MAUI COMMUNITY COLLEGE
COURSE OUTLINE
1. COURSE TITLE: MATH 203 CALCULUS FOR BUSINESS AND
SOCIAL SCIENCES
NUMBER OF CREDITS: Three (3)
ABBREVIATED COURSE TITLE: CALCULUS FOR BUSINESS & SOCIAL
SCIENCES
DATE OF OUTLINE: FEBRUARY 2004
2. COURSE DESCRIPTIONS: STUDIES THE BASIC CONCEPTS OF DIFFERENTIATION AND INTEGRATION AND THEIR APPLICATIONS IN THE AREAS OF FINANCE, MANAGEMENT, ECONOMICS, AND SOCIAL SCIENCES
3. CONTACT HOURS PER WEEK: Lecture – Three (3)
4. PREREQUISITES: MATH 135 with at least a C, or placement
at MATH 140, and ENG 100 with at least a C or concurrent enrollment, or consent.
COREQUISITES: N/A
RECOMMENDED
PREPARATION:
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.
c. To have students apply formal rules or 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 the connection and transition between the general theoretical theorems and their practical application.
f. 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 problems.
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 demonstrate 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.
i. Apply the concepts of calculus to multiple variable functions.
6. SPECIFIC COURSE COMPETENCIES:
Upon completion of this course, the student will be able to:
a. 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. This is to be done with functions of one or two variables.
b. Find the derivative, limit, and integral for the basic functions (Polynomial, exponent, logarithm) and combinations of these and use the rules and algorithms for derivatives and integrals to answer problems.
c. Compute partial derivatives of functions and describe what this tells about the function.
d. Interpret the meaning of the derivative and integral in real life situations, particularly in the area of finance and business.
e. Find maximum and minimum points and points of inflection for a function of a single variable and use these techniques of calculus to solve optimization problems, which involve symbolizing the problem, manipulative the symbols within the logical systems to find a solution, and interpreting the solution in the context of the problem with functions of one variable and several variables.
f. Sketch graphs of the derivative and the integral from a given function graph.
g. Find an approximating tangent line to a curve at a point and an approximating tangent plane to a surface.
h. Write several mathematical papers that clearly and precisely show the sequence of steps in solving problems and checking results, and to argue persuasively through logical arguments and examples in discussing a mathematical situation.
i. Use the technology of computers and calculators to plot graphs, solve equations, find derivatives and integrals, and aid in the solution to problems.
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. (a, i)
Weeks 2-5: Review of functions – linear, exponential, and power. Fitting functions to data. Limits at a point and at infinity. Continuity. The derivative its definition and interpretation. Marginal Cost and Revenue. (a, b, f, h, i)
Weeks 6- 10: Higher order derivatives. Reiman Sums and basic integration ideas. Interpretation of integration. The rules of differentiation. (b, d, e, f, h, i)
Weeks 11-15: Applications of the derivative to curve sketching, finding maximums and minimums, points of inflections and related rates. Integration both as anti-differentiation and as Riemann sums. Area between functions. Rules of integration. Fundamental Theorems of Integral Calculus. Functions of two variables their graphs, partial derivatives, and relative maxima and minima with applications. (a, b, c, d, e, f, 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: Deborah Hughes-Hallett, (1997). Brief
Calculus, John Wiley and Sons.
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) 40-80%
In-class exercises 0-30%
Homework 0-30%
Practice set 20-40%
Quizzes 0-30%
Projects/research 0-40%
Bonus projects and work 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.)