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Full Description
Discover the clear approach and digital support you need to truly understand calculus with MULTIVARIABLE CALCULUS, 12th Edition by award-winning authors Larson and Edwards. This edition effectively presents and demonstrates the concepts and rules of calculus using a thoroughly updated learning experience specifically designed to remove any typical barriers to learning. New 'Big Ideas of Calculus' notes present the overarching ideas behind chapter topics, while annotated examples and 'Concept Checks' further reinforce your understanding. Step-by-step solution videos, exercise solutions and other tutorial support are available at no cost from CalcView.com, CalcChat.com and LarsonCalculus.com. In addition, new automatically graded Proof Problems with instant feedback, Expanded Problems and 'Explore It' interactive learning modules within WebAssign digital resources help you develop a deeper conceptual understanding of calculus to succeed in this course and beyond.
Contents
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. 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: Surface Area in Polar Coordinates. 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' Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving. 16. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE. Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving. APPENDIX. A. Proofs of Selected Theorems. B. Integration Tables. C. Precalculus Review (Web). C.1. Real Numbers and the Real Number Line. C.2. The Cartesian Plane. D. Rotation and the General Second-Degree Equation (Web). E. Complex Numbers (Web). F. Business and Economic Applications (Web). G. Fitting Models to Data (Web).
