Details


12 Vectors and the Geometry of Space 
12.1 Three-Dimensional Coordinate Systems 
12.2 Vectors 
12.3 The Dot Product 
12.4 The Cross Product 
12.5 Lines and Planes in Space 
12.6 Cylinders and Quadric Surfaces

13 Vector-Valued Functions and Motion in Space 
13.1 Curves in Space and Their Tangents 
13.2 Integrals of Vector Functions; Projectile Motion 
13.3 Arc Length in Space 
13.4 Curvature and Normal Vectors of a Curve 
13.5 Tangential and Normal Components of Acceleration 
13.6 Velocity and Acceleration in Polar Coordinates 

14 Partial Derivatives 
14.1 Functions of Several Variables 
14.2 Limits and Continuity in Higher Dimensions 
14.3 Partial Derivatives 
14.4 The Chain Rule 
14.5 Directional Derivatives and Gradient Vectors 
14.6 Tangent Planes and Differentials 

14.7 Extreme Values and Saddle Points 

14.8 Lagrange Multipliers 
14.9 Taylor’s Formula for Two Variables 
14.10 Partial Derivatives with Constrained Variables 

15 Multiple Integrals 
15.1 Double and Iterated Integrals over Rectangles 
15.2 Double Integrals over General Regions 
15.3 Area by Double Integration 
15.4 Double Integrals in Polar Form 
15.5 Triple Integrals in Rectangular Coordinates 
15.6 Moments and Centers of Mass 
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 
15.8 Substitutions in Multiple Integrals 

16 Integration in Vector Fields 
16.1 Line Integrals 
16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 
16.3 Path Independence, Conservative Fields, and Potential Functions 
16.4 Green’s Theorem in the Plane 
16.5 Surfaces and Area 
16.6 Surface Integrals 
16.7 Stokes’Theorem 
16.8 The Divergence Theorem and a Unified Theory