Calculus IICalculus II

The toolkit for antiderivatives that substitution alone can't crack: parts, trig integrals, trig substitution, partial fractions, and what to do when no formula exists.

1. 1Integration by Parts
2. 2Integrals Involving Trig Functions
3. 3Trig Substitutions
4. 4Partial Fractions
5. 5Integrals Involving Roots
6. 6Integrals Involving Quadratics
7. 7Integration Strategy
8. 8Improper Integrals
9. 9Comparison Test for Improper Integrals
10. 10Approximating Definite Integrals

Slice, approximate, add up: the same idea measures the length of a curve, the skin of a solid, a balance point, the push of water on a dam, and probabilities.

1. 11Arc Length
2. 12Surface Area
3. 13Center of Mass
4. 14Hydrostatic Pressure and Force
5. 15Probability

New ways to describe curves: as a moving point (parametric) or by distance and angle (polar), and how to do calculus on them.

1. 16Parametric Equations and Curves
2. 17Tangents with Parametric Equations
3. 18Area with Parametric Equations
4. 19Arc Length and Surface Area with Parametric Equations
5. 20Polar Coordinates
6. 21Tangents with Polar Coordinates
7. 22Area with Polar Coordinates
8. 23Arc Length and Surface Area with Polar Coordinates

Infinite lists and infinite sums: when they settle on a value, the tests that tell you, and how to estimate a sum you can't compute exactly.

1. 24Sequences
2. 25Monotonic and Bounded Sequences
3. 26Series: The Basics
4. 27The Divergence Test
5. 28Geometric and Telescoping Series
6. 29The Integral Test
7. 30Comparison Tests
8. 31Alternating Series
9. 32Absolute and Conditional Convergence
10. 33The Ratio Test
11. 34The Root Test
12. 35Strategy for Series
13. 36Estimating the Value of a Series

Polynomials that never end: where they converge, how to build them from functions you know, and how they compute integrals, limits and approximations.

1. 37Power Series
2. 38Power Series and Functions
3. 39Taylor Series
4. 40Applications of Series
5. 41The Binomial Series