11 Infinite Sequences and Series

11.1 Sequences

Laboratory Project Logistic 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

Laboratory Project An Elusive Limit

Writing Project How Newton Discovered the Binomial Series

11.11 Applications of Taylor Polynomials

Applied Project Radiation from the Stars

Review

Problems Plus

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

Discovery Project The Geometry of a Tetrahedron

12.5 Equations of Lines and Planes

Laboratory Project Putting 3D in Perspective

12.6 Cylinders and Quadric Surfaces

Review

Problems Plus

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

Applied Project Kepler's Laws

Review

Problems Plus

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

Applied Project Designing a Dumpster

Discovery Project Quadratic Approximations and Critical Points

14.8 Lagrange Multipliers

Applied Project Rocket Science

Applied Project Hydro-Turbine Optimization

Review

Problems Plus

15 Multiple Integrals

15.1 Double Integrals over Rectangles

15.2 Iterated Integrals

15.3 Double Integrals over General Regions

15.4 Double Integrals in Polar Coordinates

15.5 Applications of Double Integrals

15.6 Surface Area

15.7 Triple Integrals

Discovery Project Volumes of Hyperspheres

15.8 Triple Integrals in Cylindrical Coordinates

Laboratory Project The Intersection of Three Cylinders

15.9 Triple Integrals in Spherical Coordinates

Applied Project Roller Derby

15.10 Change of Variables in Multiple Integrals

Review

Problems Plus

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

Writing Project Three Men and Two Theorems

16.9 The Divergence Theorem

16.10 Summary

Review

Problems Plus

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

Review