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:

      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
      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
      Cylindrical and spherical coordinates

Chapter 15: Multiple integrals