Math 2415: Calculus III
These notes are based on the Calculus book by Larson and Edwards, 10th Edition.
11.4: The cross product of two vectors
11.5: Lines and planes in space
11.6: Surfaces in space
11.7: Cylindrical and spherical coordinates
12.1: Vector-valued functions
12.2: Differentiation and integration of vector-valued functions
12.3: Velocity and acceleration
12.4: Tangent vectors and normal vectors
12.5: Arc length and curvature
13.1: Introduction to functions of several variables
13.2: Limits and continuity
13.3: Partial derivatives
13.4: Differentials
13.5: Chain rules for functions of several variables
13.6: Directional derivatives gradients
13.7: Tangent planes and normal lines
13.8: Extrema of functions of two variables
13.9: Applications of extrema
13.10: Lagrange multipliers
14.1: Iterated integrals and area in the plane
14.2: Double integrals and volume
14.3: Change of variables – Polar coordinates
14.4: Center of mass and moments of inertia
14.5: Surface area
14.6: Triple integrals and applications
14.7: Triple integrals in cylindrical and spherical coordinates
15.1: Vector fields
15.2: Line integrals
15.3: Conservative vector fields and independence of path
15.4: Green’s Theorem
15.5: Parametric surfaces
15.6: Surface integrals
15.7: Divergence Theorem
15.8: Stokes’ Theorem