微积分

课程介绍 Course Introduction

学分：3 | 先修课：无 | 学期：第1学期

微积分是数据科学的数学基础，主要内容包括极限、微分、积分、级数与多元微积分。课程强调函数变化率、最优化方法与积分应用，为机器学习中的梯度下降、损失函数优化提供理论支撑。学生将掌握导数与偏导数的计算技巧，理解泰勒展开与近似计算，并应用积分处理概率密度函数与期望值问题，为后续统计与算法课程打下坚实基础。

Calculus provides the mathematical foundation for data science, covering limits, differentiation, integration, series, and multivariable calculus. The course emphasizes rates of change, optimization methods, and integral applications, supporting gradient descent and loss function optimization in machine learning. Students master derivative and partial derivative computation, understand Taylor expansions and approximations, and apply integrals to probability density functions and expected values.

大作业 Final Project

作业标题：最优化问题实战

利用梯度下降算法求解实际优化问题，比较不同学习率与收敛条件下的算法表现，分析凸函数与非凸函数场景下的收敛特性，并撰写完整实验报告。

Apply gradient descent algorithms to solve real optimization problems, compare algorithm performance under different learning rates and convergence conditions, analyze convergence properties for convex and non-convex functions, and write a complete experimental report.