| 10. CONIC SECTIONS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES. Conic Sections. Plane Curves and Parametric Equations. The Calculus of Parametric Equations. Polar Coordinates. Areas and Arc Lengths in Polar Coordinates. Conic Sections in Polar Coordinates. Chapter Review. Challenge Problems. 11. VECTORS AND THE GEOMETRY OF SPACE. Vectors in the Plane. Coordinate Systems and Vectors in Three-Space. The Dot Product. The Cross Product. Lines and Planes in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Chapter Review. Challenge Problems. 12. VECTOR-VALUED FUNCTIONS. Vector-Valued Functions and Space Curves. Differentiation and Integration of Vector- Valued Functions. Arc Length and Curvature. Velocity and Acceleration. Tangential and Normal Components of Acceleration. Chapter Review. Challenge Problems. 13. FUNCTIONS OF SEVERAL VARIABLES. Functions of Two or More Variables. Limits and Continuity. Partial Derivatives. Differentials. The Chain Rule. Directional Derivatives and Gradient Vectors. Tangent Planes and Normal Lines. Extrema of Functions of Two Variables. Lagrange Multipliers. Chapter Review. Challenge Problems. 14. MULITPLE INTEGRALS. Double Integrals. Iterated Integrals. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Triple Integrals in Cylindrical and Spherical Coordinates. Change of Variables in Multiple Integrals. Chapter Review. Challenge Problems. 15. VECTOR ANALYSIS. Vector Fields. Divergence and Curl. Line Integrals. Independence of Path and Conservative Vector Fields. Green's Theorem. Parametric Surfaces. Surface Integrals. The Divergence Theorem. Stoke's Theorem. Chapter Review. Challenge Problems. APPENDICES. A. The Real Number Line, Inequalities, and Absolute Value. B. Proofs of Selected Theorems. |
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