( ) Differentiation is the evil twin of integration.
( )Integration is bringing together. Differentiation is segregation.
( )Hence the word derivative. Its what you get after segregation.
( )Example.
( ) Graphically d/dx or d/dt will give you the rate of change or slope of the graph (tan(angle)).
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( ) Conversely,
d/dr (Πr^2) = 2Πr.
( )Thus integration helps you to predict what the final structure will look like if you keep adding aling a certain direction(dx or dr or dh).
( ) And Differentiation helps you trace back out of what the final structure was made.
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Hope this helps
Binnoy
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THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5$) AT THE FOLLOWING LINK
VISUALIZING MATHS.PDF
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CONTACT
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( )Integration is bringing together. Differentiation is segregation.
( )Hence the word derivative. Its what you get after segregation.
( )Example.
- d/dt(distance) = velocity.
- d/dt(velocity) = accerleration
- d/dt(acceleration)= rate of change of acceleration w.r.t time
( ) Graphically d/dx or d/dt will give you the rate of change or slope of the graph (tan(angle)).
ANOTHER WAY TO LOOK AT DIFFERENTIATION.
( ) Differentiation can be seen as tracing back to the building blocks of anything.
Example.
( )Integration of 2 x Π x r.dr = Π x r^2.
( )Thus adding rings of incresing radiuses will eventually produce a disk like structure.
( ) Differentiation can be seen as tracing back to the building blocks of anything.
Example.
( )Integration of 2 x Π x r.dr = Π x r^2.
( )Thus adding rings of incresing radiuses will eventually produce a disk like structure.
( )Thus integration helps you to predict what the final structure will look like if you keep adding aling a certain direction(dx or dr or dh).
( ) And Differentiation helps you trace back out of what the final structure was made.
Binnoy
THE ABOVE IS A EXCERPT FROM A BOOK AVAILABLE FOR PURCHASE (5$) AT THE FOLLOWING LINK
VISUALIZING MATHS.PDF
AVAILABLE FOR PURCHASE FOR 5$ (INR 300) HERE (PDF)
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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.
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.
Visualizing Math & Physics is a blog dedicated to you and all such similar minds searching for answers.
CONTACT
binnoypanicker@gmail.com
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