Videos
AP Calculus BC
Pick a topic to watch.
10 video lessons
17:56
Topic 1
Limits & Continuity
Start with a puzzle. A car's speedometer reads sixty kilometres per hour. But what does that mean at a single instant? Speed is distance over time. Yet in one…
7:52
Topic 2
Defining the Derivative
Draw a journey as a curve. Pick two points, join them with a straight line, and its slope gives the average rate over an interval. But we want the rate at one…
7:58
Topic 3
The Chain Rule
Think of two gears joined together. Turn the first one, and it drives the second. If the second turns three times as fast as the first, and the first turns…
8:26
Topic 4
Interpreting the Derivative in Context
A tank is draining. A cup of coffee is cooling. A city is growing. Every one of those sentences hides the same phrase. The rate at which something changes. And…
9:33
Topic 5
Using the Mean Value Theorem
You drive two hundred kilometres in two hours. Your average speed was one hundred kilometres per hour. Now here is a claim. At some moment during that drive…
10:02
Topic 6
Exploring Accumulations of Change
Water flows into a tank. The meter shows litres per minute. That is a rate of change. Now, how much water arrived in the first ten minutes? Draw the rate…
8:26
Topic 7
Modeling with Differential Equations
Normally you are handed a function and asked for its slope. A differential equation turns that around. You are handed a rule for the slope at every point, and…
9:59
Topic 8
Applications of Integration
Here is a bumpy graph, and the area underneath it. Now imagine pouring that area into a rectangle over the same interval, and letting it level off. The height…
6:06
Topic 9
Parametric, Vector & Polar
Some curves cannot be written as y equals a function of x. Think of a particle looping around, or a path that crosses itself — for one x there would be two y…
8:20
Topic 10
Infinite Series
Can you add infinitely many numbers and get a finite answer? Surprisingly, yes. Add forever, and sometimes the total runs away to infinity — but sometimes it…