Here are the lecture notes, that are designed with the previously posted advanced calculus assignments. The course is designed for a group of students who has basic acquaintanceship with introductory calculus material. The purpose of the course is to introduce the theoretical background in a self contained manner. There are 22 lectures, each is approximately 90 minutes.
If you have any questions, please let me know. Any standard introductory analysis book may accompany the above lecture notes. There were intended to be self contained.