Newton
- Newton compiled a book in 1671.
- In the book he shaped and defined his fluxional calculus.
- In the book he also exploited instantaneous motion and infinitesimals informally.
- He used this math to help explain the physical world.
- The base of his revised calculus became continuity.
- Tried to avoid the use of infinitesimal by forming calculations based on rates of change
- Defined the rate of generated change as a fluxion.
- In a 1676 text he defined the present day derivative as the ultimate ration of change.
- This was defined as a ratio between increments, purely at the moment in question.
Newton
- Many of Newton's insights from 1665-1666
- He determined the area under the curve by determining the momentary rate of change, then extrapolating the total area.
- These calculations lead to the building of the fundamental theorem of calculus.
- Newton never had a definitive publication on Fluxional Calculus.
- Started mathematical training at Cambridge where he quickly learned the current theorems.
- His first contribution was to the binomial theorem, extending it to include fractional and negative exponents.
The Real Role of Newton in the Development of Calculus