Chapter 1: Vectors and the Geometry of Space
1.1: Three Dimensional Coordinate Systems; Vectors and the Dot and Cross Products
1.2: Equations of Lines and Planes
1.3: Cylinders and Quadric Surfaces
Chapter 2: Parametric Equations and Polar Coordinates
2.1: Curves Defined by Parametric Equations
2.2: Calculus with Parametric Curves
2.3: Polar Coordinates + Areas and Lengths in Polar Coordinates
2.4: Conic Sections + Conic Sections in Polar Coordinates
Chapter 3: Vector Functions
3.1: Vector Functions and Space Curves
3.2: Derivatives and Integrals of Vector Functions
3.3: Arc Length and Curvature
3.4: Velocity and Acceleration
Chapter 4: Partial Derivatives
4.1: Functions of Multiple Variables
4.2: Limits and Continuity
4.3: Partial Derivatives
4.4: Tangent Planes and Linear Approximation
4.5: The Chain Rule
4.6: Directional Derivatives and Gradient Vector
4.7: Maximum and Minimum Values
4.8: Lagrange Multipliers
Chapter 5: Multiple Integrals
5.1: Double Integrals over Rectangles and General Regions
5.2: Double Integrals in Polar Coordinates
5.3: Applications of Double Integrals
5.4: Surface Area
5.5: Triple Integrals
5.6: Triple Integrals in Cylindrical Coordinates
5.7: Triple Integrals in Spherical Coordinates
5.8: Change of Variables in Multiple Integrals
Chapter 6: Vector Calculus
6.1: Vector Fields
6.2: Line Integrals
6.3: Fundamental Theorem for Line Integrals
6.4: Green’s Theorem
6.5: Curl and Divergence
6.6: Parametric Surfaces and their Areas
6.7: Surface Integrals
6.8: Stokes’ Theorem
6.9: Divergence Theorem
Link to Textbook: Calculus Early Transcendentals, 8th Edition by James Stewart