IMPORTANCE OF DISCRIMINATING AND UNDERSTANDING THE MEANING OF CALCULUS IN COLLEGE PHYSICS

This article conducts a detailed exploration around a classic electromagnetic induction problem in the teaching of “College Physics, ” analyzing the confusions and common mistakes students encounter when solving the problem. The analysis reveals that accurately grasping the physical meanings of various quantities in mathematical integration operations is key to avoiding these issues. The article systematically discusses the differences in integration calculation results under three different scenarios: time-varying magnetic field <i>B</i>(<i>t</i>), spatially-varying magnetic field <i>B</i>(<i>x</i>), and spatiotemporally-varying magnetic field <i>B</i>(<i>x</i>,<i>t</i>). It provides a comprehensive explanation from the perspective of physical implications, clarifying the essence of the problem and highlighting the importance of correctly understanding the meaning of calculus operations when solving practical problems.