Differential Calculus
You learn the two big ideas that start calculus -- the limit and the derivative -- and use the derivative to find slopes, rates, maximums and minimums, and to sketch how any function behaves.
Class 1Functions and the idea of a limit
What a limit is, and why calculus needs it.
Class 2Computing limits
The rules that let you find a limit without guessing.
Class 3Continuity
When a graph has no breaks, and why it matters.
Class 4The derivative
The slope of a curve, and the rate something changes.
Class 5Derivative rules: power, product, quotient
The shortcuts that make derivatives quick.
Class 6Derivatives of trig, exponential and log functions
The derivatives of the functions you already know.
Class 7The chain rule
Differentiating a function inside another function.
Class 8Implicit differentiation and related rates
Derivatives when y is tangled with x, and rates that drive each other.
Class 9Maximum and minimum values
Finding the highest and lowest points of a function.
Class 10Curve sketching
Reading a function's whole shape from its derivatives.
Class 11Optimization problems
Using calculus to find the best possible answer.
Class 12Semester 1 review: differentiation
Pulling limits, derivatives and their uses together.