Posts Tagged ‘sum’
Tuesday, November 24th, 2009
How to Find the Absolute Value of a Complex Number
Description
A detailed tutorial on the absolute value of a complex number. Step by step tutorial including several examples on the absolute value of a complex number for reference.
Overview
The absolute value of a complex number is a little different than the absolute value of a real number, because complex numbers deal with imaginary numbers. However, the answer is still a non-negative real number, just like the numbers you deal with in other math classes every day. Say that a complex number z is equal to a + bi, where i is an imaginary number. The |z| is equal to the square root of a^2 plus b^2. In other words, square both a and b, add them together, and find the square root in order to have to absolute value of a complex number z.
Tags: a, absolute, add, addition, b, complex, imaginary, number, real, root, square, squareroot, sum, trigonometry, z
Posted in Trigonometry | No Comments »
Thursday, November 12th, 2009
Zero Pairs Explained
Description
A detailed tutorial on zero pairs. Step by step tutorial including several examples of how to solve equations using zero pairs for reference.
Overview
Zero pairs are a method of adding and subtracting integers, and simplifying expressions with addition and subtraction in them. A zero pair is any pair of numbers that when added or subtracted, equal zero. Based on this definition, the only numbers that can form a zero pair, besides two zeros, are a negative number n and a positive number n. When in equations, zero pairs can be cancelled out, therefore simplifying the expression. This is very useful when more complicated equations are given.
Tags: adding, arithmetic, cancelled, difference, equation, expression, integer, negative, number, pair, positive, simplification, simply, subtracting, sum, zero
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
An Overview of Magic Squares
Description
A detailed tutorial of magic squares. Step by step tutorial including several examples of magic squares for reference.
Overview
Magic squares are a fun mathematical trick and puzzle. It is an arrangement such as 3×3, 4×4, or any other nxn pattern of numbers. Typically a magic square will contain any of the integers between 1 and n^2. Magic squares are set up so that all rows and columns, and both diagonals, add up to the same constant. It does not matter what constant it is, as long as all rows, columns, and diagonals add up to the same one.
Tags: arithmetic, column, constant, diagonal, integer, magic, n!, normal, number, perfect, real, row, square, sum, word
Posted in Arithmetic | No Comments »
Thursday, November 12th, 2009
How to Identify Perfect Numbers
Description
A detailed tutorial on how to identify perfect numbers. Step by step tutorial including several examples of perfect numbers for reference.
Overview
A perfect number is a number that is the sum of all it’s divisors (excluding the number itself, which is also a proper divisor). The way that you identify a perfect number is to find all of its divisors. Once you have them all, add them together. If they equal the number, then it is a perfect number. If they don’t, then it is not a perfect number.
Tags: add, addition, arithmetic, division, divisor, excluding, identify, integer, natural, number, perfect, proper, real, sum
Posted in Arithmetic | No Comments »
Tuesday, November 3rd, 2009
How to Find the Trace
Description
A detailed tutorial on find the trace of a matrix. Step by step tutorial including several examples of how to find the trace for reference.
Overview
The trace of a square matrix is defined to be the sum of the elements on the main diagonal of the matrix. This can be mathematically expressed as:
Remember, the trace is only defined for square matrices – not any other kind of matrix.
Tags: algebra, diagonal, eigenvalue, element, invariant, linear, main, matrices, matrix, Spur, square, sum, trace
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 »
Thursday, October 1st, 2009
Introduction to the Parallelogram Law
Description
A detailed tutorial of the parallelogram law. Step by step tutorial including several examples of the parallelogram law for reference.
Overview
The parallelogram law shows up in many forms, but the simplest form states that the sum of the squares of the lengths of the four sides of a parallelogram equals the sum of the squares of the lengths of the two diagonals. Assuming that a rectangle has four corners A, B, C, and D, this can be expressed as:
Typically, the two diagonals of a parallelogram are not equal in length. If they are, then the equation simplifies to the Pythagorean theorem. A more complicated version of the parallelogram law is often found when calculating vectors.
Tags: diagonals, Geometry, law, length, Math, parallelogram, pythagorean theorem, rule, side, square, sum
Posted in Geometry | No Comments »
Friday, September 25th, 2009
Using the Midpoint Rule to Solve Error Bounds
Description
A detailed tutorial on using the midpoint rule and solving error bounds. Step by step tutorial including examples of solving error bounds using the midpoint rule for reference.
Overview
The midpoint rule, also known as the rectangle method, is the easiest way of solving error bounds. The region under the graph of a function is sectioned off into rectangles of equal width. You then must find the areas of these rectangles. Then all the areas are added together to find the approximation of the integral. The formula for this is:
The least complicated form of the midpoint rule is expressed as:
Tags: addition, approximation, area, Calculus, definite integral, error bounds, formula, function, graph, Math, mid-ordinate rule, midpoint rule, rectangle, rectangle method, sum, width
Posted in Calculus | 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 »
