# Math 1a Spring 2020

## 1a Introduction to Calculus

# Proto Calculus

In the first lecture we looked at**Proto calculus**. It is a calculus which predates even Archimedes. The derivative of f is defined there as Df(x) = f(x+1)-f(x) and the integral is defined as Sf(x) = f(0)+f(1) + ... + f(x-1). We have seen in class that DS f(x) = f(x) and S D f(x) = f(x)-f(0). This is the fundamental theorem of discrete calculus. It is completely analogue to the fundamental theorem of calculus ∫

_{0}

^{x}(d/dt) f(t) dt =f(x)-f(0) and (d/dx) ∫

_{0}

^{x}f(t) dt = f(x). You see the 20 second proofs here: