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Parametric Equations and Polar Coordinates | |
Curves Defined by Parametric Equations | |
Laboratory Project: Families of Hypocycloids | |
Calculus with Parametric Curves | |
Laboratory Project: Bezier Curves | |
Polar Coordinates | |
Areas and Lengths in Polar Coordinates | |
Conic Sections | |
Conic Sections in Polar Coordinates | |
Review | |
Problems Plus | |
Infinite Sequences and Series | |
Sequences | |
Laboratory Project: Logistic Sequences | |
Series | |
The Integral Test and Estimates of Sums | |
The Comparison Tests | |
Alternating Series | |
Absolute Convergence and the Ratio and Root Tests | |
Strategy for Testing Series | |
Power Series | |
Representation of Functions as Power Series | |
Taylor and Maclaurin Series | |
Writing Project: How Newton Discovered the Binomial Series | |
Applications of Taylor Polynomials | |
Applied Project: Radiation from the Stars | |
Review | |
Problems Plus | |
Vectors and The Geometry of Space | |
Three-Dimensional Coordinate Systems | |
Vectors | |
The Dot Product | |
The Cross Product | |
Discovery Project: The Geometry of a Tetrahedron | |
Equations of Lines and Planes | |
Cylinders and Quadric Surfaces | |
Cylindrical and Spherical Coordinates | |
Laboratory Project: Families of Surfaces | |
Review | |
Problems Plus | |
Vector Functions | |
Vector Functions and Space Curves | |
Derivatives and Integrals of Vector Functions | |
Arc Length and Curvature | |
Motion in Space: Velocity and Acceleration | |
Applied Project: Kepler's Laws | |
Review | |
Problems Plus | |
Partial Derivatives | |
Functions of Several Variables | |
Limits and Continuity | |
Partial Derivatives | |
Tangent Planes and Linear Approximations | |
The Chain Rule | |
Directional Derivatives and the Gradient Vector | |
Maximum and Minimum Values | |
Applied Project: Designing a Dumpster | |
Discovery Project: Quadratic Approximations and Critical Points | |
Lagrange Multipliers | |
Applied Project: Rocket Science | |
Applied Project: Hydro-Turbine Optimization | |
Review | |
Problems Plus | |
Multiple Integrals | |
Double Integrals over Rectangles | |
Iterated Integrals | |
Double Integrals over General Regions | |
Double Integrals in Polar Coordinates | |
Applications of Double Integrals | |
Surface Area | |
Triple Integrals | |
Discovery Project: Volumes of Hyperspheres | |
Triple Integrals in Cylindrical and Spherical Coordinates | |
Applied Project: Roller Derby | |
Discovery Project: The Intersection of Three Cylinders | |
Change of Variables in Multiple Integrals | |
Review | |
Problems Plus | |
Vector Calculus | |
Vector Fields | |
Line Integrals | |
The Fundamental Theorem for Line Integrals | |
Green's Theorem | |
Curl and Divergence | |
Parametric Surfaces and Their Areas | |
Surface Integrals | |
Stokes' Theorem | |
Writing Project: Three Men and Two Theorems | |
The Divergence Theorem | |
Summary | |
Review | |
Problems Plus | |
Second-Order Differential Equations | |
Second-Order Linear Equations | |
Nonhomogeneous Linear Equations | |
Applications of Second-Order Differential Equations | |
Series Solutions | |
Review | |
Problems Plus | |
Appendixes | |
Intervals, Inequalities, and Absolute Values | |
Coordinate Geometry and Lines | |
Graphs of Second-Degree Equations | |
Trigonometry | |
Sigma Notation | |
Proofs of Theorems | |
Complex Numbers | |
H | |
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