Description
Book SynopsisTable of Contents12 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
