本文旨在探讨《高等代数》课程在思政教育与学生文化自信培养方面的作用。通过分析《高等代数》课程内容与思政教育的结合点,以及该课程在学生文化自信形成中的独特价值,本文提出了一系列教学改革措施,以期在传授数学知识的同时,提升学生的思政素养和文化自信。 This paper aims to explore the role of the Advanced Algebra course in ideological and political education and the cultivation of students’ cultural confidence. By analyzing the integration points between the content of the Advanced Algebra course and ideological and political education, as well as the unique value of this course in shaping students’ cultural confidence, this paper proposes a series of teaching reform measures. These measures are intended to enhance students’ ideological and political literacy and cultural confidence while imparting mathematical knowledge.
利用积分因子把非恰当微分方程转化为恰当微分方程是求解非恰当微分方程的重要手段。如何寻找合适的积分因子是转化问题关键之所在。首先,给出非恰当微分方程存在三种类型积分因子的充要条件。然后,给出相应的例子说明这些充要条件的应用。最后,对这些充要条件进行简单总结并提出一些研究展望。It is an important means to solve non-exact differential equations by transforming them to exact differential equations using integral factors. How to find the appropriate integrating factors is the key to the transformation problem. Firstly, we present the sufficient and necessary conditions for the existence of three types of integral factors for non-exact differential equations. Then, some examples are given to illustrate the application of these necessary and sufficient conditions. Finally, these necessary and sufficient conditions are summarized briefly and some research prospects are put forward.
