Topics

• Vector Functions and Space Curves
• Derivatives and Integrals of Vector Functions
• Arc Length and Curvature
• Motion in Space: Velocity and Acceleration


• Functions of Several Variables
• Limits and Continuity
• Partial Derivatives
• Tangent Plane and Linear Approximations
• The Chain Rule
• Directional Derivatives and the Gradient Vector
• Maximum and Minimum Values
• Lagrange Multipliers


• Double Integrals over Rectangles
• Double Integrals over General Regions
• Double Integrals in Polar Coordinates
• Applications of Double Integrals
• Surface Area
• Triple Integrals
• Change of Variables in Multiple Integrals


• Vector Fields
• Line Integrals
• Fundamental Theorem for Line Integrals
• Green's Theorem
• Curl and Divergence
• Parametric Surfaces and their Areas
• Surface Integrals
• Stokes' Theorem
• The Divergence Theorem