Posts Tagged ‘system’
Thursday, November 19th, 2009
The X and Y Axis on a Cartesian Graph
Description
A detailed tutorial of the x axis and the y axis. Step by step tutorial including several examples of the x axis and the y axis for reference.
Overview
The the Cartesian coordinate system, there is an x axis and a y axis. The x axis runs horizontally across the system and all first terms in ordered pairs are x coordinates, from the x axis. The y axis runs vertically across the system and all second terms in ordered pairs are y coordinates, from the y axis. The x and y axis work together to use a pattern of right angles and perpendicular lines in order to find ordered pairs and coordinates of x and y on the graph.
Tags: algebra, angle, axis, basic, cartesian, coordinate, graphing, graphs, horizontal, lines, ordered, pairs, perpendicular, right, system, vertical, x, y
Posted in Algebra | No Comments »
Tuesday, November 3rd, 2009
Overview of Quaternions
Description
A detailed tutorial on quaternions. Step by step tutorial including several examples and a visual example of what a quaternion is for reference.
Overview
Quaternions form a four-dimensional normed division algebra over real numbers. The original quaternions that were described in mathematics had a slightly definition – they formed a noncommutative number system that extends the complex numbers. However, the most recent definition, the one that is used in mathematics today, is the first one that was given. Quaternions are often denoted as the letter H, often written in the same script style as the number sets R and N. H in this case stands for Hamilton, named after the mathematician who first introduced quaternions to math.
Tags: algebra, complex, division, four-dimensional, H, Hamilton, noncommutative, normed, quaternion, system
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
How to Find the Component of a Vector
Description
A detailed tutorial on finding the component of a vector. Step by step tutorial including several examples of how to find the component of a vector for reference.
Overview
There are three different kinds of components that can be found in vectors: axial components, radial components, and tangential components. Just like the vectors themselves, different types of components are found in different coordinate systems. Axial components are found in the Cartesian coordinate system, while radial and tangential components are found in the polar coordinate system. A component is exactly the same as it’s dictionary definition: it is just a small part that makes up a whole, so in this case they are small parts of a vector. The vector itself is also a component.
Tags: algebra, axial, cartesian, component, coordinate, polar, radial, system, tangential, vector
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
The Cross Product of Vectors
Description
A detailed tutorial on the cross product of two vectors. Step by step tutorial including several examples of how to find the cross product for reference.
Overview
A cross product is very similar to a dot product. However, the result of a cross product is a vector, and the result of a dot product is a scalar. In mathematical terms, the cross product can be defined as 
. Theta represents the meausre of the angle between a and b, and n is a unit vector perpendicular to both a and b. The vector this forms is a right-handed system.
Tags: a, algebra, b, cross, dot, n!, outer, perpendicular, product, right-handed, rule, scalar, system, unit, vector
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
Overview of Euclidean Vectors
Description
A detailed tutorial on Euclidean vectors. Step by step tutorial including several examples and visual examples of Euclidean vectors for reference.
Overview
A vector is a geometric object that has both a magnitude (also known as the length) and a direction. They are usually drawn as arrows that have a similar starting point and connect two points together. The difference between different kinds of vectors is what coordinate system is used to describe them. Euclidean vectors are vectors that are described by the Cartesian coordinate system.
Tags: algebra, arrow, cartesian, coordinate, direction, Euclidean, geometric, graph, initial, length, magnitude, point, system, terminal, vector
Posted in Algebra | No Comments »
Friday, October 9th, 2009
Lissajous Curve Explained
Description
A detailed tutorial of a lissajous curve. Step by step tutorial including several visual examples of lissajous curves for reference.
Overview
A Lissajous curve represents the graph of a system of parametric equations, which can be mathematically expressed as 
. This also decribes complex harmonic motion. The way that the figure appears is very sensitive to the ratio a / b, so the figure can appear in many different forms.
Tags: Bowditch, Calculus, complex, curve, equation, figure, form, graph, harmonic, Lissajous, Math, motion, paramentric, ratio, system
Posted in Calculus | No Comments »
Tuesday, October 6th, 2009
Plotting Points in the Polar Coordinate System
Description
A detailed tutorial on plotting points in the polar coordinate system. Step by step tutorial including several examples of how to plot points on the polar coordinate system for reference.
Overview
By this point, everyone should know how to plot points on a normal graph. But what about a circular graph? This circular graph is called the polar coordinate system or the polar plane. Instead of using the points (x, y), the polar coordinate system uses the points (r, theta). Theta is a greek letter that looks like a zero with a horizontal line drawn through the center. Most of the points you will be finding for the polar coordinate system will be used with trigonometric functions – sine, cosine, and tangent. Graphing occurs in about the same way as it would on a normal graph – just match up the points, even if they are on a circle.
Tags: Calculus, circle, coordinate, cosine, function, functions, graph, Math, points, polar, r, sine, system, tangent, theta, trig, trigonometric, x, y
Posted in Calculus | No Comments »
