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1
What is a Double Integral?
2
Double Integral Example (Ravioli)
3
Changing order of integration
4
A multivariable integral
5
Frullani Integral #shorts
6
Polar integral
7
Integral over a ring
8
Volume of an ice cream cone
9
Gaussian Integral
10
Integral of sin(x^2) from -infinity to infinity
11
Another golden integral
12
Intersection of 2 cylinders volume
13
Triple Integrals
14
Cylindrical Coordinates Example (Cannoli)
15
Triple Integral Example (Gouda Cheese)
16
Cylindrical Coordinates
17
Triple Integrals Hard Example (Princess Cake)
18
Integral over SIMS
19
Intersection of 3 cylinders volume
20
Spherical Coordinates
21
Spherical Coordinates Derivation
22
Spherical coordinates Example
23
Mass of the sun
24
Spherical Limit
25
Gauss cubed
26
Change of Variables
27
The Jacobian
28
The Jacobian 2
29
Polar coordinate integral
30
Hyperbolic Coordinates
31
Distance squared on disk and square
32
Fubini Counterexample
33
Fubini Counterexample (full version)
Description:
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.

Double and Triple Integrals

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