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WHY CALCULUS

 

     Let us say, you are buying 10 chocolates for 20 dollars.  If you divide 20 by 10, you get 2.  So 2 dollar is the price of 1 chocolate.  Division always gives the rate.  In this case cost per unit.

      Another example:  a car covers 120 km in 2 hours.  120/2 = 60 km, It is the speed of the car.  Also rate of distance traveled by the car.  (distance traveled in one hour)

      In general Division y/x, gives the value of y when x is unity.

     Now let us assume that, we have two series as follows.

 x = 1,2,3,4,5,6....
y = 1,4,9,16,25,36...    = x^2

 Here, I want to find y/x.  But the values are not uniform and  they are growing.  What to do?  Here calculus comes to our help.

     It says, if y=x^2, then y/x or more correctly   dy/dx = 2x.

 Let us verify,
x = 3; y = 9
x  =4; y=16
For unit change in x(4-3=1), the change in y is 16 - 9 =7
The average of x = 3 and 4 is 3.5
So 2x=2*3.5 = 7
Hence, for unit change in x, the change in y is 2x - verified.

 For functions like, y =x^3, y = log(x) 
y=sin x and y = 3x+2x^2, the calculus gives us the division of dy/dx(differentiation) or the rate of change of y with respect to x.

 Using calculus, we can calculate, velocity, acceleration, inflation, current, voltage etc for continuously varying quantities.  

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