1. signs, symbols and relationships

 

= equal

≠ not equal        

<smaller than

≤ smaller or equal

> greater than

≥ greater than or equal to

≈ about the same

→ implication between two statements: if the first statement is true, then the second is. 

↔ If the first statement is true, then it is the second and vice versa

+ plus

– minus

x or * multiplication sign = value of the product. The character is often omitted. a x b or a * b becomes too ab

For multiplication, we usually use the character (*), or leave it off x is also used in linear algebra in the treatment of matrices, (m x n) matrix, where m is the number of rows and n is the number of columns

 / __ fraction or divided by. For example, (a + b) / (a ​​– b) : Relationship to: Example 1: 2 read 1 to 2

! Faculty, cf. Probability 3! = 1 * 2 * 3 = 6, 0! = 1

π Greek letter pi = 22/7

ε Greek letter Epsilon, means element in set theory

√ root out (root exponent = 2)

f (x) Function of some formula x eg ax + b

f ‘(x) first derivative of the function f (x), slope of the tangent of f (x) at xa

f ” (x) is the second derivative of the function f (x)

∫f (x) Integral of the function f (x), calculation of the area between x and f (x) eg between x1 and x2

Σ(xi, n, j)  summation of x₁ + x₂ + x₃ + x₄ + … + xn, 1 + n are called the j summation limits, n = number of summands a1, a2, … an,  j is the summation index j = 1  

R real numbers, above all infinite decimal fractions, like 3.14159265 or 0.33333. The real numbers also include the irrational numbers, such as the number euler number e = 2.7182 …, the numbers π, √2, and √3

Q rational numbers, ½, -1/3, 7/1 (= 7)

Z integers, …, -3, -2, -1, 0, 1, 2, 3, ….

N natural numbers, 0, 1, 2, 3, ….

C Complex numbers i² = -1 (read more in higher lessons)

a ε R means that a is an element of R, which means that a is a real number

|a| a number between absolute bars |a| = a if a ≥ 0 or -a if a <0) ↔ |a| = √a²  

 

Commutative law a + b = b + a, a * b = b * a  

Associative law (a + b) + c = a + (b + c),  

Distributive law (a + b) c = a * c + b * c

 

The problem with the minus sign  

a (-b) = -ab

-a * (- b) = a * b

-a * -a = a²

a – (b + c) = a – b – c

a – (b – c) = a – b + c

-a / b = a / -b

-a / -b = a / b

 

Important relationships  

(a + b)²  = a²  + 2ab + b²

(a – b)² = a² – 2ab + b²

(a + b)³ = a³ + 3a²b + 3a b² + b³

(a – b)³ = a³ – 3a²b + 3a b² – b³

a² – b² = (a – b) (a + b)

 

Division and fractions

a / b / c = ac / b

(a / b) / (c / d) = a / b * d / c

  

Compute with roots and exponents  

a * a = aexp2 = a²

a¹ * a² = aexp (1 + 2) = a³

a ° = 1

a ° * a² = aexp (0 + 2) = a²

1 / a = a-1

√a = a½ or aexp (½)

√a³ = a³ / 2

1 / √a = a-½ or aexp (-½)

n√aexp (m) = aexp (m / n) (n> 0

 

The greek alphabeth 

Α	α	Alpha	Ι	ι	Iota	Ρ	ρ	Rho
Β	β	Beta	Κ	κ	Kappa	Σ	σ	Sigma
Γ	γ	Gamma	Λ	λ	Lambda	Τ	τ	Tau
Δ	δ	Delta	Μ	μ	Mü	Υ	υ	Ypsilon
Ε	ε	Epsilon	Ν	ν	Nü	Φ	φ	Phi
Ζ	ζ	Zeta	Ξ	ξ	Xi	Χ	χ	Chi
Η	η	Eta	Ο	ο	Omikron	Ψ	ψ	Psi
Θ	θ	Theta	Π	π	Pi	Ω	ω	Omega

 

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