12 Functions to Several Variables 693 12.1 Functions to Two Variables 694 12.2 Graphs and Surfaces 702 12.3 Contour Diagrams 711 12.4 Linear Functions 725 12.5 Functions to Three Variables 732 12.6 Limits and Continuity 739 13 a Fundamental Tool: Vectors 745 13.1 Displacement Vectors 746 13.
2 Vectors In General 755 13.3 The Dot Product 763 13.4 The Cross Product 774 14 Differentiating Functions to Several Variables 785 14.1 The Partial Derivative 786 14.2 Computing Partial Derivatives Algebraically 795 14.3 Local Linearity and The Differential 800 14.4 Gradients and Directional Derivatives In The Plane 809 14.5 Gradients and Directional Derivatives In Space 819 14.
6 The Chain Rule 827 14.7 Second-Order Partial Derivatives 838 14.8 Differentiability 847 15 Optimization: Local and Global Extrema 855 15.1 Critical Points: Local Extrema and Saddle Points 856 15.2 Optimization 866 15.3 Constrained Optimization: Lagrange Multipliers 876 16 Integrating Functions to Several Variables 889 16.1 The Definite Integral to a Function to Two Variables 890 16.2 Iterated Integrals 898 16.
3 Triple Integrals 908 16.4 Double Integrals In Polar Coordinates 916 16.5 Integrals In Cylindrical and Spherical Coordinates 921 16.6 Applications to Integration to Probability 931 17 Parameterization and Vector Fields 937 17.1 Parameterized Curves 938 17.2 Motion, Velocity, and Acceleration 948 17.3 Vector Fields 958 17.4 The Flow to a Vector Field 966 18 Line Integrals 973 18.
1 The Idea to a Line Integral 974 18.2 Computing Line Integrals Over Parameterized Curves 984 18.3 Gradient Fields and Path-Independent Fields 992 18.4 Path-Dependent Vector Fields and Green's Theorem 1003 19 Flux Integrals and Divergence 1017 19.1 The Idea to a Flux Integral 1018 19.2 Flux Integrals For Graphs, Cylinders, and Spheres 1029 19.3 The Divergence to a Vector Field 1039 19.4 The Divergence Theorem 1048 20 The Curl and Stokes' Theorem 1055 20.
1 The Curl to a Vector Field 1056 20.2 Stokes' Theorem 1064 20.3 The Three Fundamental Theorems 1071 21 Parameters, Coordinates, and Integrals 1077 21.1 Coordinates and Parameterized Surfaces 1078 21.2 Change to Coordinates In a Multiple Integral 1089 21.3 Flux Integrals Over Parameterized Surfaces 1094 Appendices Online A Roots, Accuracy, and Bounds Online B Complex Numbers Online C Newton's Method Online D Vectors In The Plane Online E Determinants Online Ready Reference 1099 Answers to Odd Numbered Problems 1107 Index 1129.