Calculus Multivariable, International Edition

Front Matter. 11. VECTORS AND THE GEOMETRY OF SPACE. Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates Review Exercises P.S. Problem Solving. 12. VECTOR-VALUED FUNCTIONS. Vector-Valued Functions Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature Review Exercises P.S. Problem Solving. 13. FUNCTIONS OF SEVERAL VARIABLES. Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives Section Project: MoirÚ Fringes. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline. Lagrange Multipliers Review Exercises P.S. Problem Solving. 14. MULTIPLE INTEGRATION. Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail. Surface Area Section Project: Capillary Action. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians Review Exercises P.S. Problem Solving. 15. VECTOR ANALYSIS. Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green's Theorem Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes's Theorem Review Exercises Section Project: The Planimeter P.S. Problem Solving. Bonus Online