The two authors have been teaching advanced mathematics in Peking University for forty years. They have rich teaching experience and are well aware of students' difficulties and puzzles. Focusing on the basic content and teaching requirements of this course, according to the difficulties and mistakes students encounter when they are beginners, the typical examples are carefully analyzed, explained and commented, and summarized to help students better understand the content of Advanced Mathematics and master its basic theory and correct problem-solving methods and skills. The book is divided into 13 chapters, including: one-dimensional calculus, spatial analytic geometry, multivariate calculus, infinite series (including Fourier series) and ordinary differential equations. In each section, there is a summary of the basic theoretical content, the explanation and analysis of typical examples, and the exercises done by the students themselves. At the end of the book, there are the answers to the exercises. In order to meet the requirements of students at different levels, this book also systematically explains a proper amount of comprehensive problems and examples (marked with ") with certain difficulty, which can not only open up students' problem-solving ideas, help them learn advanced mathematics well, but also serve as a review for postgraduate entrance examination.
This book can be used as a study guide for college students majoring in science, technology, medicine and agriculture in comprehensive universities, science and engineering universities and normal universities to learn advanced mathematics. Adult education and self-taught students can also read it. This book is also a good teaching reference book and a review book for postgraduate students and young teachers. The first chapter is the preparatory knowledge of calculus.
1 function
abstract
Typical case analysis
This section outlines
Exercise 1. 1
2. The concept and properties of limit and several methods to find it.
abstract
Typical case analysis
This section outlines
Exercise 1.2
Zhou Jianying of three functions, Zhou Jianying of Li Zhengyuan's guide to solving advanced mathematics problems, and Li Zhengyuan's answers to after-class exercises * continuity, the nature of continuous functions.
abstract
Typical case analysis