Posts Tagged ‘real’
Friday, October 23rd, 2009
How to Solve Vectors Using Scalar Multiplication
Description
A detailed tutorial on how to solve vectors using scalar multiplication. Step by step tutorial including several examples on scalar multiplication for reference.
Overview
Scalar multiplication is when you multiply, or re-scale, vectors by a real number. These real numbers are referred to as scalars, so that they can be distinguished from vectors. So, scalar multiplication is when you multiply a vector by a scalar. When you multiply a scalar and a vector, you will get another vector. Your resulting vector will be:
When a vector is multiplied by a scalar, the vector is getting stretched out by a factor of the scalar. If the scalar is negative, then the vector changes direction. A property of scalar multiplication is that it is distributive.
Tags: algebra, direction, distributive, flippied, multiplication, multiply, negatve, number, property, real, rescale, scalar, stretched, vector
Posted in Algebra | No Comments »
Friday, October 23rd, 2009
The Notation of Basic Number Sets
Description
A detailed tutorial on basic number sets. Step by step tutorial including several examples of the notation of basic number sets for reference.
Overview
There are four basic number sets – N, Z, Q, R. N belongs to Z, and Z and Q belongs to R. This means N also belongs to R. N is the set of all natural numbers. Z is the set of all integers. Q is the set of all rational numbers. R is the set of all real numbers. All the notations of these sets were picked because they relate to certain words. N and R were chosen because they stand for natural and real – which is what the sets are. Q means quotient, because rational numbers are a quotient of any integer provided the denominator is not 0. Z was picked because it stands for zahlen – a German word meaning numbers, and Z is indeed a set of (almost) all numbers.
Tags: all, arithmetic, integer, n!, natural, notation, number, Q, quotient, r, rational, real, set, z, zahlen
Posted in Arithmetic | 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 Expand Binomials
Description
A detailed tutorial on the solving of problems using the binomial theorem. Stepby step tutorial including several examples of how to solve problems using the binomial theorem for reference.
Overview
The binomial theorem is something you should all be familiar with – it is the alternative to the F.O.I.L. technique. It is used when you are given a binomial that is raised to a power. The simplest version of it is expressed like this:
This can also be expressed as a factorial notation, in the form:
Tags: algebra, binomial, binomial theorem, coefficient, complex, exponent, F.O.I.L., factorial, FOIL, integer, Math, power, real, sum
Posted in Algebra | No Comments »
Thursday, September 24th, 2009
The History of the Number Zero
Description
A detailed tutorial on the history of the number zero. Step by step tutorial including several citations of the history of the number zero for reference.
Overview
Zero is a number we’ve heard about a lot. It’s not a counting number, it’s not negative or positive, it’s not even or odd. It’s not a prime number, it doesn’t even really fit the definitions of a real number or a whole number although it is considered to be both. It is certainly one of the most interesting numbers you can work with. In writing, 0 is distinguished from the capital letter O by either being a bit smaller or having a bit more of an oval shape. Often when handwriting as opposed to typing a line will be drawn through the zero, although this can be confused with an empty set if you are learning set theory. The name zero came from several different lanuages, in which words similar to zero translated to “is empty” “nothing”, and “void”. When doing calculations you must be sure to know the difference between 0 and NaN – “not a number”. Often things that look like they should be zero (0 / 0, for example) are really not numbers at all.
Tags: 0, arithmetic, empty, even, Math, NaN, negative, nil, not a number, nothing, nought, null, number, odd, oh, positive, prime, real, void, whole, zero
Posted in Arithmetic | No Comments »
Tuesday, September 22nd, 2009
Definition of a Prime Number
Description
A detailed tutorial on the solving of prime numbers. Step by step tutorial including several examples of what a prime number is and the definition of a prime number for reference.
Overview
A prime number is a type of number you will hear a lot about. It is any number greater than 1 that is not divisible by anything other than itself and one. This also tells us that it must be a positive number – there are no negative numbers that are greater than 1. Also, except for one prime number, only odd numbers can be prime numbers. This is because all even numbers are divisible by 2. So the only even prime number is 2, which is only divisible by itself and 1. Examples of prime numbers are 2, 3, 5, 7, 11, and 13. You can easily check to see if a larger number is a prime number by using algebra tricks for divisibility. Remember that it must divide evenly – if you get a known fraction or decimal then it is considered to not be divisible by that number.
Tags: decimal, divisibility, even, fraction, greater than 1, Math, non-divisible, number, odd, positive, prime, prime numbers, real, whole
Posted in Arithmetic | No Comments »
Tuesday, September 22nd, 2009
How to Solve De Moivre’s Theorem
Description
A detailed tutorial on the solving of De Moivre’s Theorem. Step by step tutorial including several examples of how to solve De Moivre’s Theorem for reference.
Overview
De Moivre’s Theorem was named after Abraham de Moivre. It states that any complex number (or any real number) x and any integer n that 
This is called De Moivre’s Formula. This formula is important because it connects complex numbers with trigonometry.
Tags: Abraham de Moivre, complex, de moivre's formula, de moivre's theorem, differential equations, euler's formula, imaginary, induction, Math, numbers, real, trigonometry
Posted in Differential Equations | No Comments »
Friday, September 18th, 2009
Introduction to Irrational Numbers
Description
A detailed tutorial on the definition of an irrational number. Step by step tutorial including several examples of irrational numbers for reference.
Overview
An irrational number is a number that cannot be written as the ratio of 2 integers. However, this does not mean they have no place on a number line. One of the most famous irrational numbers is pi, which is approximately equal to 3.14 – however, this is just a simplified version of the actual number. Another famous irrational number is the square root of 2. This is equal to around 1.41. Both irrational numbers and rational numbers are real numbers, which include all integers.
Tags: arithmetic, imaginary, integers, irrational, Math, natural, number, numbers, pi, ratio, rational, real, sqrt(2), square root
Posted in Arithmetic | No Comments »
Friday, September 11th, 2009
An Introduction to Imaginary Numbers
Description
A detailed tutorial on imaginary numbers. Step by step tutorial including several examples of how to solve problems using imaginary numbers for reference.
Overview
An imaginary number is a number that is considered to not be real – for instance, the square root of a negative number. You could never take a square root of a negative number – until you met i. i stands for “imaginary”, and it is the square root of negative one. Many previously impossible problems can now be solved by pulling out i from the equation.
Tags: -1, algebra, i, imaginary, imaginary number, Math, negative, real, real number, sqrt(-1), square root
Posted in Math | No Comments »
