Mastering the fundamental rules that drive modern mathematical analysis

Ideas & Philosophy · Published 7 October 2026 Swipe more like this →

In short: This MIT OpenCourseWare lecture explores the essential mechanics of calculus. Learn how specific mathematical rules allow us to derive new information from known derivatives and how integration serves to invert the process.

In this session from the Fall 2015 MIT RES.18-009 course, instructors Gilbert Strang and Cleve Moler examine the core principles of differential equations. The video details how the sum rule, product rule, and chain rule function to generate new derivatives from existing ones.

The discussion also covers the Fundamental Theorem of Calculus, which establishes that the integral acts as the inverse of the derivative.

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