Thursday, 5 December 2013

Some Important Portals & their
Founders -
1. Google— Larry Page & Sergey Brin
2. Facebook— Mark Zuckerberg
3. Yahoo— David Filo & Jerry Yang
4. Twitter— Jack Dorsey & Dick
Costolo
5. Internet— Tim Berners Lee
6. Linkdin— Reid Hoffman, Allen
Blue& Koonstantin Guericke
7. Email— Shiva Ayyadurai
8. Gtalk— Richard Wah kan
9. Whats up— Laurel Kirtz
10. Hotmail— Sabeer Bhatia
11. Orkut— Buyukkokten
12. Wikipedia— Jimmy Wales
13. You tube— Steve Chen, Chad
Hurley & JawedKarim
14. Rediffmail— Ajit Balakrishnan
15. Nimbuzz— Martin Smink & Evert
Jaap Lugt
16. Myspace— Chris Dewolfe & Tom
Anderson
17. Ibibo— Ashish Kashyap
18. OLX— Alec Oxenford & Fabrice
Grinda
19. Skype— Niklas Zennstrom,Janus
Friis & Reid Hoffman
20. Opera— Jon Stephenson von
Tetzchner & Geir lvarsoy
21. PagalWorld - Sanjay
22. Mozilla Firefox— Dave Hyatt &
Blake Ross
23. Blogger— Evan Willam Belli

C++ Program to create a loading flash

‪#‎include<iostream>
#include<unistd.h>

using namespace std;

main()
{
int i;
for(i=0;i<=100;i++)
{
cout<<"Loading......."<<i<<"%\r";
usleep(100000);
}

return 0;
}

COMPUTER TRICKS:

Interesting Facts About C Programming
Language ..............
Firstly When C Was Introduced Then There Was Already
Seven Life Cycle Evoked
Following By .............
1 : ALGOL Stands For Algorithm Programming System
Introduced In 1960 And Was The First To Use Block
Structure
Computer Scientist : Bohm , Jacopini And Edsger
2 : BCPL (Basic Combined Programming Language) Was
Introduced In 1967 By Richard
3 : B.B Was Later Used To Create Version Of UNIX At Bell
Lab ........

COMPUTER TRICKS:
Interesting Facts About C Programming

Language .............. Firstly When C Was Introduced Then There Was Already Seven Life Cycle Evoked Following By ............. 1 : ALGOL Stands For Algorithm Programming System Introduced In 1960 And Was The First To Use Block Structure Computer Scientist : Bohm , Jacopini And Edsger 2 : BCPL (Basic Combined Programming Language) Was Introduced In 1967 By Richard 3 : B.B Was Later Used To Create Version Of UNIX At Bell Lab ........

Ruby for Beginners V3

Lesson 1: Introduction

Welcome to the LearnStreet beginner course on Ruby. In this course, you'll learn how to code in Ruby, a flexible yet powerful programming language that’s popular over the web. Some of the most popular websites--like Twitter, Groupon, and Hulu--are built on top of Ruby on Rails (also known as RoR or Rails), a web application framework for the Ruby programming language.

If you'd like to learn more about setting up Ruby on your own PC or Mac, please click here. This step is not required for the course, but it will help you test and practice some concepts as you go along.

This course is designed for people who have no prior programming knowledge, so we'll teach you fundamental programming concepts as we go. Throughout the course, you'll write code to apply what you've learned to solve programming problems. In addition, after you complete the course, you'll code functionality to build a LearnStreet Bank project, which you’ll be able to share with your friends.

Python for Beginners V3

Lesson 1: Introduction to Python

Welcome to the LearnStreet beginner course on Python. The Python programming language is a high level programming language that is used in a wide spectrum of applications -- from web design and game programming to scientific research. Its simple and flexible syntax makes it easy to learn and understand, but still powerful and expressive. By the end of this course, you'll have a solid understanding of the Python language, and be able to complete some cool projects in the Code Garage section. Keep in mind this course uses Python version 2.7. Python 2.7 is more widely used in industry, and therefore more valuable to learn. The most recent version is 3.2, which has some key syntax differences.
We have designed this course for people who have no prior programming background. In this course, we will teach you some fundamental programming concepts through Python. Throughout this course, you will write code to apply what you've learned to solve programming problems.

Now, click on the big black box - the Python interpreter - below this to start coding away!

Beginner JavaScript Course V3

Argument

A variable that represents a value passed into a function or method.

Arithmetic Operator

One of several operators that perform arithmetic between variables or values. They include; +, -, *, /, %, ++, --

Array

An Object that represents a list of elements that are accessed by their position within the list. An Array also has built in properties and methods.

Assignment

Assigning a value to a variable or property.

Assignment Operator

One of several operators that assign a value to a variable. They include; =, +=, -=, *=, /=, %=

Booleans

Syntax

true
false

Example

expression1 && expression2
expression3 || expression4
!expression5

Break

A statement that will cause immediate exit from a loop once it is encountered and normal flow of execution will continue with the statement immediately following the loop.

Case

Used in conjunction with a Switch statement, the "case" statement identifies a value for a conditional test against the switch parameter. When the switch parameter and case value are equal, the code following the case statement is executed.

Code Block

A grouped collection of statements that are meant to be executed together and most often denoted by surrounding curly braces.

Code comments

A comment is generally used within code to explain how something works or to write necessary information about a section. Comments are very useful to make code more readable

Syntax

Single Line Comment
// Comment comment comment

Multi-Line Comment
/*Comment1
  Comment2
  .
  .
  Comment3 */

Comparison Operator

One of several operators that determine the equality of two variables or values. They include; ==, ===, !-, !===, >, >=, <, <=

Conditional Test

A test for true or false, that is; testing for a certain condition.

Constant

A fixed value such as "this is constant" or the number 10.

Construct

An idea or theory construction of operators, keywords and variables.

Continue

When a "continue" statement is encountered in a loop, all remaining statements in the current loop iteration are skipped but looping will continue.

Do...While

A flow control mechanism that can be explained as:

Argument

A variable that represents a value passed into a function or method.

Arithmetic Operator

One of several operators that perform arithmetic between variables or values. They include; +, -, *, /, %, ++, --

Array

An Object that represents a list of elements that are accessed by their position within the list. An Array also has built in properties and methods.

Assignment

Assigning a value to a variable or property.

Assignment Operator

One of several operators that assign a value to a variable. They include; =, +=, -=, *=, /=, %=

Booleans

Syntax

true
false

Example

expression1 && expression2
expression3 || expression4
!expression5

Break

A statement that will cause immediate exit from a loop once it is encountered and normal flow of execution will continue with the statement immediately following the loop.

Case

Code Block

A grouped collection of statements that are meant to be executed together and most often denoted by surrounding curly braces.

Code comments

A comment is generally used within code to explain how something works or to write necessary information about a section. Comments are very useful to make code more readable.

Syntax

Single Line Comment
// Comment comment comment

Multi-Line Comment
/*Comment1
  Comment2
  .
  .
  Comment3 */

Comparison Operator

One of several operators that determine the equality of two variables or values. They include; ==, ===, !-, !===, >, >=, <, <=

Conditional Test

A test for true or false, that is; testing for a certain condition.

Constant

A fixed value such as "this is constant" or the number 10.

Construct

An idea or theory construction of operators, keywords and variables.

Continue

When a "continue" statement is encountered in a loop, all remaining statements in the current loop iteration are skipped but looping will continue.

Do...While

A flow control mechanism that can be explained as:

do {something} 
while(condition is true)

"while", "do..while" and "for" can often accomplish the same loop result.

Element

This is a general reference to variables, objects, arrays and individual objects within objects and arrays.

Execute

Running a software program, single line of code, function a block of code or any unit of software.

Flow Control

The means by which the logic in a software program determines the flow of execution of the code.

For

A loop flow control mechanism that can be explained as:

for (i=n; condition is true; i++) 
   {do something}

"while", "do..while", and "for" can often accomplish the same loop result.

Saturday, 12 October 2013

Partial derivative: CH:5 IN ENGINEERING

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.
The partial derivative of a function f with respect to the variable x is variously denoted by

$f^\prime_x,\ f_x,\ \partial_x f, \text{ or } \frac{\partial f}{\partial x}$

The partial-derivative symbol is ∂. One of the first known uses of the symbol in mathematics is by Marquis de Condorcet from 1770, who used it for partial differences. The modern partial derivative notation is by Adrien-Marie Legendre (1786), though he later abandoned it; Carl Gustav Jacob Jacobi re-introduced the symbol in 1841

Introduction:

Suppose that ƒ is a function of more than one variable. For instance,

$z = f(x,y) = \,\! x^2 + xy + y^2.\,$

The graph of this function defines a surface in Euclidean space. To every point on this surface, there are an infinite number of tangent lines. Partial differentiation is the act of choosing one of these lines and finding its slope. Usually, the lines of most interest are those that are parallel to the xz-plane, and those that are parallel to the yz-plane (which result from holding either y or x constant, respectively.)
To find the slope of the line tangent to the function at P(1, 1, 3) that is parallel to the xz-plane, the y variable is treated as constant. The graph and this plane are shown on the right. On the graph below it, we see the way the function looks on the plane y = 1. By finding the derivative of the equation while assuming that y is a constant, the slope of ƒ at the point (x, y, z) is found to be:

$\frac{\partial z}{\partial x} = 2x+y$

So at (1, 1, 3), by substitution, the slope is 3. Therefore

$\frac{\partial z}{\partial x} = 3$

at the point. (1, 1, 3). That is, the partial derivative of z with respect to x at (1, 1, 3) is 3.

Definition:

Basic definition,

The function f can be reinterpreted as a family of functions of one variable indexed by the other variables:

$f(x,y) = f_x(y) = \,\! x^2 + xy + y^2.\,$

In other words, every value of x defines a function, denoted f_x, which is a function of one variable.^[2] That is,

$f_x(y) = x^2 + xy + y^2.\,$

Once a value of x is chosen, say a, then f(x,y) determines a function f_a which sends y to a² + ay + y²:

$f_a(y) = a^2 + ay + y^2. \,$

In this expression, a is a constant, not a variable, so f_a is a function of only one real variable, that being y. Consequently, the definition of the derivative for a function of one variable applies:

$f_a'(y) = a + 2y. \,$

The above procedure can be performed for any choice of a. Assembling the derivatives together into a function gives a function which describes the variation of f in the y direction:

$\frac{\partial f}{\partial y}(x,y) = x + 2y.\,$

This is the partial derivative of f with respect to y. Here ∂ is a rounded d called the partial derivative symbol. To distinguish it from the letter d, ∂ is sometimes pronounced "del" or "partial" instead of "dee".
In general, the partial derivative of a function f(x₁,...,x_n) in the direction x_i at the point (a₁,...,a_n) is defined to be:

$\frac{\partial f}{\partial x_i}(a_1,\ldots,a_n) = \lim_{h \to 0}\frac{f(a_1,\ldots,a_i+h,\ldots,a_n) - f(a_1,\ldots, a_i, \dots,a_n)}{h}.$

In the above difference quotient, all the variables except x_i are held fixed. That choice of fixed values determines a function of one variable $f_{a_1,\ldots,a_{i-1},a_{i+1},\ldots,a_n}(x_i) = f(a_1,\ldots,a_{i-1},x_i,a_{i+1},\ldots,a_n)$ , and by definition,

$\frac{df_{a_1,\ldots,a_{i-1},a_{i+1},\ldots,a_n}}{dx_i}(a_i) = \frac{\partial f}{\partial x_i}(a_1,\ldots,a_n).$

In other words, the different choices of a index a family of one-variable functions just as in the example above. This expression also shows that the computation of partial derivatives reduces to the computation of one-variable derivatives.
An important example of a function of several variables is the case of a scalar-valued function f(x₁,...x_n) on a domain in Euclidean space Rⁿ (e.g., on R² or R³). In this case f has a partial derivative ∂f/∂x_j with respect to each variable x_j. At the point a, these partial derivatives define the vector

$\nabla f(a) = \left(\frac{\partial f}{\partial x_1}(a), \ldots, \frac{\partial f}{\partial x_n}(a)\right).$

This vector is called the gradient of f at a. If f is differentiable at every point in some domain, then the gradient is a vector-valued function ∇f which takes the point a to the vector ∇f(a). Consequently, the gradient produces a vector field.
A common abuse of notation is to define the del operator (∇) as follows in three-dimensional Euclidean space R³ with unit vectors $\mathbf{\hat{i}}, \mathbf{\hat{j}}, \mathbf{\hat{k}}$ :

$\nabla = \bigg[{\frac{\partial}{\partial x}} \bigg] \mathbf{\hat{i}} + \bigg[{\frac{\partial}{\partial y}}\bigg] \mathbf{\hat{j}} + \bigg[{\frac{\partial}{\partial z}}\bigg] \mathbf{\hat{k}}$

Or, more generally, for n-dimensional Euclidean space Rⁿ with coordinates (x₁, x₂, x₃,...,x_n) and unit vectors ( $\mathbf{\hat{e}_1}, \mathbf{\hat{e}_2}, \mathbf{\hat{e}_3}, \dots , \mathbf{\hat{e}_n}$ ):

$\nabla = \sum_{j=1}^n \bigg[{\frac{\partial}{\partial x_j}}\bigg] \mathbf{\hat{e}_j} = \bigg[{\frac{\partial}{\partial x_1}}\bigg] \mathbf{\hat{e}_1} + \bigg[{\frac{\partial}{\partial x_2}}\bigg] \mathbf{\hat{e}_2} + \bigg[{\frac{\partial}{\partial x_3}}\bigg] \mathbf{\hat{e}_3} + \dots + \bigg[{\frac{\partial}{\partial x_n}}\bigg] \mathbf{\hat{e}_n}$

Formal definition

Like ordinary derivatives, the partial derivative is defined as a limit. Let U be an open subset of Rⁿ and f : U → R a function. The partial derivative of f at the point a = (a₁, ..., a_n) ∈ U with respect to the i-th variable a_i is defined as

$\frac{ \partial }{\partial a_i }f(\mathbf{a}) = \lim_{h \rightarrow 0}{ f(a_1, \dots , a_{i-1}, a_i+h, a_{i+1}, \dots ,a_n) - f(a_1, \dots, a_i, \dots ,a_n) \over h }$

Even if all partial derivatives ∂f/∂a_i(a) exist at a given point a, the function need not be continuous there. However, if all partial derivatives exist in a neighborhood of a and are continuous there, then f is totally differentiable in that neighborhood and the total derivative is continuous. In this case, it is said that f is a C¹ function. This can be used to generalize for vector valued functions (f : U → R'^m) by carefully using a componentwise argument.
The partial derivative $\frac{\partial f}{\partial x}$ can be seen as another function defined on U and can again be partially differentiated. If all mixed second order partial derivatives are continuous at a point (or on a set), f is termed a C² function at that point (or on that set); in this case, the partial derivatives can be exchanged by Clairaut's theorem:

$\frac{\partial^2f}{\partial x_i\, \partial x_j} = \frac{\partial^2f} {\partial x_j\, \partial x_i}.$

Examples:

The volume V of a cone depends on the cone's height h and its radius r according to the formula

$V(r, h) = \frac{\pi r^2 h}{3}.$

The partial derivative of V with respect to r is

$\frac{ \partial V}{\partial r} = \frac{ 2 \pi r h}{3},$

which represents the rate with which a cone's volume changes if its radius is varied and its height is kept constant. The partial derivative with respect to h is

$\frac{ \partial V}{\partial h} = \frac{\pi r^2}{3},$

which represents the rate with which the volume changes if its height is varied and its radius is kept constant.
By contrast, the total derivative of V with respect to r and h are respectively

$\frac{\operatorname dV}{\operatorname dr} = \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r} + \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h}\frac{\operatorname d h}{\operatorname d r}$

and

$\frac{\operatorname dV}{\operatorname dh} = \overbrace{\frac{\pi r^2}{3}}^\frac{ \partial V}{\partial h} + \overbrace{\frac{2 \pi r h}{3}}^\frac{ \partial V}{\partial r}\frac{\operatorname d r}{\operatorname d h}$

The difference between the total and partial derivative is the elimination of indirect dependencies between variables in partial derivatives.
If (for some arbitrary reason) the cone's proportions have to stay the same, and the height and radius are in a fixed ratio k,

$k = \frac{h}{r} = \frac{\operatorname d h}{\operatorname d r}.$

This gives the total derivative with respect to r:

$\frac{\operatorname dV}{\operatorname dr} = \frac{2 \pi r h}{3} + \frac{\pi r^2}{3}k$

Which simplifies to:

$\frac{\operatorname dV}{\operatorname dr} = k\pi r^2$

Similarly, the total derivative with respect to h is:

$\frac{\operatorname dV}{\operatorname dh} = \pi r^2$

Equations involving an unknown function's partial derivatives are called partial differential equations and are common in physics, engineering, and other sciences and applied disciplines.

Notation:

For the following examples, let f be a function in x, y and z.
First-order partial derivatives:

$\frac{ \partial f}{ \partial x} = f_x = \partial_x f.$

Second-order partial derivatives:

$\frac{ \partial^2 f}{ \partial x^2} = f_{xx} = \partial_{xx} f.$

Second-order mixed derivatives:

$\frac{\partial^2 f}{\partial y \, \partial x} = \frac{\partial}{\partial y} \left( \frac{\partial f}{\partial x} \right) = (f_{x})_{y} = f_{xy} = \partial_{yx} f.$

Higher-order partial and mixed derivatives:

$\frac{ \partial^{i+j+k} f}{ \partial x^i\, \partial y^j\, \partial z^k } = f^{(i, j, k)}.$

When dealing with functions of multiple variables, some of these variables may be related to each other, and it may be necessary to specify explicitly which variables are being held constant. In fields such as statistical mechanics, the partial derivative of f with respect to x, holding y and z constant, is often expressed as

$\left( \frac{\partial f}{\partial x} \right)_{y,z}.$

Antiderivative analogue:

There is a concept for partial derivatives that is analogous to antiderivatives for regular derivatives. Given a partial derivative, it allows for the partial recovery of the original function.
Consider the example of $\frac{\partial z}{\partial x} = 2x+y$ . The "partial" integral can be taken with respect to x (treating y as constant, in a similar manner to partial derivation):

$z = \int \frac{\partial z}{\partial x} \,dx = x^2 + xy + g(y)$

Here, the "constant" of integration is no longer a constant, but instead a function of all the variables of the original function except x. The reason for this is that all the other variables are treated as constant when taking the partial derivative, so any function which does not involve $x$ will disappear when taking the partial derivative, and we have to account for this when we take the antiderivative. The most general way to represent this is to have the "constant" represent an unknown function of all the other variables.
Thus the set of functions $x^2 + xy + g(y)$ , where g is any one-argument function, represents the entire set of functions in variables x,y that could have produced the x-partial derivative 2x+y.
If all the partial derivatives of a function are known (for example, with the gradient), then the antiderivatives can be matched via the above process to reconstruct the original function up to a constant