At the time of writing this article, the semester is drawing to a close, and the study of practical analysis has already had a basic framework. In this case, I want to objectively give the learning content of the practical analysis course and some of my own experiences. Please correct me if there are any mistakes.
fundamental principle
Real analysis is one of the compulsory courses for mathematics majors. Generally speaking, students majoring in this major will learn real analysis after studying mathematical analysis for three semesters. Non-math majors can study calculus for two semesters if they want to, but it will be more difficult. Students who are interested in this can try to learn the basic principles of mathematical analysis first, and it will be easier to learn real analysis after they have a certain understanding of the ideas of mathematical analysis.
main content
Before learning a course, we will inevitably ask such questions: what is the main purpose of this course, or what is the use of learning such a course. We use the following examples to introduce the content of real analysis learning.
First of all, we have studied the integral in calculus, which can be simply understood as the limit of riemann sum. In fact, the integral we have learned is also called. Let's review this part first.
Since we can split the shaft, can we split the shaft? The answer is yes. In order to get the integral in this way (in fact, this is what we call integral), mathematicians have established theories related to real analysis.
Let's look at a simple example.