About Calculus Typed
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.