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1 Vectors and the Geometry of Space 1.1 Rectangular Coordinate System 1.2 Vector 1.3 Equations for Lines and Planes 1.4 Cylinders and Quadric Surfaces 1.5 Parametric Curves and Parametric Surfaces2 Partial Derivatives 2.1 Functions of Several Variables 2.2 Limits and Continuity 2.3 Partial Derivatives 2.4 Linear Approximation 2.5 Chain Rules 2.6 Directional Derivative and Gradient 2.7 Maximum and Minimum Values 2.8 Lagrange Multiplier3 Multiple Integrals 3.1 Double Integrals and Iterated Integrals 3.2 Double Integrals over General Regions 3.3 Double Integral in Polar Coordinates 3.4 Triple Integrals in Rectangular Coordinates 3.5 Triple Integrals in Cylindrical Coordinates 3.6 Triple Integrals in Spherical Coordinates 3.7 Applications of Multiple Integrals 3.8 Change of Variables in Multiple Integrals4 Line Integrals and Surface Integrals 4.1 Line Integrals 4.2 Line Integrals of Vector Fields 4.3 Path Independence 4.4 Green's Theorem 4.5 Parametric Surface and Their Areas 4.6 Surface Integral 4.7 Surface Integrals of Vector Fields 4.8 Gauss' Theorem 4.9 Stokes' Theorem5 Infinite Series 5.1 Basic Concepts 5.2 The Integral Test 5.3 The Comparison Tests 5.4 Alternating Series 5.5 Absolute Convergence and Conditional Convergence 5.6 Power Series 5.7 Term-by-term Differentiation and Integration 5.8 Taylor and Maclaurin Series 5.9 Fourier SeriesBibliography