MAUI COMMUNITY COLLEGE
COURSE OUTLINE
1.
COURSE TITLE:
Math 205
Calculus I
NUMBER OF CREDITS:
Four (4)
ABBREVIATED COURSE TITLE: Calculus I
DATE OF OUTLINE:
February 2004
2.
COURSE DESCRIPTIONS:
Explores the basic concepts of differential
and integral calculus. Reviews functions, focuses on differentiation and its applications.
Introduces integration.
3.
CONTACT HOURS PER WEEK:
4.
PREREQUISITES:
Lecture – Four ( 4 )
MATH 140 with at least a C, or placement
at MATH 205, and ENG 100 with at least a
C or concurrent enrollment in ENG 100, or consent.
COREQUISITES:
N/A
RECOMMENDED
PREPARATION:
Recommended: at least 12th grade reading
skills.
Prepared by Alfred Wolf
APPROVED BY
DATE
5.
GENERAL COURSE OBJECTIVES:
a.
To expose students to the beauty, power, clarity and precision of formal
systems, in this case the algebraic and analytic systems found in Calculus.
b.
To expose students to the concept of proof as a chain of inferences, and to
have them practice this skill. Proofs of derivative and integral properties
are done in the course.
c.
To have students apply formal rules or algorithms, in this course the rules
and algorithms of differentiation and integration.
d.
To have students use appropriate symbolic techniques in the context of
problem solving and in the presentation and critical evaluation of
evidence.
e.
To observe and see the connection and transition between the general
theoretical and its practical application.
f.
To expose students to some interesting and exciting ideas in mathematics.
g.
To acquire the use of numeric, graphical and algebraic techniques as
mathematical tools for solving problems.
c.
To expose students to and have them acquire some knowledge of the
methods and logic of mathematics so they may use it in solving problems.
d.
To be able to use the techniques of differentiation and integration to solve
problem.
e.
To use mathematical writing and symbols in solving problems.
f.
To use the calculator/computer as a tool of mathematics.
g.
To state and demonstration the interconnection between graphical,
numerical and algebraic representation of information for the functions,
their derivatives and integrals.
h.
To interpret the derivative and integral in mathematical situations and use
them for solving problems.
6. SPECIFIC COURSE COMPETENCIES:
Upon completion of this course, the student should be able to:
a.
b.
c.
d.
Draw a complete and adequate picture of the relationship or function. Use
algebraic, numerical, and graphical techniques to locate specific points or
regions (Solve equations and inequalities). Describe the characteristics of
the relation (domain, range, asymptotes, continuity, extreme points, points
of inflection) for a function given by a data set, graph, or equation.
Be able to find the derivative, limit, and integral for the basic functions
(Polynomial, exponent, logarithm, trig and their inverses) and
combinations of them. Students will use the rules and algorithms for
limits, derivatives and integrals to answer problems.
Interpret the meaning of the derivative, limit, and integral in real life
situations.
Find maximum and minimum points and points of inflection for a
function. Use these techniques to solve optimization problems, which
involve symbolizing the problem, manipulative the symbols within the
e.
f.
g.
h.
i.
logical systems to find a solution, and interpreting the solution in the
context of the problem.
Sketch graphs of the derivative and the integral from a given graph.
Find an approximating tangent line to a curve at a point.
Write several mathematical papers that clearly and precisely show the
sequence of steps in solving problem, and checking the results, and to
argue persuasively through logical arguments and examples in discussing
a mathematical situation.
Use the computer/calculator technology as an aid in solving mathematical
problems.
Integrate functions by approximation and by the use of antiderivatives.
7. RECOMMENDED COURSE CONTENT:
Week 1:
Introduction to the course and a background check
to assess readiness for the course. Introduction to
calculator and computer technologies used in the
course. h
Weeks 2-6: Review of functions, the algebra of function. Limits at a point and
at infinity. Continuity. The derivative its definition and the rules of differentiation.
TEST 1 a, b, c, e, f, g, h
Weeks 7- 11: Higher order derivatives and implicit differentiation. Applications
of the derivative to curve sketching, finding maximums and minimums and related rates.
TEST 2 a, b, c, d, f, g, h
Weeks 12-15: Integration both as anti-differentiation and as Riemann sums. Area
between functions. Rules of integration. Fundamental Theorems of Integral Calculus.
Final Exam Test 3 a, b, c, g, h, i
Care must be taken to coordinate with the other Colleges in the UH System so that
students may transfer easily, especially to UH Manoa.
8. RECOMMENDED COURSE REQUIREMENTS:
Specific course requirements are at the discretion of the instructor at the time the
course is being offered. Suggested requirements might include, but are not
limited to:
Written or oral examinations
In-class exercises
Homework assignments
Quizzes
Projects or research (written reports and/or oral class presentations)
9. TEXT AND MATERIALS:
An appropriate text(s) and materials will be chosen at the time the course is to be
offered from those currently available in the field. Examples include:
Texts: Hughes-Hallett CALCULUS Single Variable, Third Edition, John
Wiley and Sons New York, 2002
Software: DERIVE and MPP
Materials:
Text(s) may be supplemented with:
Accompanying Practice Set if available
Articles and/or handouts prepared by the instructor
Other:
Appropriate films, videos or internet sites
Television programs
Guest Speakers
Other instructional aids
10. EVALUATION AND GRADING:
Examinations (written and/or oral)
In-class exercises
Homework
Practice set
Quizzes
Projects/research
Bonus projects and work
40-80%
0-30%
0-30%
20-40%
0-30%
0-40%
0-8%
11. METHODS OF INSTRUCTION:
Instructional methods vary considerable with instructors and specific instructional
methods will be at the discretion of the instructor teaching the course. Suggested
techniques might include, but are not limited to:
Lecture, problem solving, and class exercises or readings
Class discussions or guest lectures
Audio, visual or presentations involving the internet
Student class presentations
Group or individual projects
Other contemporary learning techniques (e.g., Service Learning, Co-op,
School-to-Work, self-paced, etc.)