1. Definition of Double Integral.

2. Description in two dimensional regions with elemental area .

3. Double integration as limit of sum as .

4. Conditions for existence of double integrals.

5. Evaluation of double integral step by step in 3 cases with illustrations in 2 dimensional figures by appropriate strips parallel to x axis, y axis along with the curves.

6. Illustrations when the limits are provided.

7. Illustrations when the limits are not provided.

8. How to find the limits for x and y by drawing the region of integration and then evaluating it.

9. Finding points of intersection in the region of integration and then evaluation the integrals.

10. Finding the appropriate region of integration.

11. Introduction to change of order of integration.

12. By change of order of integration, the evaluation of double integral becomes easy.

13. Splitting one region R in two regions R1 and R2.

When the students take this course, they will very clearly understand the concepts of double integrals, how to recognize the limits for the given integrals, draw appropriate strips slide them and cover the entire region of integration. They learn how to sketch the figure and then find the region of integration and also to evaluate and get the correct result for the given problems. They get the idea of need of change of order of integration in double integrals.