• Vectors and the Geometry of Space

  • Three-Dimensional Coordinate Systems

  • Vectors

  • The Dot Product

  • The Cross Product

  • Lines And Planes In Space

  • Cylinders And Quadric Surfaces

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• Vector-Valued Functions and Motion in Space

  • Curves In Space And Tangent Vectors

  • Integrals Of Vector Functions And Projectile Motion

  • Arc Length In Space

  • Curvature And Normal Vectors

  • Tangential And Normal Components Of Acceleration

  • Velocity And Acceleration In Polar Coordinates

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• Partial Derivatives​

  • Functions Of Several Variables

  • Limits And Continuity In Higher Dimensions

  • Partial Derivatives

  • The Chain Rule

  • Directional Derivatives And Gradient Vectors

  • Tangent Planes And Differentials

  • Extreme Values And Saddle Points

  • Lagrange Multipliers

  • Taylor’s Formula For Two Variables

  • Partial Derivatives With Constrained Variables

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• Multiple Integrals

  • Double And Iterated Integrals Over Rectangles

  • Double Integrals Over General Regions

  • Area By Double Integration

  • Double Integrals In Polar Form

  • Triple Integrals In Rectangular Coordinates

  • Applications Of Triple Integrals

  • Triple Integrals In Cylindrical And Spherical Coordinates

  • Substitutions In Multiple Integrals

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• Integrals and Vector Fields

  • Line Integrals Of Scalar Functions

  • Vector Fields And Line Integrals

  • Path Independence And Conservative Fields

  • Green’s Theorem

  • Surfaces And Surface Area

  • Surface Integrals

  • Stokes’ Theorem

  • The Divergence Theorem

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