12. Functions of Several Variables 651 12.1 Functions of Two Variables 652 12.2 Graphs and Surfaces 660 12.3 Contour Diagrams 668 12.4 Linear Functions 682 12.5 Functions of Three Variables 689 12.6 Limits and Continuity 695 Review Problems Online Projects Online 13.
A Fundamental Tool: Vectors 701 13.1 Displacement Vectors 702 13.2 Vectors in General 710 13.3 The Dot Product 718 13.4 The Cross Product 728 Review Problems Online Projects Online 14. Differentiating Functions of Several Variables 739 14.1 The Partial Derivative 740 14.2 Computing Partial Derivatives Algebraically 748 14.
3 Local Linearity and the Differential 753 14.4 Gradients and Directional Derivatives in the Plane 762 14.5 Gradients and Directional Derivatives in Space 772 14.6 The Chain Rule 780 14.7 Second-Order Partial Derivatives 790 14.8 Differentiability 799 Review Problems Online Projects Online 15. Optimization: Local and Global Extreme 805 15.1 Critical Points: Local Extreme and Saddle Points 806 15.
2 Optimization 815 15.3 Constrained Optimization: Lagrange Multipliers 825 Review Problems Online Projects Online 16. Integrating Functions of Several Variables 839 16.1 The Definite Integral of a Function of Two Variables 840 16.2 Iterated Integrals 847 16.3 Triple Integrals 857 16.4 Double Integrals in Polar Coordinates 864 16.5 Integrals in Cylindrical and Spherical Coordinates 869 16.
6 Applications of Integration to Probability 878 Review Problem Online Projects Online 17. Parameterization and Vector Fields 885 17.1 Parameterized Curves 886 17.2 Motion, Velocity, and Acceleration 896 17.3 Vector Fields 905 17.4 The Flow of a Vector Field 913 Review Problems Online Projects Online 18. Line Integrals 921 18.1 The Idea of a Line Integral 922 18.
2 Computing Line Integrals Over Parameterized Curves 931 18.3 Gradient Fields and Path-Independent Fields 939 18.4 Path-Dependent Vector Fields and Green''s Theorem 949 Review Problems Online Projects Online 19. Flux Integrals and Divergence 961 19.1 The Idea of a Flux Integral 962 19.2 Flux Integrals for Graphs, Cylinders, and Spheres 973 19.3 The Divergence of a Vector Fields 982 19.4 The Divergence Theorem 991 Review Problems Online Projects Online 20.
The Curl and Stokes'' Theorem 999 20.1 The Curl of a Vector Fields 1000 20.2 Stokes'' Theorem 1008 20.3 The Three Fundamental Theorems 1015 Review Problems Online Projects Online 21. Parameters, Coordinates, and Integrals 1021 21.1 Coordinates and Parameterized Surfaces 1022 21.2 Change of Corrdinates in a Multiple Integral 1033 21.3 Flux Integrals Over Parameterized Surfaces 1038 Review Problems Online Projects Online.