On the Application of the Infinitesimal Method to Two Categories of Problems in College Physics

The conventional approaches to solving typical problems in college physics, such as the catenary (an extremum problem) and molecular collision problems, are often abstract, making them difficult for students to comprehend. This paper explores the application of the infinitesimal method to these two categories of problems. For physical extremum problems, the method transforms global optimality conditions into constraints on infinitesimal elements, leading to the corresponding differential equations. For molecular collision problems, it utilizes infinitesimal analysis to clarify collision criteria, thereby facilitating the calculation of collision probabilities. Case studies demonstrate that the infinitesimal method can provide a more straightforward, visually clearer, and physically more robust deductive pathway for such problems. This research not only contributes to a deeper understanding of the underlying physics but also offers valuable insights for restructuring knowledge presentation in teaching practice and strengthening the training of “from-local-to-global” scientific thinking.