Posts Tagged ‘solution’
Thursday, November 19th, 2009
Overview of Vector Transformations
Description
A detailed tutorial of vector transformations. Step by step tutorial including several examples of vector transformations for reference.
Overview
Vector transformations are not as difficult as one mught think – they are done just like ordinary transformations, except in terms of vectors. Rotation is one of the main types of vector transformations, and is the most common one that is done. In order for a vector to be properly transformed, they must satisfy the orthogonality condition.
Tags: algebra, angle, common, condition, cosine, degrees, linear, orthogonality, properly, ray, rotation, solution, tranformations, vector
Posted in Algebra | No Comments »
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 »
Friday, November 13th, 2009
How to Check Your Work
Description
A detailed tutorial on how to check your work. Step by step tutorial including several examples of how to check your work for reference.
Overview
Checking your work is the process of inserting the value you solved for back into the original problem, to confirm that you came up with the correct solution. This process is quite commonly used with word problems, which nearly always have you solving for an unknown variable that would be a very important part of the original equation.
Tags: arithmetic, check, equation, guesstimation, original, problem, process, solution, unknown, value, variable, word, work
Posted in Arithmetic | No Comments »
Tuesday, October 6th, 2009
Definition of a Uniqueness Theorem
Description
A detailed tutorial on the uniqeness theorem. Step by step tutorial including several examples of how to solve a uniqueness theorem for reference.
Overview
A uniqueness theorem is any mathematical theorem that states only one mathematical object satisifies special conditions – that is, that a problem only has one solution, a unique solution. Sometimes the solution to the equation is also determined uniquely – that is, there is only way to solve the problem, instead of multiple ways.
Tags: arithmetic, condition, existence, Math, solution, solve, theorem, unique, uniqueness
Posted in Arithmetic | No Comments »
Tuesday, October 6th, 2009
How to Solve a Dirichlet Problem
Description
A detailed tutorial of solving Dirichlet problems. Step by step tutorial including several examples of how to solve Dirichlet problems for reference.
Overview
A Dirichlet problem is a problem of finding a function which solves a specified partial differential equation in the interior of a given region that takes prescribed values on the boundary of the region. It was originally supposed to be used for Laplace’s equation, although other equations can use it as well. The Dirichlet problem can be stated as: given a function f that has values everywhere on the boundary of a region in R^n, is there a unique continuous function u twice continuously differentiable in the interior and continuous on the boundary, such that u is harmonic in the interior and u = f on the boundary? A mathematical solution can be expressed as:
Tags: bounded, continuous, differential equations, Dirichlet, equation, harmonic, interior, Laplace, Math, partial differential equation, problem, region, solution, value
Posted in Differential Equations | No Comments »
Tuesday, October 6th, 2009
Definition of a Cornu Spiral
Description
A detailed tutorial on Cornu spirals. Step by step tutorial including a visual example of a Cornu spiral for reference.
Overview
The Cornu spiral is also known as a Euler spiral and clothoid. It is generated as a straight line that branches out, and then turns up on one end and down on the other, both spiraling into tight curls. It is formed by a parametric plot of S(t) against C(t). They are very closely linking to Fresnal integrals and have been sometimes thought of as a solution.
Tags: Calculus, clothoid, Cornu spiral, curl, curve, differential equations, Euler spiral, Fresnal integral, Geometry, line, Math, parametric, plot, solution, spiral
Posted in Differential Equations | No Comments »
Friday, October 2nd, 2009
Introduction to the Ambiguous Case
Description
A detailed tutorial on the ambiguous case. Step by step tutorial including several example problems of the ambiguous case for reference.
Overview
An ambiguous case is actually any case in mathematics that is open to more than one interpretation, or has more than one solution. There are many different examples of an ambiguous case. However, what most people refer to as the ambiguous case is the Law of Sines. The Law of Sines can use many different techniques to be solved, and those techniques can also be used to figure out if two triangles are congruent.
Tags: AAS, ambiguous, ASA, case, congruent, interpretation, law of sines, Math, SAS, solution, SSS, triangle, trigonometry
Posted in Trigonometry | No Comments »
