13 Vectors. - 13. 1 Vectors in the Plane. - 13. 2 Vectors in Space. - 13. 3 Lines and Distance. - 13. 4 The Dot Product. - 13. 5 The Cross Product. - 13. 6 Matrices and Determinants. - 14 Curves and Surfaces. - 14. 1 The Conic Sections. - 14. 2 Translation and Rotation of Axes. - 14. 3 Functions Graphs and Level Surfaces. - 14. 4 Quadric Surfaces. - 14. 5 Cylindrical and Spherical Coordinates. - 14. 6 Curves in Space. - 14. 7 The Geometry and Physics of Space Curves. - 15 Partial Differentiation. - 15. 1 Introduction to Partial Derivatives. - 15. 2 Linear Approximations and Tangent Planes. - 15. 3 The Chain Rule. - 15. 4 Matrix Multiplication and the Chain Rule. - 16 Gradients Maxima and Minima. - 16. 1 Gradients and Directional Derivatives. - 16. 2 Gradients Level Surfaces and Implicit Differentiation. - 16. 3 Maxima and Minima. - 16. 4 Constrained Extrema and Lagrange Multipliers. - 17 Multiple Integration. - 17. 1 The Double Integral and Iterated Integral. - 17. 2 The Double Integral Over General Regions. - 17. 3 Applications of the Double Integral. - 17. 4 Triple Integrals. - 17. 5 Integrals in Polar Cylindrical and Spherical Coordinates. - 17. 6 Applications of Triple Integrals. - 18 Vector Analysis. - 18. 1 Line Integrals. - 18. 2 Path Independence. - 18. 3 Exact Differentials. - 18. 4 Green's Theorem. - 18. 5 Circulation and Stokes' Theorem. - 18. 6 Flux and the Divergence Theorem. - Answers. Language: English