Calculus Syllabus Aaronson
2006-2007
Course
Description: This
course is designed to help prepare students who have completed Math
Analysis
and Trigonometry for the first year of Calculus in college. The course
content
is centered around properties of elementary
functions,
limits, and integral and differential calculus.
Course
Outline (subject to
change):
FIRST QUARTER
I. Algebraic and
Functions review
A. “Instant
recognition” functions
B. Properties
of functions
C. Cartesian
Plane
D. Graphs
of equations
E. Lines
and their equations
F. Review
of trigonometric functions
II. Limits and
their properties
A.
Introduction
to limits
B.
Evaluating
limits (techniques)
C.
Continuity
(Intermediate Value Theorem)
D.
Infinite
Limits (asymptotes)
E.
Limits
of trigonometric functions
SECOND QUARTER
III. Differentiation
A.
Definition
and tangent lines
B.
Rates
of change (velocity and acceleration)
C.
Basic
Rules (product, quotient, power)
D.
Chain
Rule
E.
Implicit
Differentiation
F.
Differentiation
of trig functions
IV. Applications of
Differentiation
A.
Related
rates
B.
Curve
sketching (first and second derivative tests)
C.
Maxima
and minima (optimization)
D.
Extrema
E.
Rolle’s Theorem and
Mean Value Theorem (isolating roots)
F.
THIRD QUARTER
V.
Integrations
A. Antiderivatives
and indefinite integration
B. Integration as
areas (approximating
integrals)
C. Definite
Integrals
D. Fundamental
Theorem of Calculus
E. Numerical
integration (Trapezoidal and
Simpson’s rules)
F. Integration of
trigonometric functions
FOURTH QUARTER
VI. Applications
of Integration
A.
Average
value of a function (Mean Value Theorem)
B.
Area
between curves
C.
Net
and Total Distance
D.
Volumes
(disc and shell method)
Materials
Needed:
·
Textbook-COVERED
·
3-ringed
binder
·
loose-leaf
paper
·
pencils
·
h
paper
Absences: If absent from
school, it
is the students responsibility to make up missed assignments. Because of the block system, students who are
absent shall either obtain the assignment from another student or from
the
teacher the following school day, even though they may not have math
class. Students will be responsible for
the material the next class period if they were present the previous
school
day. Work missed due to unexcused
absences cannot be made up for credit. A
maximum of one week will be given to make up missing tests and quizzes.
After
that time, a zero will be received for that assignment.
Grading
System:
Quizzes : 30%