
MATHEMATICS
Formulas, Graphs,
Tables, . . . < High School to University Level > 

CONTENTS B


ALGEBRA

11
Rules and properties of logarithms

Common logarithms

Natural
logarithms

Changing the base – different
logarithmic identities

Exponential and logarithmic equations

Exponential equations

Logarithmic equations

12
Interest
calculations

Simple interest

Amount of interest,
principal (initial amount), interest rate and amount after n
years

Compound interest

Periodic compounding

Continuous compounding

Exponential
growth and decay, application of the natural exponential
function

13
Imaginary and complex numbers

Imaginary
numbers

Imaginary unit

Complex numbers

Real and imaginary
parts

The complex plane

The set of all complex
numbers C

Absolute value,
modulus of a complex number

Complex conjugates

Addition and
subtraction of complex numbers

Multiplication and
division of
complex numbers

14
Polar or
trigonometric notation of complex numbers

Euler's formula

Multiplication
and division of complex numbers in the polar form

Exponentiation
and root extraction of complex numbers in the polar form

Powers and roots of
complex numbers, use of de Moivre’s formulas

Euler’s
formula,
relationship between trigonometric functions and the complex exponential
function

15
Polar coordinate system

Polar
and Cartesian coordinates relations

Equation
of a line in polar form

Lines
parallel to the axes, horizontal and vertical lines

Lines
running through the origin or pole (radial lines)

Polar
equation
of a line

Equation
of a circle in polar form

General
equation of a circle in polar coordinates

Polar
equation of a circle with a center on the polar axis running
through the pole

Polar
equation of a circle with a center at the pole

16
Parametric equations

Parametric
equations definition

The parametric equations of a line

Vector equation of a line

Parametric equations of a line through
two points

Parametric
curves have a direction of motion

Use
of parametric equations, example

Intersection point of a line and a plane
in threedimensional space

Parametric equation of a line in
threedimensional
space

The parametric equations of a
quadratic
polynomial,
parabola

The parametric equations of the parabola,
whose axis of symmetry is parallel
to the yaxis

The parametric equations of the parabola, whose axis of symmetry is
parallel to the xaxis

The parametric equations of a
circle

The parametric equations of a
circle
centered at the origin with radius r

The parametric equations of a
translated circle with center (x_{0}, y_{0}) and radius r

The parametric equations of an
ellipse

The parametric equations of an ellipse
centered at the origin

The parametric equations of a
translated
ellipse with center at (x_{0}, y_{0})

17
Vectors

Vectors
in a plane

Direction, length or magnitude or norm of a vector

Collinear opposite and coplanar vectors

Addition of vectors

Subtraction of vectors

Scalar multiplication or multiplication of a vector by scalar

Unit vector

Linear combination of vectors

Linear dependence of vectors

18
Vectors
and a coordinate system, Cartesian vectors

Vectors in
a coordinate plane (a twodimensional system of coordinates), Cartesian
vectors

Radius vector or
position vector and vectors components

Vectors in
threedimensional space in terms of Cartesian coordinates

Angles of vectors in relation
to coordinate axes, directional cosines  scalar components of a vector

Unit vector and directional cosines

Vectors in
a threedimensional coordinate system, examples

19
Scalar product or dot product or
inner product

Perpendicularity (or
orthogonality) of two vectors

The value of the scalar product of two vectors depends
on their position

Square of magnitude of
a vector

Scalar product of unit
vectors

Scalar or dot product
properties

Scalar product in the
coordinate system

Angle between vectors
in a coordinate plane

Scalar
product of vectors examples

Projection of a vector in the direction of another vector,
the scalar and vector components

The scalar
component

The vector component

20
Vector
product or cross product

An example for the vector product in physics

The vector products of the standard unit vectors

The vector product properties

The vector
product in component form

The mixed product

The
mixed product or scalar triple product definition

The
mixed product properties

The condition for
three vectors to be coplanar

The
mixed product or scalar triple product expressed in terms of components

The vector product
and the mixed product use, examples

















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