Calculus I
微积分I是数学专业的基础核心课程，主要内容包括函数与极限、导数与微分、中值定理与导数应用、不定积分与定积分。通过本课程的学习，学生将掌握极限的严格定义、求导法则、积分基本定理，理解微积分的基本思想方法，为后续数学课程和物理、工程等应用学科奠定坚实基础。课程注重理论与应用的结合，培养学生的逻辑思维和计算能力。
Calculus I is a foundational core course for mathematics majors, covering functions and limits, derivatives and differentials, mean value theorems and derivative applications, indefinite and definite integrals. Students will master the rigorous definition of limits, differentiation rules, and the fundamental theorem of calculus. The course emphasizes both theory and applications, developing students' logical thinking and computational abilities.
选择一个真实的物理运动问题（如自由落体、弹簧振子或抛体运动），建立数学模型，运用导数求解速度与加速度，通过积分计算位移与做功。要求包含问题描述、模型建立、详细推导过程、数值验证以及结果分析，完整展示微积分从理论到实际应用的全过程。
Choose a real physics motion problem (free fall, spring oscillator, or projectile motion), build a mathematical model, use derivatives to find velocity and acceleration, and compute displacement and work through integration. Include problem description, model formulation, detailed derivation, numerical verification, and result analysis.