Thursday, November 19th, 2009
Overview of Computation Methods
Description
A detailed tutorial on the four basic computation methods. Step by step tutorial including several examples of the four basic computation methods for reference.
Overview
Computation methods are the way you solve expressions and equations. The four basic ones are addition, subtraction, multiplication, and division. Addition and subtraction are inverses of each other, and multiplication and division are inverses of each other. All of them are extensions of counting and can easily be solved without too much effort.
Tags: add, addition, arithmetic, basic, computate, computation, counting, divide, division, method, multiplication, multiply, subtract, subtraction
Posted in Arithmetic | 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 »
