# contour plot

some collisions are so deafening
that they do not punctuate your life,
they tear a hole right through it.

some collisions are so destructive
that you must spend your entire life
studying its impact,
the contours of its craters,

plotting the safest way
to avoid getting struck twice.
Calculus I: Integrals are Gonna Carry that Weight

Calculus is the branch of mathematics that tells us how to break down mathematical objects and put them back together. Whether you credit Isaac Newton or Gottfried Leibniz with its invention, there’s no denying physics is built upon a foundation of calculus.

We frequently break calculus into two subfields:

• The derivative calculus, which–like breaking a staircase into individual steps–tells us how to deconstruct wholes into constituents, and
• The integral calculus, which does the reverse: given an assortment of steps, it manages to build a staircase.

Today, we introduce the latter topic. We do so in the context of finding the area of a shape in the real plane, and then generalize this procedure to craft our real goal: the integral. The integral is a powerful machine, capable of feats akin to mathematical alchemy.

Are you ready? Okay, 3… 2… 1… Let’s jam!