Preface

Calculus answers two questions: how fast a quantity is changing, and how large an accumulation of many tiny quantities becomes. Both answers rest on a single idea — the limit.

Route#

1. Limits: turn "arbitrarily close" into inequalities you can check.
2. Derivatives: define the instantaneous rate of change with a limit.

Prerequisites

You should be comfortable with real numbers, functions and inequalities. Linear algebra is not required, but Vectors from Linear Algebra makes the multivariable parts easier.

Conventions#

Functions are real-valued and defined on an interval of unless stated otherwise. Differentials are always written .