Calculus is the mathematics of quantities that are infinitely small or infinitely many in number. For example, in physics, the curved trajectory of a planet can be understood by splitting it into infinitely many, infinitely short straight line pieces. An area can be computed by splitting the shape into infinitely many, infinitely small squares or triangles. The paradox of Achilles and the Tortoise asks us to sum infinitely many diminishing numbers. Talking vaguely about infinity of course quickly leads to confusion or paradox; calculus is the art of handling infinity safely. It finds application in any situation involving continuous change.

This course is an introduction to calculus. However, it will cover more than a typical first course, including some integral calculus, infinite series and differential equations. The approach will be historically motivated, and will be organized around a few key problems and major applications. Note that this course is not a repetition of AP calculus.