Posts Tagged ‘value’
Friday, November 6th, 2009
Introduction to Invariants
Description
A detailed tutorial on invariants and the property of invariance. Step by step tutorial including several examples of invariants for reference.
Overview
Invariants are any function or number that displays the property of invariance. Invariance is when a function or number can go through several transformations without changing, or without going outside of its set parameters. The set parameters differ depending on the function or number. Some examples of invariant functions and numbers are the absolute value of a complex number, the degree of a polynomial, and certain parts of a square matrix
Tags: absolute, arithmetic, complex, degree, determinant, eigenvalue, eigenvector, function, invariance, invariant, matrix, number, parameters, polynomial, square, trace, transformations, value
Posted in Arithmetic | No Comments »
Thursday, November 5th, 2009
Cancellation Properties of Natural Numbers
Description
A detailed tutorial on cancellation properties of natural numbers. Step by step tutorial including several examples of cancellation properties for reference.
Overview
Cancellation properties of natural numbers state that when two terms are equal to each other, if the same number is being multiplied or added on both terms, you may cancel them out and the terms will still be equal to each other. Knowledge of the cancellation properties is extremely important for simplification of equations and when trying to find the value of a variable. Mathematically stated, the cancellation properties are that if x + z = y + z or xz = yz, then x = y.
Tags: add, arithmetic, cancel, cancellation, equal, multiply, natural, number, out, properties, property, simplification, simplify, term, value, variable
Posted in Arithmetic | No Comments »
Tuesday, November 3rd, 2009
How to Find the Determinant
Description
A detailed tutorial on how to find the determinant. Step by step tutorial including several examples of finding the determinant for reference.
Overview
The determinant is a number that is associated with a square matrix. In a mathematical sense, the determinant is a scale factor for measure when the matrix is regarded as a linear transformation. The determinant is denoted by two bars on either side of the matrix, which can be confused with the absolute value of the matrix. The determinant is found by subtracting the products of the diagonals of the matrix, at least in a 2×2 matrix.
Tags: absolute, algebra, determinant, diagonal, factor, linear, matrices, matrix, product, scale, square, subtract, transformation, value
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
Definition of a Scalar Triple Product
Description
A detailed tutorial on scalar triple products. Step by step tutorial including several examples of scalar triple products for reference.
Overview
A scalar triple product is a way of applying other multiplication operators to three vectors. Quite often, the scalar triple product is denoted as (a, b, c). It can also be defined as (a b c) = a(b x c). The scalar triple product has three main properties. The first one is that the absolute value of the scalar triple product is the volume of the three dimensional figure that is formed by the three vectors. The second one is the scalar triple product is only zero if the three vectors are linearly independent. The three vectors must lie in the same plane for this to be true. The third one is that the scalar triple product is only positive if all three of the vectors are considered right-handed.
A simple way to write the scalar triple product is to line up the coordinates of the vectors in this form: 
This is the same as saying 
Tags: absolute, algebra, box, coordinates, figure, independent, linear, mixed, multiplication, operator, parallelpiped, positive, product, properties, right-handed, scalar, three-dimensional, triple, value, zero
Posted in Algebra | No Comments »
Thursday, October 22nd, 2009
How to Identify the Phase Shift
Description
A detailed tutorial on the phase shift of a function. Step by step tutorial including several examples of the phase shift of a function for reference.
Overview
The phase shift is another way of saying a horizontal shift – that is, when a graph moves from left to right. If the phase shift is positive, the graph shifts to the left, and if the phase shift is negative, the graph shifts to the right. Finding a phase shift is not difficult – when a value is included with x (instead of included with something relating to x), then a horizontal shift or phase shift will be performed. Simply look at the equation of the function to find the value.
Tags: algebra, equation, function, graph, horizontal, left, negative, phase, positive, right, shift, value, x
Posted in Algebra | No Comments »
Friday, October 16th, 2009
How to Find Values of Quadrantal Angles
Description
A detailed tutorial on how to find values of quadrantal angles. Step by step tutorial including several examples of finding values of quadrantal angles for reference.
Overview
Quadrantal angles have a terminal side coinciding with a coordinate axis. A trigonometric functional value of such an angle can be determined by the coordinates of the point where the terminal side intersects the unit circle. When on the unit circle, the Cartesian coordinate (x, y) cooresponds to (cos(&), sin(&)) on the unit circle.
Tags: angle, axis, circle, coordinate, cosine, functional, Geometry, Math, point, quadrantal, sine, terminal, trigonometric, unit, value, x, y
Posted in Geometry | No Comments »
Tuesday, October 13th, 2009
Introduction to Present Value
Description
A detailed tutorial on solving for the present value. Step by step tutorial including several examples of solving for the present value for reference.
Overview
Present value is the value on a given date of a future payment or series of future payments. It is typically discounted to reflect the time value of money, and sometimes other factors. Because of this, the main calculation for present value is simply the calculation for the time value of money. The time value of money can be found by using the compund interest formula, which can be mathematically expressed as 
. This is equal to the present value.
Tags: algebra, calculation, compound, formula, interest, investment, Math, money, present, risk, time, value
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Introduction to Zero and Undefined Slopes
Description
Detailed tutorial on undefined and zero slopes. Step by step tutorial including several examples of zero and undefined slopes for reference.
Overview
Zero and undefined slopes are both slopes that do have a definite value to them. They represent very uinigue graphs and lines. A zero slope is a slope of zero over anything – meaning it has a run, but no rise. It is a zero slope because zero divided by anything is simply zero. Zero slopes form horizontal lines. An undefined slope is a slope of anything over zero – meaning it has a rise, but no run. It is an undefined slope because nothing can be divided by zero. Undefined slopes form vertical lines.
Tags: arithmetic, graph, horizontal, line, Math, rise, run, slope, undefined, value, vertical, zero
Posted in Arithmetic | No Comments »
Thursday, October 8th, 2009
Definition of a Mandelbrot Set
Description
A detailed tutorial on Mandelbrot sets and identifying Mandelbrot sets. Step by step tutorial including a several visual examples of a Mandelbrot set for reference.
Overview
A Mandelbrot set is defined as a set of points in the complex frame, the boundary of which forms a fractal. This can be mathematically defined as the set of complex values c for which the orbit of zero under iteration of a complex quadratic polynomial remains bounded.
Tags: boundary, complex, differential equations, fractal, iteration, Mandelbrot, Math, point, polynomial, quadratic, set, value
Posted in Differential Equations | No Comments »
Thursday, October 8th, 2009
Definition of a Julia Set
Description
A detailed tutorial on Julia sets and identifying Julia sets. Step by step tutorial including a several visual examples of a Julia set for reference.
Overview
A Julia set is a complimentary set defined from a function. A Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values. The behavior of the Julia set is classified as “chaotic”.
Tags: chaotic, complimentary, differential equations, function, iterated, Julia, Math, perturbation, set, value
Posted in Differential Equations | No Comments »
