Ch 10: Parametric Equations and Polar Coordinates

10.1: Curves Defined by Parametric Equations

10.2: Calculus with Parametric Curves

10.3: Polar Coordinates

10.4: Areas and Lengths in Polar Coordinates

10.5: Conic Sections

10.6: Conic Sections in Polar Coordinates

10: Review

Problems Plus

Ch 11: Infinite Sequences and Series

11.1: Sequences

11.2: Series

11.3: The Integral Test and Estimates of Sums

11.4: The Comparison Tests

11.5: Alternating Series

11.6: Absolute Convergence and the Ratio and Root Tests

11.7: Strategy for Testing Series

11.8: Power Series

11.9: Representations of Functions as Power Series

11.10: Taylor and Maclaurin Series

11.11: Applications of Taylor Polynomials

11: Review

Problems Plus

Ch 12: Vectors and the Geometry of Space

12.1: Three-Dimensional Coordinate Systems

12.2: Vectors

12.3: The Dot Product

12.4: The Cross Product

12.5: Equations of Lines and Planes

12.6: Cylinders and Quadric Surfaces

12: Review

Problems Plus

Ch 13: Vector Functions

13.1: Vector Functions and Space Curves

13.2: Derivatives and Integrals of Vector Functions

13.3: Arc Length and Curvature

13.4: Motion in Space: Velocity and Acceleration

13: Review

Problems Plus

Ch 14: Partial Derivatives

14.1: Functions of Several Variables

14.2: Limits and Continuity

14.3: Partial Derivatives

14.4: Tangent Planes and Linear Approximations

14.5: The Chain Rule

14.6: Directional Derivatives and the Gradient Vector

14.7: Maximum and Minimum Values

14.8: Lagrange Multipliers

14: Review

Problems Plus

Ch 15: Multiple Integrals

15.1: Double Integrals over Rectangles

15.2: Double Integrals over General Regions

15.3: Double Integrals in Polar Coordinates

15.4: Applications of Double Integrals

15.5: Surface Area

15.6: Triple Integrals

15.7: Triple Integrals in Cylindrical Coordinates

15.8: Triple Integrals in Spherical Coordinates

15.9: Change of Variables in Multiple Integrals

15: Review

Problems Plus

Ch 16: Vector Calculus

16.1: Vector Fields

16.2: Line Integrals

16.3: The Fundamental Theorem for Line Integrals

16.4: Green’s Theorem

16.5: Curl and Divergence

16.6: Parametric Surfaces and Their Areas

16.7: Surface Integrals

16.8: Stokes’ Theorem

16.9: The Divergence Theorem

16: Review

Problems Plus

Ch 17: Second-Order Differential Equations

17.1: Second-Order Linear Equations

17.2: Nonhomogeneous Linear Equations

17.3: Applications of Second-Order Differential Equations

17.4: Series Solutions

17: Review

Appendix

Complex Numbers