Core · Module 03
Newton and Leibniz's machine for handling change. Learn the idea from 3Blue1Brown, then earn it with MIT's problem sets.
By the end of this module
You can reason about instantaneous change and accumulated total, and you know why they are inverse.
What does it mean to get arbitrarily close without arriving?
3Blue1Brown
Watch this entire series before your first calculus lecture. It replaces memorisation with sight.
MIT OCW
Full course with graded problem sets and exam solutions.
Why is the slope of a curve at a single point even meaningful?
How does a derivative let me find a best answer?
Paul Dawkins, Lamar University
The reference generations of students actually use at 2am.
Why is area the opposite of slope?
How can an infinite sum equal a finite number?
Check yourself
Every answer comes with the reasoning, not just a verdict. Getting one wrong and reading why is the point.
01The fundamental theorem of calculus says:
02A function can be continuous everywhere but differentiable nowhere. This is:
03∫₁^∞ (1/x) dx is: