本课程专门为计划学习AP Calculus AB 或者AP AP Physics C: Mechanics的中学生设置。参加本课程的学员须熟悉以下数学知识：几何(geometry)、函数及反函数(function and inverse function)、三角函数 (trigonometry)。本课程为浓缩版一元函数微积分，侧重于直观理解微积分思想和正确使用微积分工具，内容主要包括：函数的极限和连续性(limit and continuity)、函数的导数及应用 (derivatives and applications)、函数的积分及应用 (integrations and applications)。课程结业后学生可报名参加AP Calculus AB 考试或者继续学习APEX Calculus-based Physics课程。 本课程采用网络授课共30小时。希望同学们使用30小时左右时间完成课后作业(每周3-4小时作业复习)。
Course Description: This a condensed course on single-variable calculus. Its aim is to equip students with the necessary skills for the first course of calculus-based university physics or its equivalent. It covers the following topics: limits and continuity, derivatives and their applications, and integrations and their applications. The content of this course is also consistent with the requirement of the AP Calculus AB exam (https://apstudents.collegeboard.org/courses/ap-calculus-ab ).
Prerequisite: Precalculus or Apex M01
Textbook: Strang, Herman, et al. Calculus, Volumes 1. Openstax.
https://openstax.org/details/books/calculus-volume-1
Contents:
Unit 1: Limits and Continuity
● the concept of the limit of a function
● the basic rules for finding the limit of a function
● the concept and precise definition of continuity
Unit 2: Derivatives and Applications
● the meaning and definition of derivatives
● the rules of derivatives
● the derivatives of trigonometry functions and exponential functions
● the derivatives of inverse functions
● derivatives of logarithmic functions
● linear approximation of a function
● extrema of a function
Unit 3: Integrations and Applications
● the meaning and definition of the definite integral
● the fundamental theorem of calculus
● common integration techniques
● geometric applications of integration
● physical applications of integration
● differential equations