SUFFOLK COUNTY COMMUNITY COLLEGE
COLLEGE-WIDE COURSE SYLLABUS
MA87 (MAT141)
I. COURSE TITLE:
Calculus with Analytic Geometry I
II. CATALOG DESCRIPTION 2006-2008:
Study
of limits, continuity, theory and application of the derivative; related rate problems;
maxima and minima; definite and indefinite integrals; and areas under
curves. (5 contact hrs.) Prerequisite: C or better in MA62 or MA70. Note: Credit
given for MA87 or MA64, but not both. A-E-G / 4 cr. hrs.
III. COURSE GOALS:
A. Introduce the basic concepts of one variable calculus.
B. Prepare students for advanced mathematics, physics and engineering courses.
C. This course satisfies the SUNY general education requirement for mathematics.
IV. STUDENT LEARNING OUTCOMES:
Upon successful completion of this course, students will be able to:
A. Use the definition of limits to calculate the value of limits; use technology to calculate the value of limits.
B. Apply the relationship between infinite limits and asymptotes to the sketching of graphs of functions; use technology to simulate asymptotic behavior numerically.
C. Apply the concept of continuity to polynomial, rational, composite, trigonometric, exponential, and logarithm functions.
D. Show and apply the relationship among the tangent to a graph of a function, the difference quotient, the two forms of the definition of the derivative, continuity, and differentiability.
E. Compute the derivative of polynomial, rational, trigonometric, exponential, and logarithmic functions. Compute derivatives using the product rule, the quotient rule, and the chain rule.
F. Apply the concept of derivatives to related rates, optimization problems, curve sketching, higher order derivatives, implicit differentiation.
G. Calculate the Taylor polynomial (degree 1,2, & 3) approximation to a function.
H. Use summation formulae to evaluate Riemann sums. Use Riemann sums to approximate the definite integral.
I. Find antiderivatives of polynomial functions and those functions whose derivatives are known.
J. State and apply the results of the Mean Value Theorem, the Fundamental Theorem of the Calculus, and the average value of a function.
K. Use definite integrals to calculate the area between curves.
V. Topics Outline with Timeline
|
Topics |
Approximate
Time (Including Examinations) |
|
A. Limits and Continuity 1. definition of
limit of a function a. definition
b. calculation
of limit 2. limit theorems:
a.
calculation
of limits b. proofs of
some basic limit theorems (such as sum, product
& quotient) 3. "one‑sided"
limits: a. definitions
b. calculations
4. infinite
limits:
a. definitions
b. calculations
c. asymptotes,
sketching 5. limits at
infinity: a. definitions
b. calculations
c. asymptotes,
sketching 6. continuity: a. definitions
b. essential
(non‑removable) and removable discontinuities
c. theorems
on continuity (with applications) 7. continuity on
an interval: a. arithmetic
of continuous functions b. polynomial functions c. rational
functions d. radical
functions e. composite
functions 8. continuity of
trigonometric functions: a. the
"squeeze" theorem b. limit and
continuity theorems applied to sine and cosine
justified using a numerical approach. i. ii. sine and cosine
functions are continuous at 0 iii. 9. continuity of
log and exponential functions |
2 ½ weeks |
