Instructor: Mr. Buys
Semester: Fall 2013
Course: Honors Calculus / AP Calculus AB
Phone: 582-4347 ext. 2224
E-Mail: buysjs@spart6.org
Website: http://www.dormanhigh.org/academics/departments/math/jeffbuys.aspx
Text:
Ross L. Finney, Franklin D, Demana, Bert K. Waits, and Daniel Kennedy, Calculus- Graphical, Numerical,
Algebraic, 4th edition.
Several other books are used for supplementary material, including Paul A. Forester, Calculus, Concepts and
Appications, Emeryville, California, 1999; Deborah Hughes-Hallet, William G., McCallum, Andrew M. Gleason,
et al, Calculus, 3rd edition. New York, John Wiley 7 Sons, Inc., 2002; Arnold Otsebee and Paul Zorn, CalculusFrom Graphical, Numerical and Symbolic Points of View, Fort Worth, Saunders College Publishing, 1997.
Course Description:
Honors Calculus is designed for the mathematically advanced student who has completed the prerequisites,
having already taken and passed Algebra I and II, Geometry, and Pre-Calculus, and wishes to bridge the gap
between high school and college mathematics. The curriculum is challenging and includes a wide variety of
topics that will be covered in depth. Students will have many opportunities to use critical thinking skills.
Extensive use of a graphing calculator will be a major requirement of this course. Technology is used regularly
by students and teachers to reinforce the relationship among the multiple representations of functions, to
confirm written work, to implement experimentation, and to assist in interpreting results.
Instructional Philosophy:
As a teacher I know all students learn differently, so in my plans I try to use different strategies. There will be
times of teacher lead instruction, teacher lead discussion, group work, partner work, and individual work. I
expect my students to participate in the classroom discussions and question and answer times. I will ask
students to answer questions or I will take volunteers. In calculus you MUST ask questions when you do not
understand because this type of math is new to the students. I plan on making a classroom environment that
is comfortable for all students to learn and be respected. I also plan to use as much technology as possible so
the students can learn how to use it themselves and the students will have a deeper understanding.
Course Goals and Power Standards:
*Students should be able to work with functions represented in a variety of ways: graphical, numerical,
analytical, or verbal. They should understand the connections among these representations.
*Students should understand the meaning of the derivative in terms of a rate of change and local linear
approximation and should be able to use derivatives to solve a variety of problems.
*Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the
net accumulation of a rate of change and should be able to use integrals to solve a variety of problems.
*Students should understand the relationship between the derivative and the definite integral as expressed in
both parts of the Fundamental Theorem of Calculus.
*Students should be able to communicate mathematics both orally and in well-written sentences and should
be able to explain solutions to problems.
*Students should be able to model a written description of a physical situation with a function, a differential
equation, or an integral.
*Students should be able to use technology to help solve problems, experiment, interpret results, and verify
conclusions.
*Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy,
and units of measurement.
*Students should develop an appreciation of calculus as a coherent body of knowledge and as a human
accomplishment.
Required Materials: Students are asked to provide the following materials each day:
Textbook
Pencils
Notecards
Three ring binder with loose leaf paper
Graphing calculator (TI-Nspire is suggested)
Grading Policy:
Grades will be calculated using the following percentages:
1st 9 weeks: 45%
2nd 9 weeks: 45%
Final Exam: 10%
Each nine weeks grade will be calculated using total points.
Tests will be given at the end of each major chapter. Quizzes will be given at least once every other week and
may or may not be announced in advance. These quizzes will be representative of the homework assignments
that have been covered since the previous quiz. Homework is checked for accuracy and effort. Your final
exam will count 10% of your final grade. Seniors with a cumulative average of 90 or higher may exempt if they
are not continuing with the course in the second semester. No exceptions.
The grading scale is the same as that given to you in your student handbook.
A:
B:
C:
D:
F:
100 – 93
92 – 85
84 – 77
76 – 70
Below 70
Major Units of Study Outlined:
This outline of topics is intended to indicate the scope of the course, but it is not
necessarily the order in which the topics are to be taught.
I. Functions, Graphs, and Limits
Analysis of graphs. With the aid of technology, graphs of functions are often easy to
produce. The emphasis is on the interplay between the geometric and analytic
information and on the use of calculus both to predict and to explain the observed local
and global behavior of a function.
Limits of a functions (including one-sided limits). An intuitive understanding of the
limiting process is sufficient for this course.
• Calculating limits using algebra
• Estimating limits from graphs or tables of data
Asymptotic and unbounded behavior.
• Understanding asymptotes in terms of graphical behavior
• Describing asymptotic behavior in terms of limits involving infinity.
• Comparing relative magnitudes of functions and their rates of change. (For example, contrasting exponential
growth, polynomial growth, and logarithmic growth.)
Continuity as a property of functions. The central idea of continuity is that close
values of the domain lead to close values of the range.
• Understanding continuity in terms of limits.
• Geometric understanding of graphs of continuous functions (Intermediate Value
Theorem and Extreme Value Theorem).
II. Derivatives
Concept of the derivative. The concept of the derivative is presented geometrically,
numerically, and analytically, and is interpreted as an instantaneous rate of change.
• Derivative defined as the limit of the difference quotient.
• Relationship between differentiability and continuity.
Derivative at a point.
• Slope of a curve at a point. Examples are emphasized, including points at which there are vertical
tangents and points at which there are no tangents.
• Tangent line to a curve at a point and local linear approximation.
• Instantaneous rate of change as the limit of average rate of change.
• Approximate rate of change from graphs and tables of values.
Derivative as a function.
• Corresponding characteristics of graphs of f and f ’.
• Relationship between the increasing and decreasing behavior of f and the sign of f ’.
• The Mean Value Theorem and its geometric consequences.
• Equations involving derivatives. Verbal descriptions are translated into equations
involving derivatives and vice versa.
Second Derivatives.
• Corresponding characteristics of the graphs of f, f ’, and f ’’.
• Relationship between the concavity of f and the sign of f ’’.
• Points of inflection as places where concavity changes.
Applications of derivatives.
• Analysis of curves, including the notions of monotonicity and concavity.
• Optimization, both absolute (global) and relative (local) extrema.
• Modeling rates of change, including related rates problems.
• Interpretation of the derivative as a rate of change in varied applied contexts,
including velocity, speed, and acceleration.
• Geometric interpretation of differential equations via slope fields and the
relationship between slope fields and derivatives of implicitly defined functions.
Computation of derivatives.
• Knowledge of derivatives of basic functions, including xr, exponential, logarithmic,
trigonometric, and inverse trigonometric functions.
• Basic rules for the derivative of sums, products, and quotients of functions.
• Chain rule and implicit differentiation.
III. Integrals
Riemann Sums
• Concept of a Riemann sum over equal subdivisions.
• Computation of Riemann sums using left, right, and midpoint evaluation points.
Interpretations and properties of definite integrals.
• Definite integral as a limit of Riemann sums.
• Definite integral of the rate of change of a quantity over an interval interpreted as
b
the change of the quantity over the interval:
 f ( x)  f b   f  a 
a
• Basic properties of definite integrals. (For example, addivity and linearity.)
Applications of integrals. Appropriate integrals are used in a variety of applications
to model physical, social, or economic situations. Although only a sampling of
applications can be included in any specific course, students should be able to adapt
their knowledge and techniques to solve other similar application problems. Whatever
applications are chosen, the emphasis is on using the integral of a rate of change to
give accumulated change or using the method of setting up an approximating Riemann
sum and representing its limit as a definite integral. To provide a common foundation,
specific applications should include finding the area of a region, the volume of a solid with known cross
sections, the average value of a function, and the distance traveled by a particle along a line.
Fundamental Theorem of Calculus.
• Use the Fundamental Theorem to evaluate definite integrals.
• Use the Fundamental Theorem to represent a particular antiderivative, and the
analytical and graphical analysis of functions so defined.
Techniques of antidifferentiation.
• Antiderivatives following directly from derivatives of basic functions.
• Antiderivatives by substitution of variables (including change of limits for definite
integrals), parts, and simple partial fractions (nonrepeating linear factors only).
• Improper integrals (as limits of definite integrals).
Applications of antidifferentiation.
• Finding specific antiderivatives using initial conditions, including applications to
motion along a line.
• Solving separable differential equations and using them in modeling.
Numerical approximations to definite integrals. Use of Riemann sums and the
Trapezoidal Rule to approximate definite integrals of functions represented algebraically, geometrically, and
by tables of values.
Classroom Rules of Conduct:
1. Come to class on time. Standing outside the door and rushing in after the bell has begun to ring will
constitute a tardy. You must be INSIDE the door when it begins ringing to be counted on time.
2. Begin the start up activity immediately after the tardy bell. Directions will be on the projection
screen or the board. Do not wait for me to remind you to begin since I need to take roll and attend to
other duties for the first few minutes of the period.
3. Attend to personal needs before coming to class. Please do not ask for a pass unless you have a true
emergency. No passes will be given to go to lockers or see other teachers.
4. Remain in your assigned seat unless you have permission to get up. Throw scraps away at the end of
the period on your way out. There should be NO standing at the door waiting for the class to end.
5. Do not cheat. Students caught cheating will receive a zero and a phone call home. Both the student
who shares his work for an independent assignment AND the person who copies it will suffer the
same consequences. This means, if you allow someone to copy your homework, you will receive a
zero!
6. Respect yourself, your classmates, and your instructor.
7. Absentee Policy: It is your responsibility to make-up work you miss while you are out. I WILL NOT
seek you out. I am available before school by appointment to make up missed assignments or for
extra help. Any work not made up within five days of return (without making further arrangements)
will become a zero.
Consequences for Discipline Infractions: If you do not refer to the rules set forth, there will be
consequences. Minor infractions will be placed on the following plan: a warning, 15 minute detention,
parent contact, and referral. More serious infractions (gross disrespect, fighting, etc.) will receive
automatic referrals to the administration to handle at their discretion.