13 Vectors.-
13.1 Vectors in the Plane.-
13.2 Vectors in Space.-
13.3 Lines and Distance.-
13.4 The Dot Product.-
13.5 The Cross Product.-
13.6 Matrices and Determinants.-

14 Curves and Surfaces.-
14.1 The Conic Sections.-
14.2 Translation and Rotation of Axes.-
14.3 Functions, Graphs, and Level Surfaces.-
14.4 Quadric Surfaces.-
14.5 Cylindrical and Spherical Coordinates.-
14.6 Curves in Space.-
14.7 The Geometry and Physics of Space Curves.-
15 Partial Differentiation.-
15.1 Introduction to Partial Derivatives.-
15.2 Linear Approximations and Tangent Planes.-
15.3 The Chain Rule.-
15.4 Matrix Multiplication and the Chain Rule.-
16 Gradients, Maxima, and Minima.-
16.1 Gradients and Directional Derivatives.-
16.2 Gradients, Level Surfaces, and Implicit Differentiation.-
16.3 Maxima and Minima.-
16.4 Constrained Extrema and Lagrange Multipliers.-
17 Multiple Integration.-
17.1 The Double Integral and Iterated Integral.-
17.2 The Double Integral Over General Regions.-
17.3 Applications of the Double Integral.-
17.4 Triple Integrals.-
17.5 Integrals in Polar, Cylindrical, and Spherical Coordinates.-
17.6 Applications of Triple Integrals.-
18 Vector Analysis.-
18.1 Line Integrals.-
18.2 Path Independence.-
18.3 Exact Differentials.-
18.4 Green’s Theorem.-
18.5 Circulation and Stokes’ Theorem.-
18.6 Flux and the Divergence Theorem.- Answers.
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