• 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

    9.4                  Radius of Convergence

                           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