Double and Triple Integrals

This course develops double and triple integration in several variables, including changes of order, polar, cylindrical, and spherical coordinates, Jacobians, and geometric applications such as volumes and mass.

Syllabus

What is a Double Integral?.
Double Integral Example (Ravioli).
Changing order of integration.
A multivariable integral.
Frullani Integral #shorts.
Polar integral.
Integral over a ring.
Volume of an ice cream cone.
Gaussian Integral.
Integral of sin(x^2) from -infinity to infinity.
Another golden integral.
Intersection of 2 cylinders volume.
Triple Integrals.
Cylindrical Coordinates Example (Cannoli).
Triple Integral Example (Gouda Cheese).
Cylindrical Coordinates.
Triple Integrals Hard Example (Princess Cake).
Integral over SIMS.
Intersection of 3 cylinders volume.
Spherical Coordinates.
Spherical Coordinates Derivation.
Spherical coordinates Example.
Mass of the sun.
Spherical Limit.
Gauss cubed.
Change of Variables.
The Jacobian.
The Jacobian 2.
Polar coordinate integral.
Hyperbolic Coordinates.
Distance squared on disk and square.
Fubini Counterexample.
Fubini Counterexample (full version).