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Introducing the double integral
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Classroom Contents
APEX Calculus - Multiple Integration
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- 1 Introducing the double integral
- 2 Defining the double integral
- 3 Iterated integrals and Fubini's theorem
- 4 Examples of integrals over rectangles
- 5 Integrals over general regions
- 6 Example: integral over a general region
- 7 Reversing the order of integration: Example 1
- 8 Reversing the order of integration: Example 2
- 9 Double integrals in polar coordinates
- 10 Polar coordinates: Examples 1 and 2
- 11 Polar coordinates: Example 3
- 12 Example: volume of a tetrahedron
- 13 Example: volume using polar coordinates
- 14 Introduction to triple integrals
- 15 Tetrahedron volume, as a triple integral
- 16 Changing order of integration in a triple integral
- 17 Volume problem leading to cylindrical coordinates
- 18 The cylindrical coordinate system
- 19 Cylindrical coordinates and volume of a cone
- 20 Introducing spherical coordinates
- 21 Integration in spherical coordinates
- 22 Volume of a spherical wedge
- 23 Volume of a conical cup
- 24 The spherical coordinate Jacobian
- 25 Transformations and change of variables
- 26 Change of variables example: parallelogram
- 27 Working with the inverse transformation (a shortcut!)
- 28 Another change of variables example
