美高微积分衔接手册

《美高微积分衔接手册》是一本专为赴美就读、以中文为母语的学生写的微积分入门与衔接读物。它假设读者只有国内初中的数学基础、从未接触过极限与导数，从零讲起，一步步把知识与语言这两道坎一起跨过。

书中每一个术语和记号第一次出现时，都会讲清它的含义、来历，以及--最关键的--用英文怎么念（f(x) 读作"f of x"；dy/dx 读作"the derivative of y with respect to x"）。中文讲解与课堂上真正会听到的英文词汇并排呈现，并特别标出中美教材在记号与说法上的差异，帮你避开最常见的误读。

本书内容包括：

地基（预备微积分）：函数、指数与对数、三角、圆锥曲线、矩阵、数列与概率

核心（相当于 AP Calculus AB）：极限与连续、导数及其应用、定积分与微积分基本定理

进阶（相当于 AP Calculus BC）：积分技巧、微分方程、无穷级数、幂级数与泰勒级数、参数方程与极坐标

大学先修：空间向量、向量值函数、偏导数与梯度、多重积分、向量微积分、二阶线性微分方程

每一章都标注了层级，读者一眼就知道该学到哪里。例题分步精讲；每章课后练习都含选择题与计算／简答题，配"像老师当面讲"一样详尽的中英双语解析，不仅给答案，更讲清思路、讲明每个错误选项错在哪里。全书配有原创黑白插图，并以脚注追溯英文数学词汇的希腊、拉丁词根，帮助记忆。

A Bridge to U.S. High School Calculus is the book Chinese-native students wish they had on their first day in an American math classroom. Written for readers with only a Chinese junior-high foundation-no prior exposure to limits or derivatives-it teaches calculus from the ground up while quietly closing the language gap that makes an all-English course so daunting.

Every term and symbol is introduced the first time it appears: what it means, where it comes from, and-crucially-how to say it aloud in English (f(x) is "f of x"; dy/dx is "the derivative of y with respect to x"). Chinese explanations sit beside the English vocabulary students will actually hear in class, and the book flags the notation differences between Chinese and American textbooks that so often trip newcomers up.

This book includes:

Foundations (precalculus): functions, exponentials and logarithms, trigonometry, conic sections, matrices, sequences, and probability

Core (AP Calculus AB): limits and continuity, derivatives and their applications, the definite integral and the Fundamental Theorem of Calculus

Advanced (AP Calculus BC): integration techniques, differential equations, infinite series, power and Taylor series, parametric and polar calculus

College preview: vectors in space, vector-valued functions, partial derivatives and gradients, multiple integrals, vector calculus, and second-order linear differential equations

Each chapter is clearly labeled by level, so readers know exactly how far to go. Worked examples are explained step by step, and every end-of-chapter problem set includes both multiple-choice and free-response questions with teacher-style bilingual solutions that explain not just the answer but the reasoning-and why the wrong options are wrong. Original black-and-white figures illustrate every key idea, and footnotes trace the Greek and Latin roots of English math vocabulary to make the terms stick.

Whether you are heading to a U.S. high school, sitting AP Calculus AB or BC, or simply learning calculus in English for the first time, this handbook helps you cross the threshold-of language and of ideas-and begin to enjoy the mathematics of change.