Syllabus
University
of Colorado at Denver (UCD): Math
2411
Platte
Canyon High School: AP Calculus BC
Instructor:
Debbi Marks
January
29, 2001 through June 8, 2001
General Information
This
class meets every school day for 90 minutes from 9:05 to 10:35.
Instructor Information
Debbi
Marks
Platte
Canyon High School, Room 215
303-838-4642
Ext 219
email:
debbimarks@uswest.net
I
am available before school, after school and during 3rd period.
You may drop in or make an appointment to see me.
Course Prerequisites
UCD
Math 1401 or permission of instructor.
Required Textbook
Calculus:
Graphical, Numerical, Algebraic
by Finney, Demana, Waits, Kennedy
publisher:
Scott Foresman Addison Wesley, 1999
Objectives
This course is an academically challenging program that
has been designed with the following objectives:
•
To
understand the meaning of the derivative in terms of rate of change and local
linear approximation.
•
To be able to work with functions represented graphically, numerically,
analytically or verbally and understand the connections among these
representations.
•
To understand the meaning of the definite integral both as a limit of
Riemann sums and as a net accumulation of a rate of change.
•
To be able to model problem situations with functions, differential equations or integrals.
•
To read, analyze, and solve challenging problems.
•
To work and communicate effectively in groups.
•
To take the AP Calculus (BC) test and score a 3, 4, or a 5.
Classroom
Procedures and Grades
Instruction in the AP Calculus class (Math
1401 and Math 2411) will include a variety of activities. Lecture and discussion, calculator explorations, lab
activities, and guided practice will all be used regularly. Students are expected to actively participate in all of these
activities. Class discussion is
important to assist understanding and to build on the ideas of classmates.
Frequent tests and quizzes will be used to monitor the
progress of students. “Pop”
quizzes will be given regularly to ensure that students keep up with their work
and understanding. Each test will
follow the format of the AP Calculus test which includes four sections.
There are two sections of multiple choice, one using a calculator and one
not. There are two sections of free
response questions, one using a graphing calculator and one not.
Grades will be based on the accumulation of points.
Homework will be worth 5 – 10 points for each assignment.
Quizzes range from 10 – 40 points.
Tests range from 60 – 145 points.
Other activities and assessments will be given points as well.
No late work will be accepted.
Materials
pencils, red grading pen, TI-83 or TI-83 Plus graphing
calculator or TI-89 graphing calculator, loose-leaf binder, notebook paper,
graph paper
Credit
Options
PCHS:
2 units of high school credit will be awarded to students passing this
class.
University
of Colorado at Denver:
This class is offered under the CU-Succeed program.
Students signing up for the CU credit will receive 4 semester hours of
second semester calculus credit.
Platte
Canyon School District will pay for this credit for any student who wishes to
receive it. Please check with the
college or university you plan to attend to see if they will accept this credit.
AP Credit:
In order to receive AP credit, you must take the AP Calculus
(AB or BC) test offered on the
morning of May 10, 2001. Most
colleges and universities will accept this credit if the student earns a 3, 4 or
5 on the test. Check with the
college or university you plan to attend
to determine their policy. The
cost of taking this test is approximately $75 and must be paid prior to taking
the test.
Calculators
A graphing calculator is essential for this class.
The College Board gives the AP tests and expects every student to know
how to use a graphing calculator. Students
are allowed to use up to two different graphing calculators on the AP test.
The test is divided into two parts, one that is calculator active and the
other that is not. The most
powerful TI (Texas Instruments) graphing calculator that is allowed on the test
and in this class is the TI-89, a relatively new calculator that came out in
late 1998. Other calculators that
can be used are the TI family of TI-81 through TI-86. The TI-92 may not be used.
Please ask if you want to know what other brands of graphing calculators
may be used.
Expectations
•
You
are expected to assume responsibility for your own learning as this is a college
class. You are expected to ask
questions to clarify your understanding and to enhance your learning experience.
•
You are expected to attend class and be on time.
•
All assignments must be turned in. All
homework is due the next day. Late
assignments will not receive credit but must be turned in.
•
Homework and tests must be done
in pencil. You will grade your homework
with a different color pen.
•
You are expected to actively participate in classroom discussion and
activities.
•
Each student must bring their materials (paper, pencils, red pen, book,
calculator) to class each day to be prepared.
•
Each student is expected to keep and organized notebook with all of their
calculus materials. This should be
brought to class every day.
•
Any test grade of lower than a C must schedule a conference within the
next 24 hours to correct mistakes and relearn the material.
Course Objectives
VI.
Differential Equations and Mathematical Modeling
A.
Construct antiderivatives using the Fundamental Theorem of Calculus.
B.
Find antiderivatives of polynomials, e kx
, and selected trigonometric functions of kx, as well as linear
combinations of these functions.
C.
Solve initial value problems of the form dy/dx
= f (x),
y 0 = f (x 0 ).
D.
Construct slope fields using technology and interpret slope fields as
visualizations of differential equations.
E.
Compute indefinite and definite integrals by the method of substitution.
F.
Solve a differential equation of the form d
y/dx =
f (x), in which the variables are separable.
G.
Use integration by parts to
evaluate indefinite and definite integrals.
H.
Use tabular integration or the method of solving for the unknown integral
in order to evaluate integrals that require repeated use of integration by
parts.
I.
Solve problems involving exponential growth and decay in a variety of
applications.
H.
Solve problems involving exponential or logistic population growth.
K.
Use Euler’s method and the improved Euler’s method to find
VII.
Applications of Definite Integrals
A.
Solve problems in which a rate is integrated to find the net change over
time in a variety of applications.
B.
Use integration to calculate areas of regions in a plane.
C.
Use integration (by slices or shells) to calculate volumes of solids.
D.
Use integration to
calculate surface areas of solids of revolution.
E.
Use integration to
calculate lengths of curves in a plane.
F.
Adapt their knowledge of integral calculus to model problems involving
rates of change in a variety of applications, possibly in unfamiliar contexts.
VIII.
L’Hôpital’s Rule, Improper Integrals, and Partial Fractions
A.
Find limits of indeterminate forms using l’Hôpital’s Rule.
B.
Use little-oh and big-oh notation in determining, investigating, and
comparing the rates of growth of functions.
C.
Use limits to evaluate improper integrals.
D.
Use the direct comparison test and the limit comparison test to determine
the convergence or divergence of improper integrals.
E.
Evaluate integrals using partial fractions, integral tables, or
trigonometric substitutions.
IX.
Infinite Series
A.
Apply the properties of geometric series.
B.
Differentiate, integrate, or substitute into a known power series in
order to find additional power series representations.
C.
Use derivatives to find the Maclaurin series or Taylor series generated
by a differentiable function.
D.
Approximate a function with a Taylor polynomial.
E.
Analyze the truncation error of a series using graphical methods or the
Remainder Estimation Theorem.
F.
Use Euler’s formula to
relate the functions sin x, cos x,
and e x
.
G.
Use the nth-Term Test, the Direct Comparison Test, and the Ratio
Test to determine the convergence or divergence of a series of numbers or the
radius of convergence of a power series.
H.
Use the Integral Test and the Alternating Series Test to determine the
convergence or divergence of a series of numbers.
I.
Determine the convergence or divergence of p-series, including the
harmonic series.
J.
Determine the absolute convergence, conditional convergence, or
divergence of a power series at the endpoints of its interval of convergence.
X.
Vectors
A.
Find derivatives and second derivatives of parametrically defined
functions.
B.
Calculate lengths of parametrically defined curves and calculate surface
areas.
C.
Represent vectors in the form
and perform algebraic computations
involving vectors.
D.
Differentiate and integrate vector-valued functions.
E.
Analyze the motion of a particle in space given its position, velocity,
or acceleration as a vector function of time.
F.
Solve problems involving ideal projectile motion and projectile motion
with air resistance.
G.
Graph polar equations and determine the symmetry of polar graphs.
H.
Convert Cartesian equations into polar form and vice versa.
I.
Calculate slopes, lengths,
areas of regions in the plane, and surface areas determined by polar curves.
UCD – CU Succeed Gold Incomplete Policy
If
a student’s final grade is below a “C”, a student may accept and “IW”
(Incomplete Withdrawal) in lieu of a final grade. Students receiving and “IW” in lieu of a grade will not
receive a tuition refund. This
option is made available to protect a student’s chances of college admittance.
An “IW” on a student’s record will not negatively affect a
student’s GPA at CU – Denver.
UCD- High School Academic Honor Code
Students
are to submit only their own work for evaluation, to acknowledge the work and
conclusion of others, and to do nothing that would provide an unfair advantage
in their academic efforts. Students
who fail to comply with the CU-Denver Academic Honor Code are subject to
disciplinary action.