First, the first volume:
1 function and limit.
Derivative and differential.
Application of 3 derivative.
4 indefinite integral.
5 definite integral.
6 differential equation.
7 multivariate function differential method.
8 double integral
Second, the second volume:
1 determinant.
2 matrix.
Three vectors.
4 linear equation.
Similarity matrix and quadratic form.
6 probability.
7 Random variables and their distribution.
Numerical characteristics of random variables.
9 theorem of large numbers and central limit theorem.
Advanced mathematics is one of the compulsory courses in universities, which is divided into two volumes. Generally, freshmen study one book each semester. This book is edited by Tian and published on 20 14. This book can be used as an advanced mathematics textbook or teaching reference book for undergraduates majoring in science and engineering, especially electronic information, and can also be used by students for self-study.
Extended data:
In China, students majoring in science and engineering (except mathematics, who study mathematical analysis) have difficulty in learning mathematics, which is often called "advanced mathematics" in textbooks; Students majoring in literature and history learn a little shallower mathematics, and their textbooks are often called "calculus". Different majors in science and engineering, literature and history have different degrees of depth.
It is advanced mathematics that studies variables, but advanced mathematics does not only study variables. As for the courses related to "advanced mathematics", there are usually: linear algebra (advanced algebra for mathematics majors), probability theory and mathematical statistics (some mathematics majors study independently).
Advanced mathematics has its inherent characteristics, that is, high abstraction, strict logic and wide application. Abstraction and computability are the most basic and remarkable characteristics of mathematics. With a high degree of abstraction and unity, we can profoundly reveal its essential laws and make it more widely used. Strict logic means that in the induction and arrangement of mathematical theory, whether it is concept and expression, or judgment and reasoning, we must use the rules of logic and follow the laws of thinking.
Therefore, mathematics is also a way of thinking, and the process of learning mathematics is the process of thinking training. The progress of human society is inseparable from the wide application of mathematics. Especially in modern times, the appearance and popularization of electronic computers have broadened the application field of mathematics. Modern mathematics is becoming a powerful driving force for the development of science and technology, and it has also penetrated into the field of social sciences extensively and deeply.
References:
Baidu encyclopedia-advanced mathematics