本书是一部系统全面的微积分教程，涵盖了从基础概念到高级应用的完整内容。书中包括了极限与连续性、微分及其基本性质、复合函数的微分、积分及其累积变化、微分方程和积分应用等主题。内容结构清晰，循序渐进，辅以大量的例题和解析，帮助学生理解并掌握微积分的核心概念及解题技巧，特别适用于准备ap微积分的学习者。这部书为学生提供了深入的理论知识和实用的数学工具，使其能更好地理解和应用微积分于实际问题中。this book is a systematic and comprehensive calculus tutorial that covers a complete range of content from basic concepts to advanced applications. the book includes topics such as limits and continuity, differentiation and its basic properties, differentiation of composite functions, integration and its cumulative change, differential equations, and applications of integration. with a clear content structure and a step-by-step approach, it is supplemented by a large number of examples and analyses to help students understand and master the core concepts of calculus and problem-solving techniques. it is especially suitable for learners preparing for ap calculus. this book provides students with in-depth theoretical knowledge and practical mathematical tools, enabling them to better understand and apply calculus to practical problems.