HONORS CALCULUS
2013/2014 SCHOOL YEAR
TEACHER: Ted Busch
Email: tbusch@firelandsschools.org
School Phone: 440-965-4255
Room:
109
Office Hours: 5’, Before and after school, FAST period
COURSE REQUIREMENTS:
Homework: Bookwork and worksheets, 3-5 assignments per week.
Quizzes:
One or two per chapter, except chapter one which has 5
Tests:
2 per Quarter, at the completion of each chapter.
Notebooks: Must bring every day
Textbook:
Calculus: Graphical, Numerical, Algebraic by Finney Demana Waits Kennedy
COURSE OBJECTIVES:
The main objective is to prepare students for the Advanced Placement Test in May.
Prerequisites:
Before studying Calculus, all students should complete four years of secondary
mathematics designed for college-bound students: courses in which they study algebra,
geometry, trigonometry, analytic geometry, and elementary functions. These functions
include those that are linear, polynomial, rational, exponential, logarithmic,
trigonometric, inverse trigonometric, and piecewise defined. In particular, before
studying Calculus, students must be familiar with the properties of functions, the algebra
of functions, and the graphs of functions. Students must also understand the language of
functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and so
   
on) and know the values of the trigonometric functions of the numbers 0, , , , ,
6 4 3 2
and their multiples.
Topic Outline:
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 Functions (Including one-sided limits) An intuitive
understanding of the limiting process, calculate limits using algebra, and
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 an intuitive understanding of a
continuity, understanding continuity in terms of limits, and geometric
understanding of graphs of continuous functions (Intermediate Value
Theorem and Extreme Value Theorem)
II.
Derivatives
Concept of the derivative. Derivative presented graphically,
numerically, and analytically. Derivatives interpreted as an instantaneous
rate of change, defined as the limit of the difference quotient, and the
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
the average rate of change, and approximate rate of change from graphs
and tables of values.
Derivative as a function. Corresponding characteristics of the graphs of
f and f ' such as the 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 translated into equations and vice versa.
Second derivatives. Corresponding characteristics of the graphs of f ,
f ' , and f ' ' . The relationship of concavity of f and the sign of f ' ' .
Points of inflection and where concavity changes.
Applications of derivatives. Analysis of curves, including the notions of
monotonicity and concavity. Optimization, both absolute (global), and
relative (local) extrema. Use implicit differentiation to find the derivative
of an inverse function. 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 solution curves for differential
equations.
Computation of derivatives. Knowledge of derivatives of basic
functions, including powers, exponential, logarithmic, trigonometric, and
inverse trigonometric functions. Basic rules for the derivatives of sums,
products, and quotients of functions, as well as the chain rule and implicit
differentiation.
III.
Integrals
Interpretation and properties of definite integrals Definite integral as a
limit of Riemann sums, the properties of basic integrals, and the rate of
change over an interval interpreted as the change of the quantity over the
interval:
b
 f ' ( x)dx  f (b)  f (a)
a
Applications of integrals Appropriate integrals are used in a variety of
applications to model physical, biological, 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 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 using the integral of a rate of change to give accumulated change,
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 of
Calculus to evaluate definite and to represent a particular antiderivative,
along with graphical analysis of functions so defined.
Techniques of antidifferentiation Antiderivatives following directly
from derivatives of basic functions or by substitution of variables
(including change of limits for definite integrals)
Applications of antidifferentiation Finding specific antiderivatives
using initial conditions, including applications to motion along a line and
solving separable equations, and using them in modeling (exponential
growth)
Numerical approximations to definite integrals Use of Riemann sums
(using left, right, and midpoint evaluation points) and trapezoidal sums to
approximate definite integrals of functions represented algebraically,
graphically, and by a table of values.
GOALS:

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 a definite integral both as a limit of
Riemann sums and as the net accumulation of change and should be able to use
integrals to solve a variety of problems.

Students should understand the relationship between the derivate 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 wellwritten sentences and should be able to explain solutions to problems.

Student 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.
HOMEWORK
Most lessons will take several days to complete. Along the way problems will be
assigned at varying rates. Some days will be more demanding than others. You will be
given an answer packet to check your own work as you complete it. At the beginning of
class the following day you will be given time to ask questions on those equations that
gave you the most difficulty. If you have more questions come to FAST to get them done
outside of class time. Be prepared to ask questions! If you don’t ask I assume you
understand and we move on. At the beginning of each quarter you will start with 10% of
your overall grade dedicated to homework. For each assignment you miss 1% will be
deducted from this total, up to 10%. If you miss five or more assignments in a single
quarter you will no longer be eligible for the 4% bonus for test corrections and notebook.
NOTEBOOK
Each student must bring a thick three-ringed binder to class everyday. This
notebook will contain this syllabus, daily notes, formulas, and old homework. The
notebook will be checked periodically for contents. A complete and well-organized
notebook may add 2% to your overall grade each quarter.
ABSENCES
You cannot learn if you are not in school!! Make every effort possible to be in
school every day. But, if not, it is your responsibility to make up any missing
assignments. Assignments and class notes will be posted on my school website.
TUTORING
Students may receive extra help during the FAST periods, 5th period, or before
and after school. However, you must see me in advance and in the case of 5th period you
must not have another class. In the morning I am available at 7:15 and after school
starting at 2:35. If these times do not fit your schedule other arrangements can be made.
Many of you should expect to be in my FAST period nearly every day if you have
questions on the homework. Class time is reserved for new lessons, tests, and
quizzes. FAST is when the majority of homework questions are answered.
GRADES
Grades will be weighed as follows:
Test
60%
Quizzes
30%
Homework
10%
Notebook
+2%
Test Corrections
+2%
I will use the school wide elevated grading scale that can be found in your student
handbook.
At the end of the year you will create a summary of what you learned this year as a final project. You
can take this with you to college as a reference for any future calculus classes.