# AP Calculus

**Description**

This is a college level course in Calculus. This course will cover all of the topics specified by the College Board for the AP Calculus AB exam. This course is normally taken by students in grade twelve. Students should have completed Precalculus before enrolling in Calculus.

This course has passed the AP Course Audit and has been approved by the College Board to bear the "AP" designation.

**Lectures and Class Time**

Class time will primarily be spent on instruction. Students should bring their Student Workbook to each class, or a printout of the pages for that week. The pages of the workbook are identical to the instructor's lecture notes, except the student version has the solutions and answers deleted. During the lecture the students take notes and solve the example problems in the workbook.

Videos of the lectures are also available online, and these videos go through the same lecture notes, point by point. Students use the videos to cover any material that time constraints did not permit us to cover in our weekly class. Or, if a student misses a class or needs to review the material, all of the course content is available online. It is possible to take the entire course online via distance learning, and many students have done so.

**Textbook**

This course was originally based on Calculus by Paul Foerster, 2nd edition, published by Key Curriculum Press, 2005. This is an excellent text and is on the College Board’s list of approved texts for this AP Calculus. Today, the course consists of Mr. Owens' own materials.

**Homework, Tests and Grades**

Students will be given specific assignments to complete each week. Assignments will consist of Practice Problems from the workbook, instructional videos online, and written assignments.

In this class there is a distinction between Practice Problems and Homework Problems. Practice Problems are found in the workbook and in the textbook, and students check their answers with the solutions provided. Homework assignments and tests are printed from the website, completed, and turned in for a grade.

To maximize instructional time in class, tests will be given at home. Students will take a cumulative exam at the end of the first semester and may choose to take the Advanced Placement exam at a location of their choosing. Students will receive a numerical grade for each semester and for the year. The grade is calculated based on tests, graded homework and the final exam.

**Difficulty Level**

AP Calculus is a college level class, as indicated by the “Advanced Placement” designation. The material is conceptually challenging. Homework assignments and tests will reflect the difficulty of the material, and will be comparable to the difficulty level of problems that students will encounter on the AP Exam.

Students are not required to sit for the AP exam in may. Students who do not intend to take the AP exam may opt to take the less difficult non-AP version of each chapter test.

**Internet Access**

Access to a computer with a high speed internet connection is strongly recommended. Instructional materials such as lecture videos, lecture notes, homework assignments and tests will be available over the internet. Graded assignments and tests will also be returned via email in order to provide more timely feedback. Progress reports will be put on the website and updated regularly.

**The Instructor**

Derek Owens graduated from Duke University in 1988 with a degree in mechanical engineering and physics. He taught physics, honors physics, AP Physics, and AP computer science at The Westminster Schools in Atlanta, GA from 1988-2000. He worked at the TIP program at Duke for two years, teaching physics and heading the Satellite Science Program. He received a National Science Foundation scholarship and studied history and philosophy of science at L’Abri Fellowship in England. He worked as a software developer for six years before returning to teaching. Since 2006, he has been a full time teacher for homeschoolers in the Atlanta area. He and his wife Amor and their two children Claire and David attend Twelve Stone Church, a non-denominational church near their home in Lawrenceville.

**Course Outline**

This course covers all of the topics required for the AP Calculus AB exam.

**Chapter 1: Introduction**

The problems that Calculus solves, introduction to derivatives, finding rates of change from graphs, from equations, and from data, Numerical derivatives, Introduction to Integrals, Approximating integrals from graphs, from equations and from data, the Trapezoid Rule

**Chapter 2: Limits**(br/>A graphical approach to limits, Describing function behavior with limits, Asymptotes, Rational Functions, Polynomial end behavior, The Limit Theorems, Evaluating limits, Continuity, The Intermediate Value Theorem

**Chapter 3: Derivatives**

A graphical look at derivatives, Difference Quotients, the Derived Function, Notation, Numerical calculations of derivatives, Tangents and Linear Approximation, Differentiability and Continuity, the Chain Rule, the Product Rule, the Quotient Rule, Leibniz' Proofs, Derivatives of Trig Functions, Implicit Differentiation, Derivatives of Inverse Functions, Derivatives of Inverse Trig Functions

**Chapter 4:**The Extreme Value Theorem, Rolle's Theorem and the Mean Value Theorem, First and Second Derivatives, Concavity and Inflection Points, Graphs and Curve Sketching, The Calculus of Motion, Max-Min problems, Related Rates, Practice

Applications of Derivatives

**Chapter 5:**Antiderivatives, Integrals, Infinitesimals, Riemann Sums, Definite Integrals, The Fundamental Theorem of Calculus, Properties of Definite Integrals, Numerical Methods, Integration by Substitution, Average Value

Integrals

**Chapter 6: Exponential Functions and Differential Equations**

Derivatives of exponential functions, Derivatives of logarithmic functions, Derivatives and integrals of base b exponents, Integrals with variable limits, Logarithmic Differentiation, Integrals of trig functions, Intro to Differential Equations, Examples and applications, Slope Fields, Euler's Identity

**Chapter 7: Applications of Integrals**

The area of a plane region, The Calculus of Motion, Real world applications, Integrating to find volumes, Plane Slicing, Solids of Revolution, Cylindrical Shells