Differential Equations
微分方程是研究未知函数及其导数所满足方程的数学学科，是连接数学理论与实际应用的重要桥梁。课程内容包括一阶常微分方程、高阶线性微分方程、常系数线性方程组、幂级数解法、拉普拉斯变换、偏微分方程初步。学生将掌握各种解析解法和数值方法，学会建立和分析数学模型，理解解的存在唯一性理论。本课程在物理、工程、生物、经济等领域有广泛应用。
Differential Equations studies equations involving unknown functions and their derivatives, serving as a bridge between mathematical theory and real-world applications. Topics include first-order ODEs, higher-order linear ODEs, linear systems with constant coefficients, power series solutions, Laplace transforms, and introduction to PDEs. Students will master analytical and numerical methods, learn to build and analyze mathematical models.
建立SIR或SEIR传染病传播微分方程模型，推导基本再生数R0的表达式，分析平衡点的稳定性。使用数值方法（欧拉法或龙格-库塔法）求解模型，研究不同参数（传染率、恢复率）对传播趋势的影响。对比理论分析与数值模拟结果，探讨模型在公共卫生政策评估中的应用。
Build an SIR or SEIR epidemic transmission differential equation model, derive the expression for the basic reproduction number R0, and analyze the stability of equilibrium points. Use numerical methods (Euler or Runge-Kutta) to solve the model, study the impact of different parameters on transmission trends.