Through theory teaching, students should master the basic concepts, basic theories, basic operations and basic question-analysis methods of monadic calculus, ordinary differential equations, space analytic geometry, multivariable calculus, and infinite series, and use the basic concepts and methods of advanced mathematics to solve practical problems. This course is one of the basic courses for science and engineering majors. Its main contributions to the development of students’ ability and quality or the achievement of various indicators for graduation requirements are summarized as follows:

(1) Mastered the basic ideas, basic concepts, and problem solutions of calculus.

(2) Established the basic concepts and methods of space analytic geometry and vector algebra; mastered the basic steps of using them to solve problems. 

(3) Mastered the basic concepts, basic operations and basic problem analysis and solving methods of ordinary differential equation and infinite series.

(4) Attention paid to the practice and innovation abilities of students to use their advanced mathematics knowledge to analyze and solve problems. 

(5) A solid mathematical foundation laid for the study of subsequent courses and carrying out scientific researches. 

通过理论教学，使学生掌握一元微积分、常微分方程、空间解析几何、多元微积分以及无穷级数的基本概念、基本理论、基本运算以及分析问题的基本方法，能够将高等数学的基本概念、方法运用到求解实际问题中。本课程是理工科专业的基础课之一，对培养学生能力和素质、对毕业要求各指标点的达成主要贡献点可概括为：

(1) 掌握了微积分的基本思想、基本概念和求解问题的方法。

(2) 建立了空间解析几何和向量代数的基本概念和方法，学会利用其求解问题的基本步骤。

(3) 掌握了常微分方程、无穷级数的基本概念、基本运算以及分析求解问题的基本方法。

(4) 注重学生利用高等数学知识分析求解问题的实践创新能力培养。

(5) 为后继课程的学习以及从事科学研究工作打下坚实的数学基础。

1．同济大学编，《高等数学》(第七版)，高等教育出版社，2014年。

2．清华大学编，《高等数学》，高等教育出版社，1985年。

3．杨有龙等编，《高等数学同步辅导》，西安电子科技大学出版社，2016年。

4．同济大学编，《高等数学习题全解指南》(同济第七版)，高等教育出版社，2014年。

5．吴玉梅等编，《高等数学》(经管类)，科学出版社，2014年。

6．潘斌等编，《Advanced Mathematics (I)》，化学工业出版社，2019 年。