Showing posts with label (005) List of Formulas. Show all posts
Showing posts with label (005) List of Formulas. Show all posts

Friday, June 12, 2015

87-Derivative-Integration Calculator

We know that every one of us has a list of formulae of so many mathematical theories from so many sources. This blog will give you the derivative integration calculator, which displays the derivative and integration of the function which you choose from the drop-down menu of the calculator.

Click on the following button:


The list of all the functions and their derivatives and integration is given below.

Saturday, April 6, 2013

50-List of Formulas - 06

Today we will see the list of formulas of the Complex Numbers part 2.
12) Polar Form of a Complex Number:
Let P (x, y) be any point at a distance of r units from an origin and make an angle

Friday, April 5, 2013

49-List of Formulas - 05

Today we will see the list of formulas of the Complex Numbers part 1. This branch of Math is very interesting and takes us to an imaginary world of Numbers.

Saturday, March 30, 2013

45-List of Formulas - 03

01) The number of elements in a set: 
            The Number of distinct elements in a finite set A is denoted by n (A).
02) Some Important Results:
Cartesian Product of two sets:
Relation:
                  If A and B are any two non-empty sets, then any subset of A x B is called a relation from A to B. If R is the relation from A to B and (x, y) belongs to R, then we say that xRy. Here Set A is the Domain and set B is the Co-Domain. Y is called the image of x under relation R. Similarly,  x is called the pre-image of y under relation R.

Range:

                  A set of all the elements of Co-Domain B associated with the elements of Domain A is called the Range of Relation R.

Function:

                  A and B are two non-empty sets. The Function f from A to B is said to be a function if every element of set A is associated with the unique element of set B and is denoted as f: A -> B. and we say that y = f(x). Here y is the image of x under function f.
                  Here we say that A is the Domain and B is Co-Domain. 

Range:

                  A set of all the elements of Co-Domain B associated with the elements of Domain A is called the Range of Function f.

 Onto Function:
                 f: A-> B is Onto function if every element of Co-Domain B is associated with some 
                 elements of A under Function f. (Note: Range of function "f" is the same as Co-Domain).

Into Function:

                 f: A ->; B is Into function if there exists at least one element extra in Co-Domain B which is not associated with any element of Domain A under Function f. (Note: Range of function "f" is not same as Co-Domain).

Even Function:

                 f : A -> B is said to be Even  Function if f (-x) = f (x).
                 Example: f (x) = cos x    
                 Example: f (x) = x2

Odd Function:

                 f : A -> B is said to be Even  Function if f (-x) = - f (x).
                 Example: f (x) = sin x    
                 Example: f (x) = x3
Composite Function: 

              If f: A ->; B, g : B-> C, then gof : A -> C where gof (x) = g[f(x)]

Inverse Function:
              If f: A -> B is one-one onto Function, then g: B ->A is known as an inverse function of f and is denoted as f-1: B -> A.

Click here for the next list of formulas.

Friday, March 29, 2013

Wednesday, March 27, 2013

43-List of Formulas - 01

Today we will see the list of Trigonometry Formulae (Formulas). 
 
In Hindi, the very beautiful prayer of the goddess "Saraswati" ( the goddess of knowledge and arts ) is there. Please see the following lines (in Hindi)

सरस्वती के भंडार की बढी अपुरब बात 
जो जो खर्चे बढी जात है बीन खर्चे घटी जात . 

The English script of the above Prayer is as follows:

Saraswati ke Bhandar ki Badhi Apurab Bat
Jo Jo Kharche Badhi Jat Hai, Bin Kharche Ghati Jat.

English meaning of the above prayer:

It is the fact of the store of knowledge and arts (Goddess "Saraswati") that if we spread our knowledge among others, it will increase else, it will decrease.

So I request all my dear Students to tell about the above method to your friends and relatives.