# Dr. Du’s AP Calculus AB/BC Summer Course

Dates: 6/14/2022 – 8/2/2022, Tues & Thurs

Time: 6:00 pm – 8:00 pm

Prerequisite: Precalculus with a satisfactory grade.

Course Materials:

• Textbook: Calculus: Early Transcendentals, 8th Edition, J. Stewart
• Course Notes
• A TI-83/TI-84 graphing calculator
• Others: 3-ring binder, loose-leaf paper/notebook, pencils, eraser, colored pen, stapler

Course Description

This course is designed to introduce basic concepts, methods, and applications of calculus of functions of a single variable and prepare students for the AP Calculus AB/BC exams. Topics covered include limits and continuity, derivatives and their applications, indefinite integrals, definite integrals and their applications, differential equations, calculus for parametric equations and polar coordinates, and infinite series . Conceptual understanding and problem solving will be emphasized throughout the course.

Homework

Homework will be assigned for each lesson. Students are expected to spend 2 to 4 hours per week to do homework and read the book.

Course Objectives

Upon completion of the course, the student should be able to:

1. Evaluate limits of functions algebraically, graphically, and numerically. Find horizontal and vertical asymptotes of function graphs.
2. Understand the concept of continuity. Identify the points of discontinuity for a function. Use the Intermediate Value Theorem.
3. Understand the concept of derivative. Find derivatives using the basic differentiation rules and formulas. Find derivatives by implicit differentiation. Solve related rates problems. 4. Know the Mean Value Theorem. Find the intervals of increase and decrease, the relative maximums and minimums, and the intervals of concavity and points of inflection of a function. Analyze and sketch the graph of a function.
4. Use L’Hôpital’s Rules to evaluate indeterminate forms.
5. Solve optimization problems.
6. Find indefinite integrals of functions using the basic integration rules, substitution, and integration by parts.
7. Understand the concept of definite integral. Evaluate definite integrals by using the Fundamental Theorem of Calculus. Use definite integrals to model net change. Evaluate improper integrals 9. Apply definite integrals to areas, volumes, and arc lengths.
8. Sketch a direction field of a differential equation. Use Euler’s Method to approximate a solution of a differential equation. Solve separable differential equations.
9. Find the slope of a parametric curve. Find the arc length of a parametric curve. Find the slope of a polar curve. Find the area under a polar curve.
10. Find the sum of a geometric series, if it converges.
11. Test series for convergence using various tests.
12. Find the radius of convergence and interval of convergence of a power series. 15. Find a power series representation of a function.
13. Apply power series in numerical approximations.

Tentative Course Schedule

(Note: The section numbers refer to the Stewart book.)

 TUESDAY THURSDAY June 14th 1 Limits and Continuity: §2.1–§2.6 16th 2 Differentiation: §2.7–§2.8, §3.1–§3.6 21st 3 Differentiation: §3.7, §3.9, §3.10 23rd 4 Applications of Differentiation: §4.1–§4.4 28th 5 Applications of Differentiation: §4.5–§4.7 30th 6 Integration: §4.9, §5.1–§5.3 July 5th 7 Integration: §5.4–§5.5, §6.1 7th 8 Applications of Integration: §6.2, §6.5, §8.1 12th 9 More on Integration: §7.1, §7.4, §7.8 14th 10 More on Applications of Integration: §6.3, §6.5, §8.1 19th 11 Differential Equations: §9.1–§9.3 21st 12 Parametric Equations and Polar Coordinates: §10.1–§10.4 26th 13 Parametric Equations and Polar Coordinates: §13.1–§13.2 28th 14 Infinite Sequences and Series: §11.1–§11.7 Aug 2nd 15 Infinite Sequences and Series: §11.8–§11.11 4th