Double Integrals and Iterated Integrals

Corresponding material in the book: Section 15.2, 15.3. Note: We are omitting the question types from the book that require three-dimensional visualization, i.e., those that require sketching figures in three dimensions to compute volumes. What students should definitely get: The procedure for computing double integrals over rectangles using iterated integrals, the procedure for computing double integrals over other regions using iterated integrals, the idea of Fubini’s theorem and its use in interchanging the order of integration. Use of symmetry and inequality-based bounding/estimation techniques. What students should hopefully get: Relation between single and double integrals, dealing with piecewise cases, breaking up domain into smaller pieces when direct integration over entire domain is infeasible. Note: The lecture notes contain only a few examples. For more examples, please refer to worked examples in Sections 15.2 and 15.3.