M408M Learning Module Pages

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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

Learning module LM 15.2: Multiple integrals over rectangles:

Learning module LM 15.3: Double integrals over general regions:

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:

Learning module LM 15.5b: Integrals in probability and statistics:

Learning module LM 15.10: Change of variables:


Learning Module 15.4: Double integrals in polar coordinates