Math Handbook

This section contains general information on mathematics, which is difficult to attribute unambiguously to either algebra or geometry.


Differentiation

Differentiation rules

Derived Simple Functions Table

The table of derived exponential and logarithmic functions

The table of derivatives of trigonometric functions

Derivative Table of Hyperbolic Functions

Integration

Integral table, rational functions

Integral table, logarithmic functions

Table of integrals, exponential functions, improper integrals

Table of integrals, irrational functions - part 1

Table of integrals, irrational functions - part 2


miscellanea


Greek alphabet


Latin alphabet


Mathematical constants


Physical constants


Pi number up to 100,000 characters


Algebraic equations

Types of algebraic equations


Linear equation ax + b = 0


The quadratic equation ax ² + bx + c = 0


The cubic equation ax ³ + bx ² + cx + d = 0


The biquadratic equation ax ⁴ + bx ² + c = 0


Returnable (algebraic) equation ax ⁴ + bx ³ + cx ² + bx + a = 0


Modified return equation ax ⁴ + bx ³ + cx ² - bx + a = 0


The generalized return equation ab ² x ⁴ + bx ³ + cx ² + dx + ad ² = 0.


The fourth-degree equation of general form ax ⁴ + bx ³ + cx ² + dx + e = 0.


The two terms algebraic equation of the nth degree x _n - a = 0.


A special case of the equation is ax ²ⁿ + bx ⁿ + c = 0.


The returnable (algebraic) equation a _o x ²ⁿ + a ₁ x ^{2n? 1} + a ₂ x ^{2n? 2} + ... + a ₂ x ² + a ₁ x + a ₀ = 0.


Algebraic equation of the nth degree of general form a _n x ⁿ + a _n-1 x ^n-1 + ... + a ₁ x + a ₀ = 0.


Systems of algebraic equations

Types of systems of algebraic equations

System of two linear equations

System of m linear equations


Ordinary differential equations of the first order

Types of ODU 1st order

Autonomous equation - y '= f (y).

Equation with separable variables - y '= f (x) g (y)

Linear equation - g (x) y '= f ₁ (x) y + f ₀ (x)

Bernoulli equation - g (x) y '= f ₁ (x) y + f _n (x) y ⁿ

Homogeneous equation - y '= f (y / x)

Special type Riccati equation - y '= ay ² + bx ⁿ

Special type Riccati equation, case 1 - y '= y ² + f (x) y - a ² - af (x)

Special type Riccati equation, case 2 - y '= f (x) y ² + ay - ab - b ² f (x)

Special type Riccati equation, case 3 - y '= y' = y ² + xf (x) y + f (x)

Special type Riccati equation, case 4 - y '= f (x) y ² - ax ⁿ f (x) y + anx ^n-1

Special type Riccati equation, case 5 - y '= f (x) y ² + anx ^n-1 - a ² x ²ⁿ f (x)

Special type Riccati equation, case 6 - y '= - (n + 1) x ⁿ y ² + x ^{n + 1} f (x) y - f (x)

Special type Riccati equation, case 7 - xy '= f (x) y ² + ny + ax ²ⁿ f (x)

Special type Riccati equation, case 8 - xy '= x ²ⁿ f (x) y ² + [ax ⁿ f (x) - n] y + bf (x))

Special type Riccati equation, case 9 - y '= f (x) y ² + g (x) y - a ² f (x) - ag (x)

Special type Riccati equation, case 10 - y '= f (x) y ² + g (x) y + anx ^n-1 λ a ² x ²ⁿ f (x) λ ax ⁿ g (x)

Special type Riccati equation, case 11 - y '= ae ^λx y ² + ae ^λx f (x) y + λf (x)

Special type Riccati equation, case 12 - y '= f (x) y ² - ae ^λx f (x) y + aλe ^λx

Special type Riccati equation, case 13 - y '= f (x) y ² + aλe ^λx - a ² e ^2λx f (x)

Special type Riccati equation, case 14 - y '= f (x) y ² + λy + ae ^2λx f (x)

Special type Riccati equation, case 15 - y '= y ² - f ² (x) + f' (x)

Special type Riccati equation, case 16 - y '= f (x) y ² - f (x) g (x) y + g' (x)

Special type Riccati equation, general form - y '= f (x) y ² + g (x) y + h (x)


Math at school

The theory of algebra for grades 5–9 of the secondary school — sets, intervals, progression, equations, etc. d.


The theory of algebra for 10-11 grades of secondary school - degrees, logarithms, polynomials, division of polynomials, Bezout theorem, Horner's scheme, it. d.


The theory of algebra for grades 10-11 high school - the beginning of the analysis. Derivative, primitive, integral, etc.


Complex numbers. Actions over them.

Complex numbers

Arithmetic operations on complex numbers

Complex plane

Trigonometric form of a complex number

Raising a complex number to a power

Extracting a root from a complex number

The exponential form of a complex number

Solving quadratic equations with complex numbers