## Sunday, 14 June 2015

### CURL AND DIVERGENCE WITH EXAMPLES AND ANALOGIES

( ).  Divergence is the rate at which any force-field like magnetism, heat, light changes.

( ). This rate of change changes along the x, y and z axis.

( ). Thus the equation of Divergence contains
a partial derivative w.r.t  x  + partial derivative w.r.t       y + partial derivative w.r.t  z.

( ). Partial derivative of x means rate of change of heat when you keep moving along the x-axis.

( ). Partial derivative of y means rate of change of heat when you keep moving along the y-axis.

( ) . Same for the z-axis.

EXAMPLE 1
( ) Imagine that there is a fire-place in your room (source of heat).

( ) Now say you are moving away from the fire-place....only along the x-axis direction...then....
1] There will be a rate of change of heat along this x-axis direction.
2] This rate of change can be given as the partial derivative w.r.t  x.
3] Since  you are not moving along the y-axis direction or z-axis direction...the partial derivatives w.r.t  y and w.r.t z will be zero.

( ) So basically,....you are moving along the x-axis direction and thus experiencing a rate of change of heat only along this direction.

This is given as partial derivative w.r.t  x.

CASE 2
MOVING ALONG Z-AXIS.

( ) Now lets say you have lit up fire in your room and you are moving up the chimney i.e along the z-axis....then

( ) You are only moving up along the z-axis...so there will be a rate of change of heat  along the z-axis direction.

( ) So there will be a partial deriviative w.r.t  z

( ) But because the chimney is so damn narrow....you wont be allowed within the chimney to move along the x or y direction.
( Actually the x and the y axis together form the x-y plane and the x-y plane is the plane of any horizontal movement)
( ) So basically....no horizontal movement allowed.

( ) So partial derivative w.r.t  y and partial derivative w.r.t  x is zero.

CASE 3
MOVING ALONG THE X - Y AND Z AXIS SIMULTANEOUSLY.

( ) Now once again lets say you come down to your senses and get down from that chimney.

( ) Now you move away from the fire such that your movement involves the x-axis direction, the y-axis direction and the z-axis direction.

( ) Thus the rate of change of heat will be equal to partial derivative of x + partial derivalive of y + partial derivate of z.

( ) The rate of change of Heat along the x, y and z dimensions is known as the divergence.

( ) In whichever direction you are not moving....the partial derivative of that direction (or axis) will be equal to zero.
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ABOUT
I hardly understood Math in school. In fact was on the verge of dropping the subject I loved the most because as much as I loved the theory of it, I could not understand the math involved in it. However I loved the subject too much to be able to live without. Hopelessly, I was continuing my love-affair with it.

Then one day....a miracle happened,....while applying a certain formula again and again.....I came to know its significance. Slowly and steadily....other equations also started clicking. I got to see a strong relationship between Maths and the Physics it was pointing towards. They both were the same. Maths was just an easy language to express a physical phenomenon. And a bit more to that in the sense that it could even predict the behaviour of a certain physical phenomenon. Equations now as if came to life.

Every equation now had as if something to say. A burning urge to share these things with the world aflamed within me. So that no one has to give up the subject that he or she loves the most.
The book on visualizing maths thus got written as a sprout of inspiration. The blog followed. Both these are dedicated to you and all such similar minds searching for answers.

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