This course covers the learning outcomes and goals of understanding double and triple integrals. Students will learn about changing the order of integration, multivariable integrals, polar integrals, cylindrical and spherical coordinates, as well as the Jacobian and hyperbolic coordinates. The course teaches skills such as calculating volumes, masses, and distances using integrals. The teaching method includes examples like ice cream cones, cylinders, and Gaussian integrals. This course is intended for learners interested in advanced calculus and mathematics.
Overview
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).
Taught by
Dr Peyam
