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Arduino

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Fig: Arduino


Arduino is an open source electronics platform based on easy-to-use hardware and software. An Arduino board is a tiny computer that has processing capabilities, RAM, memory and input-output pins. Arduino boards are able to read inputs - light on a sensor, a finger on a button, or a Twitter message - and turn it into an output - activating a motor, turning on an LED, publishing something online. You can tell your board what to do by sending a set of instructions to the microcontroller on the board. To do so you use the Arduino programming language (based on Wiring), and the Arduino Software (IDE), based on Processing.
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Octave

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What is Octave?

Octave

Octave is a Free Scientific Programming Language. Powerful mathematics-oriented syntax with built-in plotting and visualization tools. The Octave Syntax is largely compatible with Matlab. The Octave interpreter can be run in GUI mode, as a console, or invoked as part of a shell script.

Mesh created in Octave

Partial Fractions

IntroductionWe are familiar with combining two or more fractions into a single fraction by taking LCM of the denominator and so on and so forth. Sometimes it will be more convenient to express a single fraction in terms of sum of two or more fractions. The process of expressing a single proper fraction as the sum of two or more proper fractions is known as resolving into partial fractions.

Applications of partial fractionsSome integrals become easy to evaluate by splitting the terms in the integrand by using partial fractions.In some particular type of series, it is possible to split some terms into two or more terms by using partial fractions
Definitions
PolynomialAn algebraic expression of the form:
\[f(x) = A_0x^n + A_1x^{(n−1)} + A_2x^{(n−2)} + · · · + A_n\]
is called a polynomial in \(x\). Here \(A_0\), \(A_1\), \(A_2\), · · · , \(A_n\) are real constants and \(x\) is an unknown.

Degree of the PolynomialThe highest power of \(x\) that exists in the expression above is called the degr…