The History of Calculus

1
The History of Calculus

• Integral
• Differential

2
Integral Calculus

• Archimedes, in Greece, approximately 250 BC, was
  interested in the displacement of water which led
  him to finding the volume of curved solids.

3
Differential Calculus

• Sir Issac Newton, in England, in the 17th C, was
  interested in the speed of falling objects.
• Leibniz, in Germany at the same time, was
  interested in the slopes of curves.

4
The Same Problem?
Although Newton and Leibniz worked on different
problems, it was discovered that their
mathematical solutions to these problems were the
same. It was also realized that their model was
the opposite (or mathematical inverse) of what
Archimedes had come up with as the answer to his
problem almost 2000 years before.
5
Opposites Attract?

• Integral Calculus -
• areas under curves
• areas of curved regions
• volumes of solid figures
• distance travelled by moving objects

• Differential Calculus -
• slopes of lines
• slopes of curves
• tangents to curves
• velocity of moving objects

6
Integral Calculus and Differential Calculus are
inverses of each other.