Calculus Chapter 15

Ch 15  Multiple Integrals


Introduction to Double Integrals and Volume


Ch 15.1 Double integrals over rectangles


Double integrals over rectangles


Average Value of a Function of Two Variables


Ch 15.2 Iterated integrals


Iterated integrals and Fubini’s Theorem


Ch 15.3 Double integrals over General Regions


Double Integrals and Volume over a General Region


Double Integrals: Changing the Order of Integration


Ch 15.4 Double integrals in Polar Coordinates


Double Integrals in Polar Coordinates – Example 1, 2 3 and 4


Ch 15.5 Applications of Double integrals


Applications of double integrals


Ch 15.6 Surface Area


Surface area with double integrals


Ch 15.7 Triple integrals


Introduction to Triple Integrals


Triple Integrals and Volume : Part 1, Part 2 and Part 3


Application of Triple Integrals: Mass


Changing the Order of Triple Integrals


Ch 15.8 Triple integrals in Cylindrical Coordinates


Triple Integrals Using Cylindrical Coordinates


Ch 15.9 Triple integrals in Spherical Coordinates


Triple Integrals Using Spherical Coordinates : Part 1 and Part 2


Ch 15.10 Change of Variables in Multiple Integrals


Double Integral: Change of Variables Using the Jacobian : Example 1


Double Integral: Change of Variables Using the Jacobian : Example 2


Triple Integrals: Change of Three Variables Using the Jacobian