ) and vector y(θ) where R , x , y are the sides of pythagorean's right triangle

With

Vector operations[edit]

Then the following operations on vectors are true


In real coordinate , with any point (x,y) correspond to (r,θ)

Scalar value Vector





In complex coordinate , with any point (x,y)

Complex number

Scalar value Vector





Conjugate complex number

Scalar value Vector





From above, we have

Calculus[edit]

Change in variables[edit]

For any function f(x) . Over the interval of to

Derivative1.png

Change in variable x

Change in function f(x)

Rate of change[edit]

Derivative1.png

Rate of change

Limit[edit]

Finite Limit We call the limit of as approaches if becomes arbitrarily close to whenever is sufficiently close (and not equal) to .

When this holds we write

or


Infinite Limit We call the limit of as approaches infinity if becomes arbitrarily close to whenever is sufficiently large.

When this holds we write

or

Similarly, we call the limit of as approaches negative infinity if becomes arbitrarily close to whenever is sufficiently negative.

When this holds we write

or

Differentiation[edit]

Tangent as Secant Limit.svg

Let be a function. Then

wherever this limit exists.

In this case we say that is differentiable at and its derivative at is .

Integration[edit]

Mathematics operation on a continuous function to find its area under graph . There are 2 types of integration

Indefinite Integral

Riemann Integration 3.png

Where satisfies

Definite Integral

Riemann Integration 2.png

Suppose is a continuous function on and . Then the definite integral of between and is

Where are any sample points in the interval and for .}}

Applied Maths[edit]

Transformation Integral[edit]

Function of time Laplace transform Fourier transform

Ex.

Function of time Laplace transform Fourier transform

Diferential equation[edit]

Ordinal differential equation[edit]

1st ordered differential equation of the form

Has solution

Where

Ex.

With

Solution

  • One real root . .
  • Two real roots . .
  • Two complex roots . .

With

Ex.

With

Solution

  • One real root . .
  • Two real roots . .
  • Two complex roots . .

With

Special differential equation[edit]
with A =

Equation of general form

Has solution

with A =

It follows that

with A =

In general,

with A =
with A =