Posts Tagged ‘domain’
Thursday, November 19th, 2009
Overview of the Cost Function
Description
A detailed tutorial on the cost function. Step by step tutorial including several examples of the cost function for reference.
Overview
The cost function is a name for a function that is being used in optimization. It is a very important part of an optimization problem. The cost function can be any graph, because all it refers to is the function – the function could be different every time, and it could still be called the cost function. What we learn from this is that the cost function is not unique.
Tags: algebra, constraints, cost, domain, energy, function, functional, graph, linear, maximize, minimize, objective, optimization, solution, unique, variable
Posted in Algebra | No Comments »
Tuesday, October 27th, 2009
The Domain of Relations
Description
A detailed tutorial on the domain of relations. Step by step tutorial including several examples of the domain of relations for reference.
Overview
The domain of a relation is denoted as Dom(R) and looks like a normal set. For each ordered pair in a relation, there are two endpoints, x and y. The domain is the set of all x endpoints – that is to say, all the endpoints that come first in the ordered pair. If you are taking the domain of the inverse of a relation, then that would be all the y endpoints. When writing the domain, the notation used is just the normal notation, not the ordered pair notation.
Tags: cartesian, coordinates, discrete math, domain, element, endpoint, First, ordered pair, relations, set, subset
Posted in Discrete Math | No Comments »
Tuesday, October 6th, 2009
Fourier Transforms Explained
Description
A detailed tutorial on Fourier transforms. Step by step tutorial including several examples of Fourier transforms for reference.
Overview
A Fourier transform is an operation that transforms one complex-valued function of a real variable into another. The domain of the original function is typically referred to as the time domain, because it is a representation of time. The domain of the new function represetns frequency. The Fourier transform itself is often called the frequency domain representation of the original function because of this.
Tags: complex, differential equations, domain, Fourier, frequency, function, Math, Physics, real, Science, time, tranform, value, variable
Posted in Differential Equations | No Comments »
Friday, September 25th, 2009
How to Find the Domain & Range of a Function
Description
A detailed tutorial on finding the domain and range of a function. Step by step tutorial including several examples of how to find the domain and range of a function for reference.
Overview
Finding the domain and range is very important when given the graph of a function. The domain is the set of all possible x values of the function, and the range is the set of all possible y values of the function. When given a function, the first one you want to find is the domain. You want to figure out what is allowed for the x value. Typically, the domain ends up being the set of all real numbers, expressed a R. If the x is found in a fraction, it can be the set of all real numbers excluding 0. If the x is found in a square root, it is the set of all real positive numbers. It’s rare for there to only be a few values allowed for the domain. The next one you want to find is range. Very often, range also ends up being the set of all real numbers. But say you know that something has to come out negative, then it would only be the set of all negative numbers. Each function is a little bit different, but finding the domain and range is typically a very straightforward process.
Tags: algebra, domain, fraction, function, graph, Math, negative, positive, possible, range, real numbers, set, square root, values, x, y
Posted in Algebra | No Comments »
Thursday, September 24th, 2009
Intermediate Value Theorem Explained
Description
A detailed tutorial of the intermediate value theorem. Step by step tutorial including an explanation of the intermediate value theorem for reference. Knowledge of the intermediate value theorem is required in calculus.
Overview
The intermediate value theorem states that for each value between the upper bound and the greatest lower bound of the graph of a continuous function that there is a corresponding value in its domain. In mathematical terms, the intermediate value theorem states that if f is a continuous function on the closed interval [a, b] and M is a number between f(a) and f(b), then there exists at least one number c that f(c) = M. When writing proofs in calculus, you can say that something has been proven by the IVT if you used the intermediate value theorem to reach your conclusion.
Tags: a, b, c, Calculus, continuous, corresponding, domain, f(a), f(b), f(c), function, graph, greatest lower bound, intermediate value theorem, IVT, m, Math, upper bound, value
Posted in Calculus | No Comments »
