Chapter 10: Vectors and Geometry of Space.

10.1 Three-Dimensional Coordinate Systems.

10.2 Vectors.

10.3 The Dot Product.

10.4 The Cross Product.

10.5 Equations of Lines and Planes.

10.6 Cylinders and Quadratic Surfaces.

10.7 Vector Functions and Space Curves.

10.8 Arc Length and Curvature.

Motion in Space: Velocity and Acceleration.

Chapter 11: Partial Derivatives.

11.1 Functions of Several Variables.

11.2 Limits and Continuity.

11.3 Partial Derivatives.

11.4 Tangent Planes and Linear Approximation.

11.5 The Chain Rule.

11.6 Direction Derivatives and the Gradient Vector.

11.7 Maximum and Minimum Values.

11.8 Lagrange Multipliers.

Chapter 12: Multiple Integrals.

12.1 Double Integrals over Rectangles.

12.2 Double Integrals over General Regions.

12.3 Double Integrals in Polar Coordinates.

12.4 Applications of Double Integrals.

12.5 Triple Integrals.

12.6 Triple Integrals in Cylindrical Coordinates.

12.7 Triple Integrals in Spherical Coordinates.

12.8 Change of Variables in Multiple Integrals.

Chapter 13: Vector Calculus.

13.1 Vector Fields.

13.2 Line Integrals.

13.3 The Fundamental Theorem for Line Integrals.

13.4 Green’s Theorem.

13.5 Curl and Divergence.

13.6 Parametric Surfaces and Their Areas.

13.7 Surface Integrals.

13.8 Stokes’ Theorem.

13.9 The Divergence Theorem.