Handouts

Our collection of 21 handouts totaling 100+ pages closely follows the USAPhO syllabus and covers the major calculus topics that you would need to use on the exam (and, optionally, the F=ma). For your convenience, we have divided our handouts into 3 separate categories: derivatives, integrals, and differential equations. After reading our detailed handouts, you could also check out our other project, USAAAO Guide, which prepares you —  using calculus — for the Astronomy & Astrophysics Olympiad.

Derivatives

Learn topics including intuition behind derivatives, differentiation rules, chain rule, implicit differentiation, taylor series, and much more.

Integrals

Learn topics including intuition behind integrals, Fundamental Theorem of Calculus, integration rules, Gaussian integral, average value, and more.

Differential Equations

Learn topics including separable equations, exponential decay and growth, second-order differential equations, applications to Kinematics, and more.