Course 3 · Module 1
Calculus
This module covers the branch of mathematics that measures change and accumulation. You'll see how a puzzle about speed at a single instant, and another about the area under a curve, turned out to be two sides of one idea, and how that idea now drives physics, engineering, and economics. You'll do the reasoning with tables of numbers, the way the ideas began, without any of the rules that make school calculus feel like drills.
Module objectives
- Estimate a rate of change and an accumulated total from a table of values, and explain how the two are linked.
- Explain how calculus is used to model motion, find best values, and analyze cost and growth, and state one open question it raises.
Lessons
- Lesson 1 Calculus: Instantaneous speed and areas under curves: limits, derivatives, and integrals You'll take on two puzzles that troubled mathematicians for two thousand years: what speed means at a single instant, and how to find the area of a curved shape. You'll estimate… 61111h 3m
- Lesson 2 Calculus: Optimization, physics, and economics, and the questions calculus leaves open You'll see calculus at work wherever someone wants the best possible value, describes motion, or reasons about the cost of one more unit. You'll also meet questions about… 611111h 33m