Sum | Homework Help

Posts Tagged ‘sum’

Fourier Series

Thursday, September 24th, 2009

Introduction to the Fourier Series

Description

A detailed tutorial on the solving of Fourier series. Step by step tutorial including several examples of how to solve the Fourier series for reference.

Overview

The Fourier series is very common in differential equations and partial differential equations. What a Fourier series does is decompose a periodic function into the sum of simple oscillating functions, like sine and cosine. Fourier series are part of Fourier analysis and were first introduced by Joseph Fourier to solve the heat equation. So another name for the Fourier series is the heat equation, although they are considered different things. Both the heat equation and the Fourier series are partial differential equations.

Tags: cosine, decompose, differential equations, Fourier analysis, Fourier series, function, functions, heat equation, Joseph Fourier, Math, oscillating, partial differential equations, periodic function, simple, sine, sum
Posted in Differential Equations | No Comments »

The Fibonacci Numbers

Thursday, September 24th, 2009

Overview of the Fibonacci Numbers

Description

A detailed tutorial on the overview of the Fibonacci numbers. Step by step tutorial including several visual representations of the Fibonacci numbers for reference.

Overview

The Fibonacci numbers, also known as the Fibonacci sequence, is one of the most amazing sets of numbers in the world. The set begins with the two numbers 0 and 1 traditionally, although it is also commonly seen starting with 1 and 1 or 1 and 2, and could potentially start anywhere. The Fibonacci numbers follow this pattern:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89…

This sequence or pattern is that the next number is always the sum of the two number before it. That’s why it start with two numbers…you add them to get the next number, and add that number to the one before it to get the next number, etc. Sometimes this is referred to as a recurrence relation. To mathematically express the pattern, you can write it as:

$F_n = F_{n-1} + F_{n-2},\!\,$

There is also something called a Fibonacci spiral, which is in the shape of a snail shell. The Fibonacci spiral was found by tracing curves to the corners of the Fibonacci tiles, which have squares whose lengths are successive Fibonacci numbers.

Tags: algebra, Fibonacci, Fibonacci numbers, Fibonacci spiral, Fibonacci tiles, filius Bonaccio, Leonardo of Pisa, Liber Abaci, Math, recurrence relation, sequence, sum
Posted in Algebra | No Comments »

Superposition Principle

Tuesday, September 22nd, 2009

Superposition Principle Explained

Description

A detailed tutorial on the solving of the Superposition Principle. Step by step tutorial including several examples of how to solve the Superposition Principle for reference.

Overview

The Superposition Principle, or the Superposition Property (also know mathematically as additivity) states that the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. Mathematically, this is saying that for all linear systems F(x) = y, where x is some sort of stimulus or input and y is some sort of response or output, the superposition or sum of the stimuli yields a superposition of the respective reponses:

$F(x_1+x_2+\cdots)=F(x_1)+F(x_2)+\cdots$

Tags: additivity, input, linear systems, net response, output, Physics, responses, Science, stimuli, stimulus, sum, superposition, superposition principle, superposition property
Posted in Differential Equations | No Comments »

Adding Decimals

Tuesday, September 15th, 2009

How to Add Decimals

Description

A detailed tutorial on how to add decimals. Step by step tutorial including several examples of adding decimals for reference. It is a requirement to know how to add decimals for all math classes.

Overview

Decimals are really no different from regular numbers when you perform operations on them, but sometimes the numbers in the decimal places can be tricky to figure out. The operation we will be talking about is addition. The most important thing to remember when doing anything with decimals is to match up the decimal points and add zeros on the end if you need to. Then just add like you normally would, and remember to put your decimal point back in the right place.

Tags: add, addition, arithmetic, decimal points, decimals, Math, operations, point, sum
Posted in Arithmetic | No Comments »

The Closure Property

Tuesday, September 15th, 2009

An In-Depth Look at the Closure Property

Description

A detailed tutorial on how to use the closure property. Step by step tutorial including several examples of how to use the closure property for reference.

Overview

The closure property states that if a and b are both real numbers, then a + b is a unique real number, and a * b is also a unique real number. Basically what the closure property is saying is that if you add or multiply two real numbers, your only possible answer is a real number. The closure property is also saying that the sum or product of two real numbers is unique, meaning there is only one number that it could be.

Tags: add, addition, arithmetic, closure, closure property, Math, multiplication, multiply, product, property, real numbers, sum, unique
Posted in Arithmetic | No Comments »