Cálculo 2: Integrales y Series

Find areas, volumes, arc lengths, work, fluid force and centers of mass.

1. Area Between Curves
2. Volume by Slicing
3. Disks and Washers
4. Cylindrical Shells
5. Arc Length
6. Surface Area of Revolution
7. Work
8. Hydrostatic Force
9. Moments and Centers of Mass
10. Hyperbolic Functions

Integrate by parts, with trig identities and substitutions, with partial fractions, and numerically.

1. Integration by Parts
2. Trigonometric Integrals
3. Trigonometric Substitution
4. Integration by Partial Fractions
5. Choosing a Technique
6. Trapezoid and Simpson's Rules
7. Improper Integrals
8. Comparison Test for Improper Integrals

Meet differential equations, slope fields, Euler's method, separable equations and logistic growth.

1. What a Differential Equation Is
2. Direction Fields and Euler's Method
3. Separable Equations
4. The Logistic Equation

Find slopes, areas and lengths for parametric and polar curves.

1. Tangents and Arc Length for Parametric Curves
2. Area in Polar Coordinates
3. Polar Tangents and Arc Length

Decide whether sequences and series converge, and estimate sums.

1. Sequences and Their Limits
2. Monotone and Bounded Sequences
3. Series and Partial Sums
4. Geometric and Telescoping Series
5. The Divergence Test
6. The Integral Test and p-Series
7. Comparison and Limit Comparison Tests
8. Alternating Series
9. Absolute and Conditional Convergence
10. Ratio and Root Tests
11. Choosing a Convergence Test
12. Estimating the Sum of a Series

Represent functions as power series and Taylor series, and use them.

1. Power Series and Intervals of Convergence
2. Representing Functions as Power Series
3. Differentiating and Integrating Power Series
4. Taylor and Maclaurin Series
5. Taylor's Inequality
6. Working with Known Series
7. The Binomial Series
8. Applications of Series