Before liberation, this course was divided into elementary calculus and advanced calculus, which taught calculus operation and application, real number theory and limit theory respectively.
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Mathematical analysis is coordinated with the other two basic courses (Advanced Algebra and Analytic Geometry) and takes itself as the main task, which forms the same foundation of all branches of modern mathematics. Almost all professional courses need the support of this course. As the refinement and deepening of typical problems in mathematical analysis, courses such as real number construction theory, introduction to analysis and field theory can be arranged. Its follow-up courses include real variable function, complex variable function, functional analysis, point set topology and so on. It is the necessary direct foundation for studying courses with strong application such as ordinary differential equations, partial differential equations, probability theory and mathematical models, and it also has a potential far-reaching influence on the study of numerical calculation, mathematical experiments, logic and computational science.
This course aims to cultivate students' rational thinking ability, logical expression ability and mathematical literacy, respect students' subjective spirit in learning, pay attention to strengthening the cultivation of students' mathematical literacy, and improve students' creative analysis and problem-solving ability.
Mathematical analysis is one of the most important basic courses for mathematics and applied mathematics majors in colleges and universities. This course has the longest teaching span (four semesters), the most teaching hours (nearly 300 class hours) and the most credits (17 credits), and has been highly valued by schools, departments, teachers and students. Its basic contents mainly include function, limit and continuity, differential calculus, integral calculus, infinite series, multivariate function, multivariate function limit, multivariate differential calculus, multiple integral and curve and surface integral. Mathematical analysis can become the central course of analytical mathematics series because of many follow-up courses of mathematics specialty, such as real variable function, complex variable function, probability theory and mathematical statistics, topology, functional analysis, differential equations and so on. All of them are based on mathematical analysis, and some even directly extend mathematical analysis. The idea of analytical science is widely permeated in many courses. The teaching process of mathematical analysis has a direct and important influence on the teaching of advanced mathematics courses in computer, physics, chemistry, biology, geography, audio-visual education, electronics, economics and other arts and sciences. Mathematical analysis not only provides the necessary basic knowledge for the study of subsequent courses in content, but also embodies the mathematical thought, logical reasoning method and problem-solving skills of analysis, which plays a fundamental role in the whole mathematical study and scientific research. Because of this, mathematical analysis has always been one of the compulsory subjects for graduate students in basic mathematics, applied mathematics and other related disciplines.
Mathematical analysis is one of the courses with a long history in higher education. Before liberation, this course was divided into elementary calculus and advanced calculus, which taught calculus operation and application, real number theory and limit theory respectively. After the founding of New China, he studied the Soviet model and used more Soviet textbooks. The course of mathematical analysis has devoted a lot of space to teaching limit theory, overemphasizing the theoretical basis, ignoring the intuition and application of mathematics, and talking about the operation and application of differential and integral. As a result, some students can't accept it, and some students are divorced from reality, their thoughts are rigid, and they go to the other extreme. Since the late 1950s and early 1960s, China has carried out many educational reforms, and successively published a number of new teaching materials such as mathematical analysis, and the curriculum content system has gradually taken shape. Since the reform and opening up, 1977 symposium on the outline of science mathematics textbooks in colleges and universities has formulated the outline of mathematical analysis, and 1980 in May, the editorial board of science mathematics textbooks in colleges and universities revised the outline of mathematical analysis. After the promulgation and implementation of the Ministry of Education, various versions of mathematical analysis textbooks were published one after another. The characteristics of these textbooks are that they are in line with the teaching practice in China in terms of material selection, systematicness and readability. Since 1990s, especially with the implementation of "National Curriculum Textbook Plan for 2 1 Century", many mathematical analysis textbooks have been revised, even revised many times. The revised textbook is more suitable for the situation of higher education in China in the 2nd/Kloc-0th century, which embodies the advanced nature of the textbook, the integrity of the content system, the rationality of content processing, the rigorousness of theory and the teachability and readability of the textbook.
Since the establishment of 1929 mathematics department, our school has been offering mathematical analysis courses. For decades, many well-known professors have personally taught mathematical analysis, maintaining the advantages of excellent teaching team, exquisite professional level and rich teaching experience, and forming a fine tradition of connecting the preceding with the following. In the 1950s, a group of teachers with high academic attainments and deep qualifications gave lectures. The main textbooks used are Principles of Mathematical Analysis by Fichkin Goldz of the former Soviet Union, A Concise Course of Mathematical Analysis by Qin Xin, and Mathematical Analysis Problem Set by Jimmy Dovich. After 1960s, he used Mathematical Analysis written by Fudan University, China University of Science and Technology, Jilin University, Wuhan University and Wang and Zhuang Yadong respectively. In recent ten years, the teaching team of Mathematical Analysis published by East China Normal University has gradually become younger. A group of young and middle-aged teachers have taken up teaching posts, and many years of teaching practice have made them mature and become the teaching backbone of this course. One of the practices that we have been insisting on for many years is that for newly recruited young teachers, we should first arrange as much help as possible for them to carry out mathematical analysis, so that they can consolidate their analytical ability, and then be distributed to various teaching posts. Practice has proved that this method is effective.
For a long time, schools and departments have always attached great importance to this course, thinking that mathematical analysis is the foundation of mathematics specialty, and the most important thing is to actively support and promote the construction of mathematical analysis course. 1992, mathematical analysis is included in the curriculum construction plan. Through the implementation of the construction, it won the first prize of the curriculum construction evaluation of the provincial education commission and the excellent teaching achievement award of the school the following year. On this basis, through the joint efforts of all teachers, this course was included in 1999 provincial key construction course. 200 1 related teaching and research projects won the first prize of provincial teaching achievements.