M408M Learning Module Pages
Main page
Chapter 10: Parametric Equations and
Polar Coordinates
Chapter 12: Vectors and the Geometry of Space
Chapter 13: Vector Functions
Chapter 14: Partial Derivatives
Chapter 15: Multiple Integrals
Learning module LM 15.1: Multiple integrals:
Background
What is a double integral?
Volumes are double integrals
Learning module LM 15.2: Multiple integrals over rectangles:
One variable at a time!
Fubini's Theorem
Notation and order
Learning module LM 15.3: Double integrals over general regions:
Type I and Type II regions
Examples
Order of integration
Area and volume revisited
Learning module LM 15.4: Double integrals in polar coordinates:
$dA=r\; dr\; d\theta$
Examples of polar integrals
Learning module LM 15.5a: Multiple integrals in physics:
Mass, center of mass, and moment of inertia
Triple integrals in physics
Learning module LM 15.5b: Integrals in probability and statistics:
Single integrals in probability
Double integrals in probability
Learning module LM 15.10: Change of variables:
Change of variable in 1 dimension
Mappings in 2 dimensions
Jacobians
Examples
Cylindrical and spherical coordinates
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Chapter 15: Multiple integrals
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