Basic Difference Between Two Ideas

[nycmathguy]

What is the basic difference between differentiation and integration?

 

[MathLover1]

Differentiation is used to calculate the gradient of a curve. It is used to find out the instant rates of change from one point to another.
Integration is used to calculate the area under or between the curves.
Integration is the reversed process of differentiation.

 

[nycmathguy]

Differentiation is used to calculate the gradient of a curve. It is used to find out the instant rates of change from one point to another.
Integration is used to calculate the area under or between the curves.
Integration is the reversed process of differentiation.

I look forward to calculus.

 

[HallsofIvy]

Differentiation and integration were initially treated as completely different operations. Part of the reason that Newton and Leibniz are considered the founders of the Calculus is that they recognized that these are the inverse to each other.

 

[nycmathguy]

Differentiation and integration were initially treated as completely different operations. Part of the reason that Newton and Leibniz are considered the founders of the Calculus is that they recognized that these are the inverse to each other.

Newton and Leibniz hated each other, right?

 

[HallsofIvy]

I've never heard that. After their deaths, the English pretty much attributed the invention of the Calculus entirely to Newton while the French attributed it entirely to Leibniz, starting a "rivalry" that they never participated in. Speaking of Newton, Leibniz said "Taking mathematics from the beginning of the world to the time when Newton lived, what he has done is much the better part." That doesn't sound like Leibniz hated Newton!

 

[nycmathguy]

I've never heard that. After their deaths, the English pretty much attributed the invention of the Calculus entirely to Newton while the French attributed it entirely to Leibniz, starting a "rivalry" that they never participated in. Speaking of Newton, Leibniz said "Taking mathematics from the beginning of the world to the time when Newton lived, what he has done is much the better part." That doesn't sound like Leibniz hated Newton!

I simply stated what someone once said about the competition between the two math guys. Never did I read anything about the life of either of the men.

 

[HallsofIvy]

Perhaps you should not state "what someone once said" as if you knew it were a fact!

 

[nycmathguy]

Perhaps you should not state "what someone once said" as if you knew it were a fact!

Why would you say that to me? I am a math fanatic living a horrible life. Do you know what it means to work 40 overnight hours? Do you know about my physical abnormalities? Do you know about my weekly hospital visits for physical therapy? I gotta squeeze math into my daily life. It's not easy at all.