Jiazheng Chen
美国高中微积分，很多中国学生不是听不懂，而是一到做题就不知道从哪里下手：同一类题，换一个函数、改一个条件，就又卡住了。《美高微积分解题手册》专门解决这个问题。它不是题库，而是从整门课里挑出 42 道最核心的'母题'，把每一道从头到尾讲透。全书 12 章，覆盖美国高中微积分的全部内容（对应 AP® Calculus AB 与 BC 的考查范围）：极限与连续、导数与求导法则、链式法则与隐函数、用导数分析函数、导数的应用、微积分基本定理、积分技巧、定积分的应用、微分方程、参数方程与极坐标、数列与级数、泰勒级数。每道母题都按同样的八段展开：题目、识别模型、通用思路、分步详解、变式（一次只改一个条件，看解法哪里不变、哪里要变）、一题多解、易错点、母题小结。全书 150 多个变式，是本书的核心。第四章拿一个函数把求导、切线、单调、极值、凹凸、拐点、画图、中值定理、洛必达法则依次问到底；第八章拿一块区域把面积、圆盘法、垫圈法、柱壳法和换轴旋转一次讲完。本书用中文讲解，专业术语首次出现时中英对照，并配有词根词缀脚注，帮助读者把术语和英文课堂、英文考卷对上号。国内教材与美国教材在符号和说法上的不同（如对数写法、临界点、凹凸、反三角记号、收敛区间端点），书中都专门作了对照，并一律以美国写法为准。常用公式和定理大多讲清来历和使用条件；全书配 65 幅原创黑白插图。适合在美国读高中、正在学微积分的中文母语学生，也适合准备出国的学生和辅导老师使用。This Chinese-language guide helps students who understand calculus concepts but freeze when a problem changes. It works 42 classic problems from the entire high school calculus course, the full scope of AP® Calculus AB and BC, through the same eight steps: the problem, recognizing its type, the general method, a complete step-by-step solution, variations that change one condition at a time, alternative solutions, common mistakes, and a takeaway. More than 150 variations show which steps stay the same and which must change. Key terms appear in both Chinese and English with word-root notes, and U.S. notation is compared with conventions used in China. Includes 65 original black-and-white figures. An English edition is available as Practice to Mastery: Solving Classic Problems in High School Calculus.AP® and Advanced Placement® are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, this product.
