/sci/ - Science & Math

>>11592909
Daily reminder to appreciate how fortunate we are to read shitposts like this, which were pretty much impossible to imagine written down before 1993.

https://www.youtube.com/watch?v=l9G9OXtuJ4Q

The analytic functions obey the analog of the Gregory series: [eqn] f(x) = f(0) + f'(0)x + f''(0) {x^2\over 2} + f'''(0) { x^3\over 3!} … [/eqn] Which is usually called a Taylor series, but was already known to Newton and contemporaries (who were familiar with Gregory series already).
So you see that the calculus is simply a method of defining a limiting calculation method for finite differences where all the arbitrariness and ugliness of the finite differences go away. It is essential for motion, because it tells you what "velocity" means at any one time. It is essential for physics, because it describes how quantities change continuously, the same way that the finite difference business describes how quantities change discretely.