# Math 1a Spring 2020

## 1a Introduction to Calculus

# The quantum world

Calculus is an idealization where we take limits like lim_{ h → 0}(1+h)

^{(x/h)}. (This is a compound interest formula. It appears in the movie The Bank. Can we really do that? Early philosophers have thought about this: Zeno of Elea (490-430 BC) was worrying about that 200 years before Archimedes (287-212 BC).

_{h →0}[f(x+h)-f(x)]/h. An example is for f(x) = sin(x), and x=0, where sin(x)=0, so that we want to understand the limit lim

_{h →0}sin(h)/h. The fundamental theorem of trigonometry assures that this is 1. Here is a hollywood picture The Ant man and the wasp (2018) illustrating the quantum realm which somehow still suggests that the world can be scaled arbitrarily. A the end, Scott gets trapped in the quantum world. (The story then gets concluded in Avengers Endgame.)

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