Single Variable Calculus

18.01SC is the OpenCourseWare Scholar version of MIT's single variable calculus course, built around David Jerison's fall 2010 lectures and designed for independent study. It covers differentiation and integration of functions of one variable and ends with a short treatment of infinite series. The course is organised into five units. Unit 1 introduces the derivative and its basic rules, implicit differentiation and inverse functions. Unit 2 applies differentiation to approximation and curve sketching, optimisation, related rates, Newton's method, the mean value theorem and antiderivatives.

Unit 3 defines the definite integral and the two fundamental theorems, with areas, volumes, average value, probability and numerical integration. Unit 4 covers techniques of integration, including trigonometric substitution, partial fractions, integration by parts, arc length, and parametric and polar coordinates. Unit 5 explores the infinite through L'Hospital's rule, improper integrals and Taylor series. Each session combines a lecture video with written notes, recitation videos of problem-solving tips, worked examples, and problem sets with solutions; four exams and a final with solutions round it out, and interactive applets reinforce key ideas. All material is free under a Creative Commons licence; there is no registration and no certificate.