Course Description: This course is specially designed for middle school students who plan to study AP Calculus AB or AP AP Physics C: Mechanics. Students participating in this course must be familiar with the following mathematical knowledge: geometry, function and inverse function, and trigonometry. This course is a condensed version of unary function calculus, focusing on intuitive understanding of calculus ideas and correct use of calculus tools. The content mainly includes: limit and continuity of functions, derivatives and applications of functions, integrations and applications of functions. 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 ). After the course is completed, students are encoraged to take the AP Calculus AB exam or continue to study the APEX Calculus-based Physics course (APEX P03 and P05). This course is taught online for a total of 30 hours. I hope that students can complete their homework in about 30 hours (3-4 hours of homework every week).
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 precision definition of continue
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
● extreme of a function
Unit 3: Integrations and Applications
● the meaning and definition of the define integral
● the fundamental theorem of calculations
● common integration techniques
● geometric applications of integration
● applications of integration to physics
● differential equations