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TITLE
Calculus
TEXTBOOK
Calculus, Deborah Hughes-Hallett & others, John Wiley & Sons, INC, 1994
DESCRIPTION
Calculus is the study of changing quantities. Two main themes are
differentiation, which studies rates of change and integration which deals with
areas and volumes of shapes. Concepts and conceptual understanding are
emphasized through explorations with calculators. Each topic, whenever possible
is approached graphically, numerically and algebraically. Students will be
required to purchase a graphing calculator. Students who receive a grade of C or
better at the University of Nebraska in Calculus 107 will receive credit for the
course at no cost. Prerequisites are pre-calculus
NOTES
A course syllabus and test have been obtained from the University of Nebraska.
The course will roughly follow the outline of the UNL course for 106. Because a
whole year is used to complete the course additional topics will be explored.
COURSE OBJECTIVES
1. Students will be able to graph and describe the effects of the parameters on
the following types of functions: direct, indirect, linear, polynomial,
rational, trigonometric, sinusoidal, exponential, logarithmic (common and
natural) and power. (12.6.4)
2. Students will be able to apply logarithms, exponents, and trigonometry to
applications problems including compound interest, half-life, and growth.
(12.4.5) (12.6.4)
3. Students will be able to describe the difference between instantaneous and
average velocity or tangent and secant lines.
4. Students will be able to calculate using limits the instantaneous velocity or
tangent given a table, graph, or function. (12.4.2)
5. Students will be able to explain how the concept of a limit is used to
determine the slope of a tangent to a curve.
6. Students will be able to graph the first and second derivative of a curve
given its graph or determine a graph given its derivative.
7. Students will be able to calculate using sums of rectangles the definite
integral of a graph, function or table of values.
8. Students will be able to use rules and formulas to calculate the derivatives
for power, polynomial, exponential, logarithmic, and trigonometric functions.
9. Students will be able to apply general rules such as the product, quotient,
and chain rules to differentiate combinations of functions.
10. Students will be able to use the first and second derivatives to analyze the
behavior and graphs of families of functions. This will include maxima, minima,
inflection points, and concavity.
11. Students will be able to integrate or find the antiderivatives of functions.
12. Students will be able to apply the fundamental theorem of calculus to
application problems involving height, velocity and acceleration.
WRITING ACTIVITIES
1. Students will write paragraphs explaining their method and thought process
used in solving a problem or applying a concept.
2. Students will have a question on test which will require a written
explanation. (12.2.2)
3. Students will take a problem missed on and explain what they did incorrect as
well as the correct solution to the problem.
