Integrating the practice and exploration of curriculum-based ideological and political education into the classroom teaching of "Numerical Analysis" fully leverages the role of classroom instruction as the primary channel for education, achieving an organic unity between "knowledge dissemination" and "value guidance," thereby promoting the transformation from "ideological and political courses" to "curriculum-based ideological and political education." Based on the characteristics of the "Numerical Analysis" course, this paper delves into the connotation and logic of its curriculum-based ideological and political education. It systematically explores ideological and political education resources through practical pathways such as strengthening teacher moral education, focusing on chapter content design, adopting student-centered and flexible teaching methods, and integrating diverse thematic content. Emphasis is placed on increasing the proportion of practical teaching, innovating the integration methods of ideological and political elements, and guiding students to appreciate the power of dialectics through philosophical thinking, while inspiring their minds and cultivating their character through role models and contemporary issues. Taking the curriculum-based ideological and political education practice of the "Numerical Analysis" course at Tsinghua University as a typical case, combined with the actual teaching in colleges and universities, this paper showcases the practical and exploratory efforts of this teaching model through high-level and characteristic teaching, shares experiences and consensus in integrating ideological and political education into classroom teaching and talent cultivation, provides beneficial references for the construction of curriculum-based ideological and political education, and lays a solid foundation for the comprehensive quality cultivation and future career development of students.