RESEARCH ON MODELING APPLICATION OF ORDINARY DIFFERENTIAL EQUATIONS TO PRACTICAL PROBLEMS AND CASE-ORIENTED TEACHING

Ordinary differential equation is an important component of higher mathematics, and its modeling method is widely applied to solving various practical problems. Traditional teaching of ordinary differential equation lays particular emphasis on theoretical deduction, which makes it difficult for students to perceive the application value of mathematical knowledge. In this paper, the case-based teaching method is adopted, and three typical practical problems including solution dilution, identification of painting and calligraphy counterfeits and computer virus propagation are selected. The corresponding ordinary differential equation models are established and solved respectively, with the internal laws and mathematical principles of each problem analyzed. Through the modeling and solution of multi-field cases, the advantages of ordinary differential equations in depicting natural phenomena and practical problems are demonstrated, and the teaching concept of integrating theory with practice is reflected. Practice has proved that case-based teaching can effectively reduce the learning difficulty of ordinary differential equations, stimulate students' learning interest, help students grasp the idea of mathematical modeling and improve their ability of knowledge application, which plays a positive role in improving the teaching effect of the ordinary differential equation course.