Calculus is the mathematical study of things that change: cars accelerating, planets moving around the sun, economies fluctuating. To study these changing quantities, a new set of tools - calculus - was developed in the 17th century, forever altering the course of math and science.
Calculus can be tricky, but the key ideas behind it are intuitive and beautiful. In this course, you'll look at those ideas and get a firm conceptual and practical understanding of this new way of looking at the changing physical world.
A first look at wrangling with the infinitesimal.
Making quantitative sense of the moment when everything's changing.
The practitioner's toolkit: the product rule, chain rule, and more.
Linear approximation, implicit differentiation, L'Hôpital's Rule, and some physics!
What is integration, and why is it useful? We'll build up to definite integrals and the fundamental theorem of calculus.
The fundamental toolkit, from substitution to trigonometric integrals to integration by parts.
How to use integrals to find areas, volumes, arc lengths, and more - including applications in physics!