# Alignment: OpenStax • Calculus • Volume 3

• Chapter 1 Parametric Equations and Polar Coordinates
• 1.1 Parametric Equations
• 1.2 Calculus of Parametric Curves
• 1.3 Polar Coordinates
• 1.4 Area and Arc Length in Polar Coordinates
• 1.5 Conic Sections
• Chapter 2 Vectors in Space
• 2.1 Vectors in the Plane
• 2.2 Vectors in Three Dimensions
• 2.3 The Dot Product
• 2.4 The Cross Product
• 2.5 Equations of Lines and Planes in Space
• 2.7 Cylindrical and Spherical Coordinates
• Chapter 3 Vector-Valued Functions
• 3.1 Vector-Valued Functions and Space Curves
• 3.2 Calculus of Vector-Valued Functions
• 3.3 Arc Length and Curvature
• 3.4 Motion in Space
• Chapter 4 Differentiation of Functions of Several Variables
• 4.1 Functions of Several Variables
• 4.2 Limits and Continuity
• 4.3 Partial Derivatives
• 4.4 Tangent Planes and Linear Approximations
• 4.5 The Chain Rule
• 4.6 Directional Derivatives and the Gradient
• 4.7 Maxima/Minima Problems
• 4.8 Lagrange Multipliers
• Chapter 5 Multiple Integration
• 5.1 Double Integrals over Rectangular Regions
• 5.2 Double Integrals over General Regions
• 5.3 Double Integrals in Polar Coordinates
• 5.4 Triple Integrals
• 5.5 Triple Integrals in Cylindrical and Spherical Coordinates
• 5.6 Calculating Centers of Mass and Moments of Inertia
• 5.7 Change of Variables in Multiple Integrals
• Chapter 6 Vector Calculus
• 6.1 Vector Fields
• 6.2 Line Integrals
• 6.3 Conservative Vector Fields
• 6.4 Green’s Theorem
• 6.5 Divergence and Curl
• 6.6 Surface Integrals
• 6.7 Stokes’ Theorem
• 6.8 The Divergence Theorem
• Chapter 7 Second-Order Differential Equations
• 7.1 Second-Order Linear Equations
• 7.2 Nonhomogeneous Linear Equations
• 7.3 Applications
• 7.4 Series Solutions of Differential Equations

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