← Calculus
Semester 2
Integral Calculus and Series
You learn the other half of calculus -- the integral -- from the area under a curve to the techniques that solve real integrals, and finish with infinite series and the Taylor series that power a calculator.
Class 1Antiderivatives and the area problem
Undoing a derivative, and the area under a curve.
Class 2The definite integral
The exact area, as a limit of rectangles.
Class 3The Fundamental Theorem of Calculus
The bridge that ties derivatives and integrals together.
Class 4Integration by substitution
The chain rule, run backwards.
Class 5Areas and volumes
Using integrals to measure real shapes.
Class 6Integration by parts
The product rule, run backwards.
Class 7Trigonometric integrals and substitution
Integrals full of sines, cosines and square roots.
Class 8Partial fractions
Breaking a hard fraction into easy pieces to integrate.
Class 9Improper integrals
Integrals that run to infinity, or blow up.
Class 10Sequences and series
Adding up infinitely many numbers.
Class 11Convergence tests
Deciding whether an infinite series adds up.
Class 12Power series and Taylor series
Writing a function as an endless polynomial.