Vectors And The Geometry Of Space / 9: |
Three-Dimensional Coordinate Systems |
Vectors |
The Dot Product |
The Cross Product |
Discovery Project: The Geometry of a Tetrahedron |
Equations of Lines and Planes |
Laboratory Project: Putting 3D in Perspective |
Functions and Surfaces |
Cylindrical and Spherical Coordinates |
Laboratory Project: Families of Surfaces |
Review |
Focus on Problem Solving |
Vector Functions / 10: |
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 |
Parametric Surfaces |
Partial Derivatives / 11: |
Functions of Several Variables |
Limits and Continuity |
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 |
Multiple Integrals / 12: |
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 |
Vector Calculus / 13: |
Vector Fields |
Line Integrals |
The Fundamental Theorem for Line Integrals |
Green's Theorem |
Curl and Divergence |
Surface Integrals |
Stokes' Theorem |
Writing Project: Three Men and Two Theorems |
The Divergence Theorem |
Summary |
Appendixes |
Intervals, Inequalities, and Absolute Values / A: |
Coordinate Geometry / B: |
Trigonometry / C: |
Precise Definitions of Limits / D: |
A Few Proofs / E: |
Sigma Notation / F: |
Integration of Rational Functions by Partial Fractions / G: |
Polar Coordinates / H: |
Complex Numbers / I: |
Answers to Odd-Numbered Exercises / J: |
Vectors And The Geometry Of Space / 9: |
Three-Dimensional Coordinate Systems |
Vectors |
The Dot Product |
The Cross Product |
Discovery Project: The Geometry of a Tetrahedron |