# AP Calculus BC Syllabus

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```					Hewitt-Trussville High School
Course Syllabus
Subject: AP Calculus BC
Teacher: Ryan James
E-mail: ryan.james@trussvillecityschools.com
Web Site: http://tiny.cc/mrjameshths

All topics covered in this course will be reinforced with the use of graphing
calculators. I will be using a TI-84 and a TI-89 in class regularly. Calculus calculator
labs will be offered to extend the ideas and methods taught in the classroom and
highly recommended for all students. The understanding of Calculus depends on
numerical, graphical, analytical, and verbal connections. In this course, students will
complete the following with the use of a graphing calculator:
 Plot the graph of a function within the appropriate viewing window.
 Find the zeros of a function.
 Calculate the derivative of a function at a point.
 Evaluate a definite integral.

Course Outline:
Unit 1: Functions, Limits, and Continuity
1. Basic Functions and Domain, Range, and Symmetry
2. Families of functions
3. Vertical and Horizontal Asymptotes, Holes, and End Behavior
4. Piecewise Functions
5. Trig Functions and Unit Circle
6. Appropriate window for a graph on the graphing calculator
7. Graphical limits
8. Limits at a point algebraically
9. Limits involving infinity algebraically (and dominance)
10. Limits of piecewise functions graphically and algebraically
11. Use of table feature of graphing calculator to determine limits
12. Continuity graphically and as defined by limits.
13. Apply graphical interpretations of continuity using the Intermediate Value
Theorem.
Unit 2: Differentiation
1. Definition of the derivative
2. Differentiability and continuity
3. Derivatives of polynomial functions using the power rule
4. Product and Quotient Rules
5. Derivatives of trigonometric, exponential and logarithmic functions
6. The Chain Rule
7. Implicit Differentiation
8. L’Hopital’s Rule
Unit 3: Differentiation and Applications of Differentiation
1. Derivative of inverse trigonometric functions
2. Logarithmic differentiation and derivative of
3. Related Rates
4. Tangent line to a curve at a point and using the line to approximate the value
of the function
5. Rolle’s Theorem and Mean-Value Theorem
6. Extreme-Value Theorem and Optimization
Unit 4: More Applications of Differentiation and Integration
1. Analysis of graphs using the first and second derivatives
a. Local and Global Extrema
b. Intervals of increasing and decreasing
c. Points of inflection
d. Intervals of concavity
2. Make the connections between f, f’, and, f’’ in tables and graphs
3. Use of graphing calculator to find the numerical derivative at a point and the
graph of the derivative of a function
4. Applications to speed, velocity, and acceleration
5. Riemann sums to approximate area using right, left, midpoint and trapezoid.
6. Definite integral as a limit of Riemann sums
7. Fundamental Theorem of Calculus (Part 1)
8. Fundamental Theorem of Calculus (Part 2)
9. Net Change Theorem
Unit 5: Integration and Applications of Integration
1. Basic integration
2. Integration by u-substitution
3. Area of a region
4. Volume of a solid with known cross section
5. Volume of solids of revolution
6. Average Value Theorem
7. Total distance traveled by an object (Net Change Theorem)
8. Summing rate of change (Net Change Theorem)
9. Arc length
Unit 7: Differential Equations, Parametric and Vector Equations, and Polar
Equations
1. Separable Differential Equations and their use in modeling different types of
growth
2. Logistic Growth
3. Motion Problems
4. Slope Fields
5. Graphing of Polar, Parametric and Vectors
6. Derivatives of Polar, Parametric and Vectors including position, velocity and
acceleration
7. Area and arc length of polar curves
8. Arc length of parametric curves
Unit 8: Series, Convergence, and Taylor Polynomials
1. Limits of partial sums
2. Geometric series, Telescoping series and      term test
3. Integral test
4. P-series and harmonic series
5. Direct comparison and Limit comparison test
6. Alternating series test and error bound
7. Ratio test
8. Taylor polynomials as approximations to functions
9. Taylor and Maclaurin series centered at
10. Maclaurin series for ,        ,      , and
11. Taylor series for      centered at       and
12. Manipulation of Taylor Series
a. Substitution
b. Differentiation
c. Antidifferentiation
13. Functions defined by power series
14. Radius and Intervals of convergence of power series
15. Lagrange error bound
AP Exam Review
1. Review of limits and derivatives
2. Applications of derivatives
3. Integration and Application of derivatives
4. Go over practice exam

Class Expectations:

My grading scale is as follows:
Homework               10%
In class quizzes        15%
Tests                 75%

Each day there will be a homework check that will contribute to a weekly
homework grade. If a student does not complete at least 3 homework assignments
in the week, that student will be assigned Saturday School. Also, there will be at
least one online homework assignment using UT Quest Homework. Homework can
be taken up randomly at any time. All assignments taken up will be graded for
accuracy giving partial credit where it has been earned. All exams will be composed
of AP Exam questions and thus there will be options for points through test
corrections.

In addition, students should expect to complete their homework, quizzes, and tests
where they are required to communicate and justify their answers with complete
sentences. I expect questions and group collaboration. Mathematics was created by
several brilliant mathematicians building off of each others’ ideas until theorems
and rules were created. Make up exams when permitted by school policy will be
completed either before or after school. When you do not understand a concept, I
expect you to come to me for out of class help, either before school, during lunch, or
after school. I am here for you. I want you to know that you have plenty of help
available. The student is expected to understand that part of an AP course is the AP
exam which will be before the end of the school year and be adequately prepared for
the exam.

*Important Dates:

Dec. 3/4 – Weekend review session for Semester Exam at HTHS
Feb. 4th – AP Review Session at UAB (mandatory)
March 3rd – AP Review Session at UAB (mandatory)
April 21st – AP Review Session at UAB (mandatory)
April 28/29th – Weekend review session for AP Exam at HTHS
May 5/6th – Weekend review session for AP Exam at HTHS
May 9th – AP Calculus AB/BC Exam

Also, I will be having weekly review sessions for AP Calculus students every
Thursday after school.

1. AP Calculus BC Information:
2. http://apcentral.collegeboard.com/apc/public/courses/teachers_corner/21
18.html
3. AP Calculus BC Free Response Questions:
4. http://apcentral.collegeboard.com/apc/members/exam/exam_information/
8031.html
5. AP Calculus AB/BC Calculator Policy:
http://apcentral.collegeboard.com/apc/members/courses/teachers_corner/
2109.html#name6
6. UT Quest Online Homework: https://quest.cns.utexas.edu/student
7. AP Calculus AB/BC Wiki: http://apcalculusnmsi.wikispaces.com/
8. Winplot – Free Graphing Software:
http://math.exeter.edu/rparris/winplot.html
9. Mr. James’s Blog: http://epsilontodelta.wordpress.com/
10. MIT Calculus Lecture Videos:
http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-
fall-2006/

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