MATHEMATICS   Formulas, Graphs, Tables, . . .  < High School to University Level >
CONTENTS B
ALGEBRA
11
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 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 three-dimensional space
Parametric equation of a line in three-dimensional space The parametric equations of a quadratic polynomial, parabola
The parametric equations of the parabola, whose axis of symmetry is parallel to the y-axis
The parametric equations of the parabola, whose axis of symmetry is parallel to the x-axis 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 (x0, y0) 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 (x0, y0)
17  Vectors Vectors in a plane
Direction, length or magnitude or norm of  a vector
Collinear opposite and coplanar 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 two-dimensional system of coordinates), Cartesian vectors
Radius vector or position vector and vectors components
Vectors in three-dimensional 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 three-dimensional 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    