Mathematical analysis is a basic course for mathematics majors. Learning mathematical analysis (and advanced algebra) well is the necessary basis for learning other subsequent mathematics courses such as differential geometry, differential equations, complex variable functions, real variable functions and functional analysis, calculation methods, probability theory and mathematical statistics. As one of the most important basic courses in the department of mathematics, the logic and historical inheritance of mathematical science determine the decisive position of mathematical analysis in mathematical science, and many new ideas and applications of mathematics come from this solid foundation. Mathematical analysis is based on the rigor and accuracy of calculus in the theoretical system, thus establishing its basic position in the whole natural science and applying it to various fields of natural science. At the same time, the subject of mathematical research is the object after abstraction, and the mathematical thinking mode has distinct characteristics, including abstraction, logical reasoning, optimal analysis, symbolic operation and so on. The cultivation of these knowledge and abilities needs to be realized through systematic, solid and strict basic education, and the course of mathematical analysis is the most important link. We are based on cultivating outstanding talents with solid mathematical foundation, wide knowledge, innovative consciousness, pioneering spirit and application ability to meet the requirements of the new century.

From the perspective of personnel training, whether a student can learn mathematics well depends largely on whether he can really master the course of mathematical analysis after entering the university. The goal of this course is to master the basic theoretical knowledge of mathematical analysis through systematic study and strict training; Cultivate strict logical thinking ability and reasoning ability; Skilled computing ability and skills; Improve the ability of establishing mathematical model and applying calculus to solve practical application problems. Calculus theory is inseparable from the development of physics, astronomy, geometry and other disciplines. Calculus theory has shown great application vitality since its birth. Therefore, in the teaching of mathematical analysis, we should strengthen the connection between calculus and adjacent disciplines, emphasize the application background and enrich the application content of theory. The teaching of mathematical analysis should not only reflect the strict logical system of this course, but also reflect the development trend of modern mathematics, absorb and adopt modern mathematical ideas and advanced processing methods, and improve students' mathematical literacy. Fudan University has a very good source of students and attracts many excellent students, which makes it possible to realize this training goal and requirement. On the other hand, many excellent students are limited by the teaching plan and study advanced mathematics. However, they have a strong desire to learn mathematical analysis to improve their mathematical literacy (some of them become students majoring in mathematics by changing majors). The course "Principles of Mathematical Analysis" introduced by us came into being, which provided these students with an appropriate opportunity to learn and improve.