Fundamental Mathematics/Arithmetic

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Arithmetic Number[edit]

Natural number The numbers which are generally used in our day to day life for counting are
termed as natural numbers. They are also referred to as "counting" numbers
,
Even number Number divides by 2 without remainder . Even number is denotes as 2N
Odd number Number divides by 2 with remainder Odd number is denotes as 2N+1
Prime number Number divides by 1 and itself without remainder . Prime number is denoted as P
Integer Signed numbers
Fraction
Complex Number number made up of real and imaginary number
Imaginary Number

Arithmetic Operation[edit]

Mathematical Operations on arithmetic numbers

Mathematical Operation Symbol Example
Addition
Subtraction
Multiplication
Division
Exponentiation
Radical
Log
Ln

Arithmetic Function[edit]

Function is an arithmetical expression relate 2 variables . Function is denoted as

meaning for any value of x there is a corresponding value y=f(x)

Where

x - indepent variable
x - depent variable
f(x) - function of x

Types and Graphs of function[edit]

Polynomial Functions[edit]

Straight Line function
Parabola function 20170525 Parabola y = (x^2)-(4q) 00.png
Hyperbolic function Hyperbolic functions-2.svg

Trigonometry Functions[edit]

Sine Function

Sin.svg

Cosine Function Cos.svg
Secant Function Sec.svg
CoSecant Function Csc.svg
Tan Function Tan.svg
Cotan Function Cot.svg

Mathematical operation on arithmetic function[edit]

Mathematical Operations Symbol Example
Change in variables , ,
Rate of change
Limit
Differentiation
Integration

Arithmetic Equation[edit]

Polynomial Equation[edit]

1st ordered polynomial equation

1st ordered polynomial equation has general form  . The solution to the 1st ordered polynomial equation    

Divide the quadratic equation by a, which is allowed because a is non-zero:

2nd ordered polynomial equation

1st ordered polynomial equation has general form  . The solution of the 2nd ordered polynomial equation 

Divide the quadratic equation by a, which is allowed because a is non-zero:

Subtract c/a from both sides of the equation, yielding:

The quadratic equation is now in a form to which the method of completing the square can be applied. Thus, add a constant to both sides of the equation such that the left hand side becomes a complete square:

which produces:

Accordingly, after rearranging the terms on the right hand side to have a common denominator, we obtain:

The square has thus been completed. Taking the square root of both sides yields the following equation:

Isolating x gives the quadratic formula:

The plus-minus symbol "±" indicates that both

are solutions of the quadratic equation.[1] There are many alternatives of this derivation with minor differences, mostly concerning the manipulation of a.

Some sources, particularly older ones, use alternative parameterizations of the quadratic equation such as ax2 − 2bx + c = 0[2] or ax2 + 2bx + c = 0,[3] where b has a magnitude one half of the more common one. These result in slightly different forms for the solution, but are otherwise equivalent.

A lesser known quadratic formula, as used in Muller's method, and which can be found from Vieta's formulas, provides the same roots via the equation:

Differential Equation[edit]

1st ordered differential equation

 . Solution of the 1st ordered differential equation above is 


2nd ordered differential equation

The solution of the 2nd ordered polynomial equation above

One real root
Two real roots
One complex roots

Special nth derivative differential equation




Go to the School of Mathematics
  1. Sterling, Mary Jane (2010), Algebra I For Dummies, Wiley Publishing, ISBN 978-0-470-55964-2, https://books.google.com/books?id=2toggaqJMzEC&pg=PA219&dq=quadratic+formula#v=onepage&q=quadratic%20formula&f=false 
  2. Kahan, Willian (November 20, 2004), On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic, http://www.cs.berkeley.edu/~wkahan/Qdrtcs.pdf 
  3. "Quadratic Formula", Proof Wiki, http://www.proofwiki.org/wiki/Quadratic_Formula