Fudan University undergraduate mathematics and applied mathematics majors use this set of textbooks to teach mathematical analysis. Personally, I think it is an excellent textbook that is very systematic and clear, can keep up with the times, and the exercises are well written (this set of books also has supporting exercises). The first edition of this set of books won the first prize of excellent teaching materials in national colleges and universities in 2002. The first editor-in-chief, Mr. Chen Jixiu, is the first national famous teacher who has been devoted to the teaching of mathematical analysis in the lower grades of undergraduate courses, and is a very excellent teacher.
Annex: Executive Summary
This book is the result of the Ministry of Education's Reform Plan of Higher Education Teaching Content and Curriculum System Facing 2 1 century, the Ministry of Education's Mathematical Analysis of Establishing Excellent Famous Courses in Basic Science Talent Training Base and the Higher Education Press's Construction Plan of 100 Excellent Courses Textbooks for Higher Education, and it is a course textbook facing 2 1 century. This book is based on "Mathematical Analysis" published by the Department of Mathematics of Fudan University in recent 20 years, and is written to meet the needs of mathematics teaching reform in 2 1 century. Based on many years' teaching experience, the author has carried out beneficial reforms in teaching materials from the aspects of system, content, viewpoint, method and treatment.
This book is published in two volumes.
The first volume consists of eight chapters: set and mapping, sequence limit, function limit and continuous function, differential, differential mean value theorem and its application, indefinite integral, definite integral and generalized integral.
The second volume consists of eight chapters: series of several terms, series of function terms, limit and continuity in Euclidean space, differential calculus of multivariate functions, multiple integrals, curve integrals and surface integrals, parametric variable integrals and Fourier series.
This book can be used as a teaching material for mathematical analysis courses of mathematics majors in colleges and universities, and can also be used by other related majors.
In addition, the so-called reference, you can also look at the "Principles of Mathematical Analysis" written by Fylking Goltz (a set seems to have six volumes), which is a very classic old book on mathematical analysis, very detailed. There is also a new handout on mathematical analysis (three volumes) from Peking University, which is also very good. You can refer to it.
As for Midovic's problem solving, I think it is more suitable for the study of engineering mathematical analysis, because the proportion of calculation problems is large, and the basic theoretical analysis and proof are not paid enough attention. Of course, this is a good exercise book for practicing calculation. But if you ask yourself not only to use calculus tools, but to master the theory more comprehensively and thoroughly, a few Midovic are not enough. I recommend a book "Typical Problems and Methods in Mathematical Analysis" published by Higher Education Press and written by Pei, which is quite thick and helpful to master mathematical analysis comprehensively.