Welcome!

In Calculus Typed you'll find a modern presentation of Calculus that favors certain ways of working:

We use different types for different behaviors.
Algebraic tools have geometric explanations.
We learn Calculus by calculating.

You can read online or download the e-book!

Features

Types

We study several types of mathematical objects: numbers, points, metrics, vectors, rulers, and boxes. Each type has its own algebraic operations and geometric interpretations.

Composition explained

By decomposing functions as schematics, we gain insight into functional dependence.

Unified differential laws

We present a single set of differential laws. These can be used to take derivatives, partials, metric differentials, and ruler differentials.

No chain rule

Our differential laws have the chain rule baked in. As a consequence, dependence works in a natural way: we substitute.

Coherent geometry

We choose geometric interpretations that build in a coherent way.

Metrics and polymetrics

Polymetrics give an algebraic approach to studying the slope, bend, and warp of a graph.

Measurement

By studying rulers we see how integrals generalize the familiar act of measuring.