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| Vectors and the Geometry of Space | |
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| Three-Dimensional Coordinate Systems | |
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| Vectors | |
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| The Dot Product | |
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| The Cross Product | |
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| Discovery Project: The Geometry of a Tetrahedron | |
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| Equations of Lines and Planes | |
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| Laboratory Project: Putting 3D in Perspective | |
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| Functions and Surfaces | |
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| Cylindrical and Spherical Coordinates | |
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| Laboratory Project: Families of Surfaces | |
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| Review | |
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| Focus on Problem Solving | |
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| Vector Functions | |
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| Vector Functions and Space Curves | |
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| Derivatives and Integrals of Vector Functions | |
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| Arc Length and Curvature | |
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| Motion in Space: Velocity and Acceleration | |
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| Applied Project: Kepler's Laws | |
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| Parametric Surfaces | |
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| Review | |
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| Focus on Problem Solving | |
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| Partial Derivatives | |
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| Functions of Several Variables | |
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| Limits and Continuity | |
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| Partial Derivatives | |
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| Tangent Planes and Linear Approximations | |
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| The Chain Rule | |
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| Directional Derivatives and the Gradient Vector | |
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| Maximum and Minimum Values | |
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| Applied Project: Designing a Dumpster | |
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| Discovery Project: Quadratic Approximations and Critical Points | |
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| Lagrange Multipliers | |
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| Applied Project: Rocket Science | |
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| Applied Project: Hydro-Turbine Optimization | |
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| Review | |
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| Focus on Problem Solving | |
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| Multiple Integrals | |
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| Double Integrals over Rectangles | |
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| Iterated Integrals | |
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| Double Integrals over General Regions | |
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| Double Integrals in Polar Coordinates | |
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| Applications of Double Integrals | |
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| Surface Area | |
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| Triple Integrals | |
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| Discovery Project: Volumes of Hyperspheres | |
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| Triple Integrals in Cylindrical and Spherical Coordinates | |
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| Applied Project: Roller Derby | |
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| Discovery Project: The Intersection of Three Cylinders | |
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| Change of Variables in Multiple Integrals | |
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| Review | |
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| Focus on Problem Solving | |
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| Vector Calculus | |
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| Vector Fields | |
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| Line Integrals | |
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| The Fundamental Theorem for Line Integrals | |
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| Green's Theorem | |
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| Curl and Divergence | |
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| Surface Integrals | |
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| Stokes' Theorem | |
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| Writing Project: Three Men and Two Theorems | |
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| The Divergence Theorem | |
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| Summary | |
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| Review | |
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| Focus on Problem Solving | |
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| Appendixes | |
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| Intervals, Inequalities, and Absolute Values | |
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| Coordinate Geometry | |
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| Trigonometry | |
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| Precise Definitions of Limits | |
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| A Few Proofs | |
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| Sigma Notation | |
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| Integration of Rational Functions by Partial Fractions | |
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| Polar Coordinates | |
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| Complex Numbers | |
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| Answers to Odd-Numbered Exercises | |