Abstract: Under the background of new engineering construction, advanced mathematics, as an important basic core course of science and engineering majors in applied undergraduate colleges, its teaching innovation reform is imminent. In order to cultivate innovative and application-oriented talents, the article constructs a three-dimensional innovative initiative of optimizing the integration of teaching contents, multifaceted hybrid teaching based on BOPPPS, and optimizing assessment and evaluation, which aims to continuously improve teachers'teaching level, students'learning effect, students'engineering practical application ability and course teaching quality. The innovative measure can provide reference suggestions for the reform of advanced mathematics courses under the new engineering background.

Key words: New engineering, Advanced mathematics, Teaching innovation, Multifaceted hybrid teaching, Formative assessment of competences, Applied undergraduate