北京雁栖湖应用数学研究院

教学目的与要求：
本课程为面向应用数学、物理学及相关专业高年级学生的强化课。课程主要分为三部分：第一部分介绍量纲分析和物理方程的建立，让学生深刻认识到物理量和数学量的关系，如何正确建立物理方程(应用数学的过程)。第二部分除了对麦氏方程组进行再讨论外(如初值表述、纳米尺度边界条件、含磁荷的方程组等)，增加了相对论电磁学、拓扑电磁学等前沿研究成果，让学生掌握电磁场现象、概念和核心数学方程，深刻理解物理现象的相对性和物理规律的绝对性。第三部分讲解定量分析所需的数值算法、软件知识基础、以及最新发展趋势(如AI计算电磁学)。总之，通过本课程的学习可提高学生运用基本物理规律、数值算法解决应用数学问题的能力，为以后从事专业理论研究和交叉学科研究打下坚实的基础。

Teaching Objectives and Requirements:
This advanced course provides senior undergraduate students in applied mathematics, physics, and related engineering disciplines with a rigorous foundation in electromagnetic theory and computational modeling. The curriculum is structured around three core modules:
Part I: Dimensional Analysis & Mathematical Modeling:
Establishes the principles of scaling, dimensional analysis, and the formal mathematical formulation of physical laws.
Part II: Advanced & Frontier Electromagnetism:
Re-examines Maxwell’s equations—incorporating initial value formulations, nanoscale boundary conditions, and magnetic charges—while introducing cutting-edge topics such as relativistic electrodynamics and topological electromagnetism.
Part III: Computational Methods & AI Frontiers:
Covers core numerical algorithms (FEM, FDM, MoM), simulation tools (MATLAB, COMSOL), and modern paradigms including Mimetic FEM, Finite Integration Technique (FIT), and Physics-Informed Neural Networks (PINNs).
Ultimately, students will be equipped to translate fundamental physical laws into rigorous mathematical models, implement state-of-the-art computational algorithms, and address complex interdisciplinary research challenges.