Posts Tagged ‘equations’
Thursday, November 19th, 2009
Overview of the Additive Identity
Description
A detailed tutorial on how to solve equations using the additive inverse. Step by step tutorial including several examples of how to solve equations with the additive inverse for reference.
Overview
The additive inverse is the inverse of the additive identity – which should be very easy to guess. However, the problem is not guessing the definition of the additive inverse – the problem is knowing what the inverse of the additive identity is. The additive identity states that any number plus zero equals itself. The additive inverse states that any positive number minus its true value or any negative number plus its true value is equal to zero – in other words, that two inverses together equal zero. You solve equations by using the additive inverse.
Tags: add, additive, arithmetic, basic, divide, equations, identity, inverse, itself, multiply, nothing, plus, property, same, subtract, zero
Posted in Arithmetic | No Comments »
Tuesday, November 17th, 2009
Overview of Green’s Function
Description
A detailed tutorial on Green’s function. Step by step tutorial including several examples of Green’s function for reference.
Overview
Green’s function is used in deifferential equations as a method of solving certain types of equations that are subject to boundary conditions. There equations are called inhomogeneous differential equations. Unlike many other functions, Green’s function is not studied by how to use it to solve equations, but it is studied by the fundamental solutions.
Tags: boundary, conditions, differential, differential equations, equations, function, fundamental, George Green, Green's function, inhomogeneous, solutions
Posted in Differential Equations | No Comments »
Tuesday, November 10th, 2009
The Numerator and Denominator of a Fraction
Description
A detailed tutorial on the numerator and denominator of a fraction. Step by step tutorial including several examples of numerators and denominators for reference.
Overview
Fractions are well known in the world of mathematics. But when first starting out, you may ask yourself why the fraction appears like it does – split into two parts. You will see a fraction either written horizontal or vertical. In a horizontal fraction, the numerator is the number to the left, and the denominator is the number to the right. In the more common and proper vertical fraction, the numerator is on the top and the denominator is on the bottom. This works when there are whole equations in either the numerator and denominator as well, not just for simpler numbers. The numerator and the denominator should never be split, but algebra tricks can sometimes help to simplify them.
Tags: algebra, arithmetic, bar, denominator, equations, fraction, horizontal, number, numerator, parts, simplify, split, tricks, two, vertical
Posted in Arithmetic | No Comments »
Tuesday, November 10th, 2009
An Overview of Pi
Description
A detailed tutorial on what pi is. Step by step tutorial including several examples of what pi is for reference.
Overview
Pi is a special number in mathematics. It is the ratio of a circle’s circumference to its diameter. No matter what size circle you use, your answer will always be pi, showing that all circles are proportional to one another. Pi is denoted by the Greek letter pi, which looks a little bit like an “n”. The numerical value of pi is 3.1415926535… but is typically shortened to the simple 3.14. Pi is very important in math and is used in all equations dealing with circles.
Tags: 3.14, arithmetic, circle, circumference, denoted, diameter, equations, Greek, letter, pi, propertional, radius, ration, size, value
Posted in Arithmetic | No Comments »
Friday, October 16th, 2009
Overview of the Conjugate Zeros Theorem
Description
A detailed tutorial on the conjugate zeros theorem. Step by step tutorial including several examples of the conjugate zeros theorem for reference.
Overview
The conjugate zeros theorem states that if a + b * i is a zero of a polynomial with real coefficients, then so is a – b * i. The conjugate zeros theorem can be proved by taking any function in this form and setting it equal to zero. The conjugate zeros theorem makes many equations easier to solve, especially complex equations when you get to higher levels of math.
Tags: a, b, Calculus, complex, conjugate, equations, function, i, imaginary, Math, number, theorem, zero, zeros
Posted in Calculus | No Comments »
Thursday, October 15th, 2009
Introduction to the Inverse Matrix
Description
A detailed tutorial on the inverse matrix and how to calculate the inverse matrix. Step by step tutorial including several examples of the inverse matrix for reference.
Overview
All square matrices have an inverse, except for the rare invertible matrices, called singular matrices. The inverse of a square matrix can be defined in mathematical terms as the matrix times the inverse of the matrix is equal to I, which represents the identity matrix. The inverse of a matrix may be found by using the inverse function. This makes the inverse easy to find, as you follow basic rules for finding the inverse of other types of equations.
Tags: algebra, equations, function, identity, inverse, invert, invertible, Math, matrices, matrix, rules, singular, square
Posted in Algebra | No Comments »
Tuesday, September 15th, 2009
How to solve polynomials
Description
A detailed tutorial on the solving of Polynomial. Step by step tutorial including several examples of how to solve Polynomial for reference.
Overview
In mathematics, a polynomial is a finite length expression constructed from variables (also known as indeterminates) and constants, by using the operations of addition, subtraction, multiplication, and constant non-negative whole number exponents. For example, x2 − 4x + 7 is a polynomial, but x2 − 4/x + 7x3/2 is not, because its second term incorporates division and because its third term contains a fractional index.
Tags: algebra, algebraic geometry, Calculus, economics, equations, Math, mathematics, Polynomials, word problems
Posted in Algebra, Calculus, Chemistry, Physics | No Comments »
Friday, September 11th, 2009
How to Solve Systems of Equations by Elimination
Description
A detailed tutorial on how to solve systems of equations by elimination. Step by step tutorial including several examples of how to solve systems of equations by elimination for reference.
Overview
There are two different ways to solve systems of equations – substitution and elimination. We will focus on elimination. Elimination is when you want to add or subtract the equations from each other, and eliminate one of the variables that way. If one of the variables is already opposite (Example: -2x on the first equation and 2x on the second) then all we have to do is solve. It is more common for there to not be an opposite, and then we must create one by using multiplication on both the first and second equation. Once you add or subtract your equations, you should find that one variable has cancelled out, leaving you free to solve for the numerical value of the other one. Once you have this numerical value, plug it in for that variable in any of your original equations to find the value of the other variable.
Tags: algebra, elimination, equations, Math, solve, systems of equations, variables
Posted in Algebra | No Comments »
Friday, September 11th, 2009
How to Solve Systems of Equations by Substitution
Description
A detailed tutorial on how to solve systems of equations using substitution. Step by step tutorial including several examples of how to solve systems of equations using substitution for reference.
Overview
There are two different ways to solve systems of equations – substitution and elimination. We will focus on substitution. Substitution is when you take one equation in you system of equations,and solve for one of the variables. You then plug the solution in for your variable in the other equation, and solve for the value of the remaining variable. You can then take the number only solution and insert it into your solution for the first variable you solved for. It is very easy to come up with no solution when using the substitution formula, because it relies very heavily on your algebra skills, and even the best mathematicians miss things sometimes. But as long as you pay attention to detail you shouldn’t have any problem using this method of solving for systems of equations.
Tags: algebra, equations, Math, solve, substitution, systems of equations, variables
Posted in Algebra | No Comments »
Tuesday, September 8th, 2009
How to Add and Subtract Matrices
Description
This video explains the different types and sizes of matrices and what makes up each of them. It explains how to match up the sizes so you know if addition is possible. Several sample problems for addition are provided in the video.
Overview
While with normal numbers, you can add anything, some sets of matrices cannot be added. Matrices can only be added when they are the same size. Sizes of matrices are recorded by the numbers that are in each row and colum. For instance, a matrix with 3 rows and 3 columns would be referred to as a 3×3 matrix. If your matrices are the same size, you can add them. You then simply match up the numbers in your matrices to add them. This means that the number in the top right corner of the first matrix is added to the number in the top right corner of the second matrix, and the number they add up to will go in the same place in the matrix that is the solution to the problem. Subtraction works the exact same way as addition.
Tags: addition, algebra, equation, equations, linear algebra, Math, matrices, matrix, set
Posted in Algebra | No Comments »
