Posts Tagged ‘product’
Tuesday, December 29th, 2009
How to Use the Product Rule in Algebra
Description
A detailed tutorial on the algebraic product rule. Step by step tutorial including several examples of the algebraic product rule for reference.
Overview
There are many product rules in the world of math. This tutorial focuses on a product rule that is used in algebra and statistics. The product rule states that if two independent tasks T1 and T2 are to be performed, then T1 can be performed m ways and T2 can be performed n ways. Therefore, the number of ways the tasks can be performed together is m * n ways. Remember that this is only the number of possible ways to do something, not how much time it takes to do something. Also, the same method is used no matter how many different tasks you are given.
Tags: algebra, combination, multiplication, multiply, number, permutation, product, rule, statistics, task
Posted in Algebra | No Comments »
Thursday, November 19th, 2009
Defining the Angles Between Vectors
Description
A detailed tutorial on how to define the angles between vectors. Step by step tutorial including several examples of angles between vectors for reference.
Overview
In general, it is easier to find the angle between 2D vectors, rather than 3D vectors. In order to define the angles between vectors, we need to use the dot product in conjunction with a few other functions. The angles between vectors can be expressed as angle = arccos(v1xv2), where v1xv2 is how the dot product is expressed.
Tags: 2D, 3D, absolute, algebra, angle, arccos, conjunction, cosine, define, degrees, dot, function, linear, magnitude, product, radians, value, vector
Posted in Algebra | No Comments »
Thursday, November 19th, 2009
Overview of Revenue, Cost, and Product Functions
Description
A detailed tutorial on revenue, cost, and product functions. Step by step tutorial including several examples of revenue, cost, and product functions for reference.
Overview
The revenue, cost, and product functions are parts of economics and business math. The cost function is how much something costs, and it can be expressed as C(q) = 100 + 2q. The revenue function is how much money you get from selling what you bought, and it can be expressed as R(q) = 2.5q. The profit function is how much money was actually made, and it is the revenue function minus the cost function.
Tags: algebra, business, cost, economics, function, gained, lost, Math, money, product, revenue, subtraction
Posted in Algebra | No Comments »
Tuesday, November 17th, 2009
Introduction to Orthogonal Vectors
Description
A detailed tutorial on orthogonal vectors. Step by step tutorial including several examples of orthogonal vectors for reference.
Overview
Orthogonal vectors are vectors that are perpendicular. You can determine if vectors are perpendicular by finding the dot product. If the dot product is equal to zero, then the vectors are perpendicular. In certain dimensions, it is possible for three vectors to be perpendicular to each other. In this case, all three of those vectors are considered to be orthogonal. However, in general, orthogonal vectors is a term used to describe a pair of vectors.
Tags: algebra, dot, linear, pair, perpendicular, product, space, three, three-space, two, vectors, zero
Posted in Algebra | No Comments »
Friday, November 6th, 2009
Overview of Orthogonal Complements
Description
A detailed tutorial on orthogonal complements. Step by step tutorial including several examples of orthogonal complements for reference.
Overview
The orthogonal complement of a subspace of an inner product space is the set of all vectors in the inner product space that are orthogonal to every vector in the subspace. This can be expressed mathematically in the formula 
, where W is the subspace and V is the inner product space. The orthogonal complement is sometimes also called the perpendicular complement, shortened to the informal form perp.
Tags: algebra, complement, formula, inner, orthogonal, perp, perpendicular, product, set, space, subspace, v, vector, W
Posted in Algebra | No Comments »
Thursday, November 5th, 2009
Introduction to Projections
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Description
A detailed tutorial on projections. Step by step tutorial including several examples of what a projection is for reference.
Overview
A projection is another term for a transformation. But a projection is a different kind of transformation than a real transformation is. A projection is a transformation of points and lines from one plane to another plane. This is done by connecting corresponding points on the planes with parallel lines. Typically projections are used with vectors, which are entirely composed of points and lines.
Tags: corresponding, dot, infinity, lines, parallel, plane, point, product, projection, transformation, vector
Posted in Algebra | 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, November 3rd, 2009
Rule of Sarrus Explained
Description
A detailed tutorial on the Rule of Sarrus. Step by step tutorial including several examples of the Rule of Sarrus and determinants for reference.
Overview
The Rule of Sarrus is a method used to compute the determinant of a 3×3 matrix. Mathematically stated, if you are given a 3×3 matrix, you can compute the determinant by repeating the first two columns of the matrix behind the third column, so that you have 5 columns in a row. This forms a 3×5 matrix. Then you add the products of the diagonals going from top to bottom (left to right), and subtract the products going from bottom to top (left to right). This can also be used for 2×2 matrices, but the rule used is a little different.
Tags: 2x2, 3x3, 3x5, add, algebra, bottom, column, determinant, diagonal, left, matrices, matrix, product, right, row, rule, sarrus, scheme, subtract, top
Posted in Algebra | No Comments »
Friday, October 30th, 2009
Overview of Summation by Parts
Description
A detailed tutorial on summation by parts. Step by step tutorial including several examples of summation by parts for reference.
Overview
Summation by parts transforms the summation of products of sequences into other summations. Often it will simplify the computation of certain sums. Summation by parts is also referred to as Abel’s lemma or Abel’s transformation. Summation by parts is similar to integration by parts, only by using summation instead of integration. In mathematical notation, summation by parts can be written as: ![\sum_{k=m}^n f_k(g_{k+1}-g_k) = \left[f_{n+1}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1}- f_k)](http://s.wordpress.com/latex.php?latex=%5Csum_%7Bk%3Dm%7D%5En%20f_k%28g_%7Bk%2B1%7D-g_k%29%20%3D%20%5Cleft%5Bf_%7Bn%2B1%7Dg_%7Bn%2B1%7D%20-%20f_m%20g_m%5Cright%5D%20-%20%5Csum_%7Bk%3Dm%7D%5En%20g_%7Bk%2B1%7D%28f_%7Bk%2B1%7D-%20f_k%29&bg=ffffff&fg=000000&s=0 "\sum_{k=m}^n f_k(g_{k+1}-g_k) = \left[f_{n+1}g_{n+1} - f_m g_m\right] - \sum_{k=m}^n g_{k+1}(f_{k+1}- f_k)")
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Tags: Abel, algebra, computation, integration, lemma, mathematical, parts, product, sequence, sum, summation, transformation
Posted in Algebra | No Comments »
Friday, October 30th, 2009
How to Find Higher Order Derivatives
Description
A detailed tutorial on higher order derivatives. Step by step tutorial including several examples of higher order derivatives for reference.
Overview
A higher order derivative is a derivative with a power other than one – that is, a derivative is referred to as a first derivative, and the higher order derivatives are a second derivative, third derivative, etc. The second derivative is the derivative of the first derivative, and the third derivative is the derivative of the second derivative. When you know all the rules of taking derivatives, taking second and third derivatives are simple. Simply take the derivative and pretend it is another equation. When you go up beyond the third derivative this can get more challenging, as there will be many more parts to the equation.
Tags: antiderivative, Calculus, chain, derivative, First, higher, integral, order, power, product, quotient, rule, second, third
Posted in Calculus | No Comments »
