Math 21D Class Handouts
Double Integrals
Constructing Bounds of Integration for Double Integrals
Average Value of f over 2D Region
Double Integrals in Polar Coordinates
Converting a Double Integral from Polar to Rectangular Coordinates Example
Triple Integrals
Constructing Bounds of Integration for Triple Integrals
Moments, Center of Mass, Centroid, and Moment of Inertia in 2D Space
Moments, Center of Mass, Centroid, and Moment of Inertia in 3D Space
Cylindrical Coordinates
Spherical Coordinates
dV in Spherical Coordinates
Vector Function Review
Projectile Motion Review
A Projectile Motion Example
Arc Length, Unit Tangent Vector, Unit Normal Vector, and Curvature
Line Integrals
Vector Fields, Work, and Flow
Flux
Path Independence and Conservative Vector Fields
Green's Theorem in the Plane, Divergence, and k-component of Curl
Green's Theorem (2 curves), Area using Line Integral
Parametrized Surfaces
Surface Integrals
Curl and Stoke's Thoerem
Divergence Thoerem
Divergence Thoerem Example