Multivariable Calculus

12.1 Three-Dimensional Coordinate Systems +

12.2 Vectors +

12.3 The Dot Product +

12.4 The Cross Product +

12.5 Equations of Lines and Planes +

12.6 Cylinders and Quadric Surfaces +

13.1 Vector Functions and Space Curves +

13.2 Derivatives and Integrals of Vector Functions +

13.3 Arc Length and Curvature +

13.4 Motion in Space: Velocity and Acceleration +

14.1 Functions of Several Variables +

14.2 Limits and Continuity +

14.3 Partial Derivatives +

14.4 Tangent Planes and Linear Approximations +

14.5 The Chain Rule +

14.6 Directional Derivatives and the Gradient Vector +

14.7 Maximum and Minimum Values +

14.8 Lagrange Multipliers +

15.1 Double Integrals over Rectangles +

15.2 Double Integrals over General Regions +

15.3 Double Integrals in Polar Coordinates +

15.4 Applications of Double Integrals +

15.5 Surface Area +

15.6 Triple Integrals +

15.7 Triple Integrals in Cylindrical Coordinates +

15.8 Triple Integrals in Spherical Coordinates +

15.9 Change of Variables in Multiple Integrals +

◆ Change of Variables Summary +

16.1 Vector Fields +

16.2 Line Integrals +

16.3 The Fundamental Theorem for Line Integrals +

16.4 Green's Theorem +

16.5 Curl and Divergence +

16.6 Parametric Surfaces and Their Areas +

16.7 Surface Integrals +

16.8 Stokes' Theorem +

16.9 The Divergence Theorem +

◆ Vector Calculus Summary +