Explore the world of multivariable calculus through a comprehensive series of video lectures covering double and triple integrals. Learn about various integration techniques, including changing the order of integration, polar coordinates, cylindrical coordinates, and spherical coordinates. Dive into practical applications such as calculating volumes of ice cream cones, intersecting cylinders, and even the mass of the sun. Master advanced concepts like the Gaussian Integral, Frullani Integral, and the Jacobian. Tackle challenging examples involving ravioli, cannoli, Gouda cheese, and princess cake to solidify your understanding. Investigate special topics such as hyperbolic coordinates, Fubini's theorem, and its counterexamples. Enhance your mathematical skills and gain a deeper appreciation for the power and versatility of multivariable integration.
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
