This course is designed to meet the needs of preparatory teaching for foreign students, improve the learning quality, and do a good job in the connection between middle school mathematics and college mathematics. The course content closely follows the basic requirements and extension of elementary mathematics in calculus teaching, focuses on helping students review the knowledge points of elementary mathematics, promotes the improvement of students' thinking methods, pays attention to the foundation and ability, and emphasizes summary and improvement. The main task of the course is to make basic theoretical, methodological and ideological preparations for foreign students to further study calculus. In terms of content arrangement, it not only reflects the connection between middle school and university courses, in line with students' cognitive law, but also reflects some calculus ideas, which is conducive to undergraduate learning.