Collection | Homework Help

Posts Tagged ‘collection’

Vector Space

Friday, October 23rd, 2009

Introduction to Vector Space

Description

A detailed tutorial on vector space. Step by step tutorial including several examples of vector space and how to solve for vector space for reference.

Overview

Vector space is simply a structure in mathematics that is formed by a collection of vectors. Vector space can be calculated using vector addition and scalar multiplication. Vector space is very dependent on the definition of a vector. Some vectors are simply arrows on a fixed plane. But in general, the term vector just means there is an object for which two operations can be performed. The definition of vector space is defined in algebraic terms, as opposed to the geometric terms that can sometimes be applied.

Tags: addition, algebra, arrow, collection, definition, Geometry, multiplication, object, operation, plane, scalar, space, vector
Posted in Algebra | No Comments »

Set Theory: Disjoint Sets

Friday, October 2nd, 2009

Disjoint Sets in Set Theory

Description

A detailed tutorial on disjoint sets. Step by step tutorial including several examples of disjoint sets and how to identify disjoint sets for reference.

Overview

A disjoint set is a term applied in set theory when two or more sets have no elements in common. For example, the sets {1, 2, 3} and {7, 8, 9} are disjoint sets because none of the numbers in the sets are the same. The formal way to say this is that two sets are disjoint sets if their intersection creates an empty set, in other words, nothing at all. An intersection is when you only take the values that are found in both sets. If none of the values are the same, this would be an empty set. Disjoint sets can be classified into further categories of piecewise, pairwise, or mutually disjoint provided that in a collection, at least two sets are disjoint.

Tags: collection, discrete math, disjoint, elements, empty set, intersection, Math, mutually, pairwise, piecewise, set theory, sets, value
Posted in Discrete Math | No Comments »

Scatter Plots

Friday, October 2nd, 2009

Introduction to Scatter Plots

Description

A detailed tutorial on scatter plots. Step by step tutorial including several examples of scatter plots for reference.

Overview

A scatter plot is more of a diagram than a graph. but it uses Cartesian coordinates to display the values in a set of data. A scatter plot is normally defined as a collection of points – it is almost like a regular Cartesian graph, but the points are not connected and there are typically more of them. Scatter plots can also be 3D.

Tags: algebra, cartesian, collection, coordinates, horizontal, Math, points, scatter chart, scatter diagram, scatter graph, scatter plot, values, vertical
Posted in Algebra | No Comments »

Dirichlet Kernel

Thursday, September 24th, 2009

Dirichlet Kernel Explained

Description

A detailed tutorial on the solving of the Dirichlet kernel. Step by step tutorial including several examples of how to solve the Dirichlet kernel for reference.

Overview

The Dirichlet kernel is this collection of functions: $D_n(x)=\sum_{k=-n}^n e^{ikx}=1+2\sum_{k=1}^n\cos(kx)=\frac{\sin\left(\left(n +\frac{1}{2}\right)x\right)}{\sin(x/2)}.$ The Dirichlet kernel is important because of its realtionship with the Fourier series. Other noteable things about the Dirichlet kernel is that it uses the Delta function, and also it uses a trigonometric identity.

Tags: collection, convolution, Delta, differential equations, Dirichlet kernel, Fourier series, function, Johann Peter Gustav Lejeune Dirichlet, Math, trigonometric identity
Posted in Differential Equations | No Comments »