AP Calculus BCMrs. Phillips

2018-2019e-mail:

phone: 742-2900

Course Overview:

Calculus BC is a college-level course designed to meet the Advanced Placement curricular requirements and is equivalent to one full year of college calculus. The major topics of this course are limits, derivatives, integrals, the Fundamental Theorem of Calculus, and series. Students will investigate and analyze course topics using equations, graphs, tables, and words, with a particular emphasis on a conceptual understanding of calculus. Applications will be studied as appropriate.

Objectives:

Upon completion of this course students will be able to:

1)Understand the major problems of differential and integral calculus.

2)Understand the importance of linear functions in mathematics.

3)Understand and recognize other important classes of functions (such as trig and rational functions), and be able to use calculus fluidly with these functions.

4)Appreciate how calculus allows us to solve important practical problems in an optimal way.

Topics:

Unit 1: Limits and Continuity (3 weeks)

  1. Rates of Change
  2. Limits at a point
  3. Limits involving infinity
  4. Continuity
  5. Instantaneous rates of change

Unit 2: The Derivative (5 weeks)

  1. Definition of the derivative
  2. Differentiablility
  3. Derivatives of different types of functions
  4. Derivative rules when combining functions

E. Applications to velocity and acceleration

F. Implicit derivative

Unit 3: Applications of the Derivative (4 weeks)

  1. Extreme values
  2. Using the derivative
  3. Analysis of graphs using the first and second derivatives
  4. Optimization problems
  5. Linearization models
  6. Related Rates

Unit 4: The Definite Integral (3 weeks)

  1. Approximating areas
  2. The Fundamental Theorem of Calculus
  3. Indeterminate Forms and L’Hôpital’s Rule
  4. Definite integrals and antiderivatives

Unit 5: Differential Equations and Modeling ( 3 weeks)

  1. Antiderivatives
  2. Integration using u-substitution
  3. Separable differential equation

Unit 6: Applications of Definite Integrals (3 weeks)

  1. Summing rates of change
  2. Particle motion
  3. Areas in the plane
  4. Volumes
  5. Arc Length
  6. Surface area of revolution

Unit 7: Integration Techniques

A. Integration by Parts

B. Trigonometric Substitution

C. Improper Integrals

Unit 8: Sequences and Series

A. Sequences

B. Convergence and divergence of sequences

C. Tests for convergence and divergence in series

G. Taylor Polynomials and Approximations

H. Power Series

I. Representations of Functions by Power Series

J. Taylor and Maclaurin Series

Unit 9: Conics, Parametric Equations, and Polar Coordinates

A. Conics and Calculus

B. Plane curves and parametric equations

C. Parametric equations and calculus

D. Using vectors to model motion in a plane.

E. Analysis of curves given in parametric and vector form.

F. Calculate Arc Length and the Area of a Surface of Revolution in parametric form

G. Polar Coordinates and Polar Graphs

H. Area and Arc Length of Polar Graphs

I. Polar Equation of Conics and Kepler’s Laws

Materials:

Pencil, pen, highlighter, lined paper and graphing calculator. *All students have a textbook that should be kept at home. We have a class set that will be used at school*

Grading:

Grades will be based on the total points earned on test (70%), quizes (15%), and class and homework (15%). The grading scale is as follows:

90 - 100 % A

80 – 89 % B

70 – 79 % C

60 – 69 % D

Grades will be updated weekly and posted online at the LUSD Q website as well as in the classroom.

Homework:

Homework will be assigned daily. Students are expected to turn in their own work (not “borrowed” work from other students or from the internet).

Support:

I am available before school or after school for help. In addition, all class notes and assignments can be accessed from my faculty page on the Cabrillo website ( ).

Classroom Norms:

Students are expected to follow the classroom norms listed below:

Be Prompt – in your seat when the bell rings

Be Prepared – bring materials to class EVERYDAY

Be Productive – turn cell phones off, follow directions, and do not leave the room without

permission

Be Positive – have a good attitude

Be Polite – be kind to others

Student Signature: ______Date: ______

Parent Signature: ______Date: ______