Heartland Community College
Master Course Syllabus
Division Name: STEM and Business
Course Prefix and Number: MATH 151
Course Title: Calculus for Business & Social Science
DATE PREPARED: August, 1995
DATE REVIEWED:
DATE REVISED: September, 2014
PCS/CIP CODE: 1.1-270301
IAI NO. (if available): M1900-B
EFFECTIVE DATE OF FIRST CLASS: Fall 2015
CREDIT HOURS:
CONTACT HOURS: 4
LECTURE HOURS: 4
LABORATORY HOURS: 0
CATALOG DESCRIPTION (Include specific prerequisites):
Prerequisite:
- Completion of MATH 106 with a grade of C or better [OR]
- Completion of MATH 109 with a grade of C or better [OR]
- Assessment
Note, a graphing calculator is required for this course (instruction will be based on a TI-83+).
This calculus course is designed specifically for students in business and the social
sciences and does not count toward a major or minor in mathematics. It emphasizes
applications of the basic concepts of calculus rather than proofs. Topics include limits;
techniques of differentiation applied to polynomial, rational, exponential, and logarithmic
functions (this includes partial derivatives and derivatives of higher order); maxima and
minima of functions; elementary techniques of integration including substitution and
integration by parts; and applications (business and social science applications
are stressed throughout the course).
TEXTBOOKS:
Barnett, Byleen, Ziegler (2011). Calculus for Business, Economics, Life Science, and Social
Sciences, 12th edition, Upper Saddle River, NJ: Prentice Hall; or a comparable text that
addresses at a minimum the topics listed in the Course Outline and that provides students
with the opportunity to achieve the learning outcomes for this course.
RELATIONSHIP TO ACADEMIC DEVELOPMENT PROGRAMS AND
TRANSFERABILITY:
MATH 151 fulfills 4 of the semester hours of credit in Mathematics required for the A.A. or A.S.
degree. This course should transfer as part of the General Education Core Curriculum
described in the Illinois Articulation Initiative to other Illinois colleges and universities
participating in the IAI. However, students should consult an academic advisor for transfer
information regarding particular institutions. Refer to www.iTransfer.org. for information.
LEARNING OUTCOMES:
Course Outcomes
Essential
Competencies
Interpret graphs of functions.
Recognize, graph, and formulate linear, power,
polynomial, rational, exponential, and logarithmic
functions.
Perform basic operations (addition, subtraction,
multiplication, and division) on functions and express a
function as a composition of two functions.
Apply the interest formulas for compound and
continuously compounded interest to determine the value
of the investment, length of time of investment, etc.
Define the average rate of change. Know the relationship
between average rate of change and the slope of the
secant line.
Evaluate limits of functions.
Define the derivative. Know the relationship between the
derivative, the instantaneous rate of change and the
slope of the tangent line.
Describe the relationship between the tangent line to the
curve of a function and the derivative of the function.
Apply appropriate method(s) of Calculus to determine the
equation of the tangent line to the curve of a function at a
particular point.
Apply basic rules of differentiation, including the chain
rule, to determine the derivatives.
Determine higher order derivatives.
Use derivatives to determine intervals for which a function
is increasing or decreasing, and concave up or concave
down, points of local maxima and minima, and points of
inflection; then sketch the graph of a function.
Apply techniques of integration (including substitution and
by parts) to determine indefinite integrals.
Use Riemann sums to estimate definite integrals.
Apply appropriate method(s) of Calculus to determine the
area bounded by the curves of functions.
Apply the Fundamental Theorem of Calculus to determine
the value of a function at a particular input value.
Evaluate and interpret multivariable functions.
Determine and interpret partial derivatives.
Determine the extrema of a multivariable function.
Apply Lagrange Multipliers to determine the maxima and
minima of a multivariable function subject to a given
constraint.
Apply calculus to solve practical problems such as
maximizing profits, minimizing costs, determining
marginal cost and revenue, determining consumer and
producer’s surplus, determining the present and future
values of an income stream, etc. Interpret the derivative
and definite integral for these applications.
Range of Assessment
Methods
Assessments will
include exams, and
may include but not
limited to homework,
quizzes, and projects.
CT 2
PS 4
CO 2
CT 2: Students determine value of multiple sources or strategies and select those most
appropriate in a given context. Students compare various perspectives, strategies or concepts
and respond using the most appropriate alternative.
CO 2: Students effectively deliver a message via various channels/modalities. Students
prepare written, oral, visual, and/or experiential materials for an area of study.
PS 4: Students analyze the situation, explore different outcomes from multiple frameworks,
apply the appropriate solution, analyze the results, and refine the solution. Students see
problem solving as a process and are not satisfied with the first answer to a problem – review
answers for validity. Students transfer problem solving ability across the disciplines.
COURSE/LAB OUTLINE:
1.
2.
3.
4.
5.
6.
7.
8.
9.
Functions and their graphs
The derivative
Techniques of differentiation
Applications and interpretations of the derivative
The definite and indefinite integral
Techniques of integration
Curve sketching
Applications and interpretations of the definite integral
Multivariable Calculus
METHOD OF EVALUATION (Tests/Exams, Grading System):
Instructors may determine the most appropriate methods of evaluation for their course. These
methods of evaluation will include unit tests and a comprehensive final exam, and may include
but not limited to homework, quizzes, and projects.
GRADING SCALE:
S.P.: Student Performance
90  S.P.  100  A
80  S.P.  90  B
70  S.P.  80  C
60  S.P.  70  D
00  S.P.  60  F
REQUIRED WRITING AND READING:
Students are expected to read the material in the textbook for each section studied, which is
approximately 650 pages for the semester. Required writing will be part of most activities.
Students are expected to explain solution processes, describe solutions analytically and
graphically, and interpret the answer in the context of the problem. Instructors may incorporate
writing assignments as part of the course grade, in keeping with learning outcomes. Other
reading assignments may be assigned, possibly in conjunction with writing assignments.