Active Calculus — Multivariable

9.1 Functions of Several Variables and Three Dimensional Space 9.2 Vectors 9.3 The Dot Product 9.4 The Cross Product 9.5 Lines and Planes in Space 9.6 Vector-Valued Functions 9.7 Derivatives and Integrals of Vector-Valued Functions 9.8 Arc Length and Curvature

10.1 Limits 10.2 First-Order Partial Derivatives 10.3 Second-Order Partial Derivatives 10.4 Linearization: Tangent Planes and Differentials 10.5 The Chain Rule 10.6 Directional Derivatives and the Gradient 10.7 Optimization 10.8 Constrained Optimization: Lagrange Multipliers

11.1 Double Riemann Sums and Double Integrals over Rectangles 11.2 Iterated Integrals 11.3 Double Integrals over General Regions 11.4 Applications of Double Integrals 11.5 Double Integrals in Polar Coordinates 11.6 Surfaces Defined Parametrically and Surface Area 11.7 Triple Integrals 11.8 Triple Integrals in Cylindrical and Spherical Coordinates 11.9 Change of Variables

12.1 Vector Fields 12.2 The Idea of a Line Integral 12.3 Using Parametrizations to Calculate Line Integrals 12.4 Path-Independent Vector Fields and the Fundamental Theorem of Calculus for Line Integrals 12.5 Line Integrals of Scalar Functions 12.6 The Divergence of a Vector Field 12.7 The Curl of a Vector Field 12.8 Green's Theorem 12.9 Flux Integrals 12.10 Surface Integrals of Scalar Valued Functions 12.11 Stokes' Theorem 12.12 The Divergence Theorem