Calculus III: Multivariable

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Calculus: Multivariable, 12th Edition by Howard Anton (Author), Irl C. Bivens (Author), Stephen Davis (Author) In Calculus: Multivariable, 12th Edition, an expert team of mathematicians delivers a rigorous and intuitive exploration of calculus, introducing concepts like derivatives and integrals of multivariable functions. Using the Rule of Four, the authors present mathematical concepts from verbal, algebraic, visual, and numerical points of view. The book includes numerous exercises, applications, and examples that help readers learn and retain the concepts discussed within. 11 THREE-DIMENSIONAL SPACE; VECTORS 767 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 767 11.2 Vectors 773 11.3 Dot Product; Projections 785 11.4 Cross Product 795 11.5 Parametric Equations of Lines 805 11.6 Planes in 3-Space 813 11.7 Quadric Surfaces 821 11.8 Cylindrical and Spherical Coordinates 832 12 VECTOR-VALUED FUNCTIONS 841 12.1 Introduction to Vector-Valued Functions 841 12.2 Calculus of Vector-Valued Functions 848 12.3 Change of Parameter; Arc Length 858 12.4 Unit Tangent, Normal, and Binormal Vectors 868 12.5 Curvature 873 12.6 Motion Along a Curve 882 12.7 Kepler’s Laws of Planetary Motion 895 13 PARTIAL DERIVATIVES 906 13.1 Functions of Two or More Variables 906 13.2 Limits and Continuity 917 13.3 Partial Derivatives 927 13.4 Differentiability, Differentials, and Local Linearity 940 13.5 The Chain Rule 949 13.6 Directional Derivatives and Gradients 960 13.7 Tangent Planes and Normal Vectors 971 13.8 Maxima and Minima of Functions of Two Variables 977 13.9 Lagrange Multipliers 989 14 MULTIPLE INTEGRALS 1000 14.1 Double Integrals 1000 14.2 Double Integrals over Nonrectangular Regions 1009 14.3 Double Integrals in Polar Coordinates 1018 14.4 Surface Area; Parametric Surfaces 1026 14.5 Triple Integrals 1039 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 1048 14.7 Change of Variables in Multiple Integrals; Jacobians 1058 14.8 Centers of Gravity Using Multiple Integrals 1071 15 TOPICS IN VECTOR CALCULUS 1084 15.1 Vector Fields 1084 15.2 Line Integrals 1094 15.3 Independence of Path; Conservative Vector Fields 1111 15.4 Green’s Theorem 1122 15.5 Surface Integrals 1130 15.6 Applications of Surface Integrals; Flux 1138 15.7 The Divergence Theorem 1148 15.8 Stokes’ Theorem 1158anton