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| MATHEMATICS
Formulas, Graphs,
Tables, . . . < High School to University Level > |
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CONTENTS B
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ALGEBRA
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11
Rules and properties of logarithms
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Common logarithms
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Natural
logarithms
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Changing the base – different
logarithmic identities
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Exponential and logarithmic equations
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Exponential equations
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Logarithmic equations
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12
Interest
calculations
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Simple interest
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Amount of interest,
principal (initial amount), interest rate and amount after n
years
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Compound interest
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Periodic compounding
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Continuous compounding
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Exponential
growth and decay, application of the natural exponential
function
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13
Imaginary and complex numbers
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Imaginary
numbers
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Imaginary unit
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Complex numbers
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Real and imaginary
parts
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The complex plane
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The set of all complex
numbers C
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Absolute value,
modulus of a complex number
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Complex conjugates
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Addition and
subtraction of complex numbers
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Multiplication and
division of
complex numbers
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14
Polar or
trigonometric notation of complex numbers
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Euler's formula
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Multiplication
and division of complex numbers in the polar form
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Exponentiation
and root extraction of complex numbers in the polar form
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Powers and roots of
complex numbers, use of de Moivre’s formulas
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Euler’s
formula,
relationship between trigonometric functions and the complex exponential
function
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15
Polar coordinate system
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Polar
and Cartesian coordinates relations
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Equation
of a line in polar form
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Lines
parallel to the axes, horizontal and vertical lines
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Lines
running through the origin or pole (radial lines)
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Polar
equation
of a line
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Equation
of a circle in polar form
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General
equation of a circle in polar coordinates
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Polar
equation of a circle with a center on the polar axis running
through the pole
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Polar
equation of a circle with a center at the pole
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16
Parametric equations
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Parametric
equations definition
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The parametric equations of a line
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Vector equation of a line
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Parametric equations of a line through
two points
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Parametric
curves have a direction of motion
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Use
of parametric equations, example
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Intersection point of a line and a plane
in three-dimensional space
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Parametric equation of a line in
three-dimensional
space
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The parametric equations of a
quadratic
polynomial,
parabola
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The parametric equations of the parabola,
whose axis of symmetry is parallel
to the y-axis
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The parametric equations of the parabola, whose axis of symmetry is
parallel to the x-axis
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The parametric equations of a
circle
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The parametric equations of a
circle
centered at the origin with radius r
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The parametric equations of a
translated circle with center (x0, y0) and radius r
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The parametric equations of an
ellipse
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The parametric equations of an ellipse
centered at the origin
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The parametric equations of a
translated
ellipse with center at (x0, y0)
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17
Vectors
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Vectors
in a plane
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Direction, length or magnitude or norm of a vector
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Collinear opposite and coplanar vectors
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Addition of vectors
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Subtraction of vectors
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Scalar multiplication or multiplication of a vector by scalar
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Unit vector
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Linear combination of vectors
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Linear dependence of vectors
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18
Vectors
and a coordinate system, Cartesian vectors
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Vectors in
a coordinate plane (a two-dimensional system of coordinates), Cartesian
vectors
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Radius vector or
position vector and vectors components
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Vectors in
three-dimensional space in terms of Cartesian coordinates
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Angles of vectors in relation
to coordinate axes, directional cosines - scalar components of a vector
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Unit vector and directional cosines
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Vectors in
a three-dimensional coordinate system, examples
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19
Scalar product or dot product or
inner product
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Perpendicularity (or
orthogonality) of two vectors
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The value of the scalar product of two vectors depends
on their position
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Square of magnitude of
a vector
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Scalar product of unit
vectors
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Scalar or dot product
properties
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Scalar product in the
coordinate system
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Angle between vectors
in a coordinate plane
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Scalar
product of vectors examples
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Projection of a vector in the direction of another vector,
the scalar and vector components
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The scalar
component
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The vector component
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20
Vector
product or cross product
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An example for the vector product in physics
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The vector products of the standard unit vectors
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The vector product properties
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The vector
product in component form
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The mixed product
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The
mixed product or scalar triple product definition
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The
mixed product properties
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The condition for
three vectors to be coplanar
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The
mixed product or scalar triple product expressed in terms of components
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The vector product
and the mixed product use, examples
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