• Classroom Information
I teach Advanced Placement Calculus AB, Advanced Placement Calculus BC, and AIS.  Homework can be accessed on Schoology.

CALCULUS BC SYLLABUS

Unit One:       Limits and Continuity

2.1            Rates of Change and Limits

Formal Definition of Limit

Evaluate limits analytically, one-sided limits

Trig limits

2.2            Limits Involving Infinity

Vertical Asymptotes

2.3             Continuity

2.4             Rates of Change and Tangent Lines

Intermediate Value Theorem

Review and Test

Unit Two:       Derivatives

3.1                   Derivative of a Function

3.2                    Differentiability

3.3                   Rules for Differentiation

3.4                   Velocity and other Rates of Change

3.5                   Derivative of Trigonometric Functions

3.6                   Chain Rule

3.7                   Implicit Differentiation

3.8                   Derivatives of Inverse Trig Functions

3.9                   Derivatives of Exponential and Logarithmic Functions

Review and Test

Unit Three:    Applications of Derivatives

4.1                   Extreme Values of Functions

4.2                  Mean Value Theorem

4.3                  Connecting f’ and f” with the graph of f

4.4                  Modeling and Optimization

4.5                   Linearization and Differentials

4.6                   Related Rates

Review and Test

Unit Four:      The Definite Integral

5.1                  Estimating with Finite Sums

5.2                  Definite Integrals

5.3                  Definite Integrals and Antiderivatives

5.4                  Fundamental Theorem of Calculus

5.5                  Trapezoidal Rule

Simpson’s Rule

Review and Test

Unit Five:       Differential Equations and Modeling

6.1                     Antiderivatives and Slope Fields

6.2                    Integration by Substitution

6.3                    Integration by Parts

8.4                    Partial Fraction and Completing the Square

Solving Differential Equations

6.4                    Population Growth

Exponential Model

Logistic Model

6.5                    Numerical Methods, including Euler's Method

Review and Test

Midterm Review and Exam after  section 6.1

Unit Six:         Applications of the Definite Integral

7.1                 Integral as Net Change

7.2                 Areas in the Plane

7.3                 Volumes

Volume by Revolution (Disk, Washer, Shell)

Volume by Cross Section

7.4                 Lengths of Curves

Surfaces of Revolution

7.5                 Applications from Science

Work and Hooke’s Law

Work Pumping

Fluid Force and Fluid Pressure

Review and Test

Unit Seven:   L’Hopital’s Rule, Improper Integrals, and Partial Fractions

8.1                  L’Hopital’s Rule

8.2                  Relative Rates of Growth

8.3                  Improper Integrals

Direct Comparison Test

Limit Comparison Test

Review and Test

Unit Eight:     Infinite Series

9.1                  Power Series

9.2                  Taylor Series

Approximating functions by polynomials

9.3                  Taylor’s Theorem

Remainder Estimation Theorem

Estimating a Remainder

nth Term Test

Direct Comparison Test

Ratio Test

Absolute Convergence

9.5                  Testing Convergence at Endpoints

Integral Test

Harmonic Series and p-series

Limit Comparison Test

Alternating Series Test

Absolute and Conditional Convergence

Review and Test

Unit Nine:      Parametric, Vector, and Polar Functions

10.1                  Parametric Functions

10.2                  Vectors in the Plane

10.3                  Vector-Valued Functions

10.4                  Modeling Projectile Motion

10.5                  Polar Coordinates and Polar Graphs

10.6                  Calculus of Polar Curves

Review and Test

Review for the AP Exam

# Course Overview

This course is designed to cover all of the topics included in the Calculus BC topic outline as described in Calculus BC Course Description published by the College Board.

The objective of this course is to have students come away with a very strong understanding of calculus concepts, strong skills in the mechanics of calculus, and the ability to use available technology to make them successful in both future pursuits in their mathematical course work and on the Advanced Placement Exam.

# Textbook and  Resources

Finney, Demana, Waits, and Kennedy.   Calculus- Graphical, Numerical, Algebraic.  Menlo Park: Scott Foresman-Addison Wesley, 1999, 1st Ed.

Lederman, David.  Multiple Choice and Free Response Questions in Preparation for the AP Calculus (BC) Examination.  D&S Marketing, 2003, 8th Edition.

McMullin, Lin.  Teaching AP Calculus.   D&S Marketing, 2002.

Released AP Exams

AP Calculus Course Description

AP Central Website