Heartland Community College
Master Course Syllabus
Division Name:
MS
Course Prefix and Number:
MATH 151
Course Title:
Calculus for Business & Social Science
DATE PREPARED: August, 1995
DATE REVISED: Dec, 2012
PCS/CIP CODE: 1.1-270301
IAI NO. (if available): M1 900-B
EFFECTIVE DATE OF FIRST CLASS:
CREDIT HOURS:
CONTACT HOURS: 4
LECTURE HOURS: 4
LABORATORY HOURS: 0
CATALOG DESCRIPTION (Include specific prerequisites):
Prerequisite: Completion of Math 106 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; partial
derivatives and applications; maxima and minima of functions; and elementary techniques of
integration including substitution, integration by parts and multivariate integration. Business
and social science applications are stressed throughout the course.
TEXTBOOKS:
Barnett, Byleen, Ziegler (2011). Calculus for Business, Econ, 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 3 (A.A.) or 6 (A.S.) 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 the IAI web page for information
as well at www.itransfer.org.
LEARNING OUTCOMES:
Course Outcomes
HCC General Education Outcomes
Interpret graphs of functions.
Recognize, graph, and formulate linear,
exponential, power, logarithmic, and
polynomial functions.
Perform basic operations (addition,
subtraction, multiplication, division) on
functions and express a function as a
composition of two functions.
Use the interest formulas for compound
and continuously compounded interest.
Define average rate of change. Know
the relationship between average rate of
change and the slope of the secant line.
Define derivative. Know the
relationship between the derivative to
the instantaneous rate of change and the
slope of the tangent line.
Understand the concept of tangent line
and find the equation of the tangent line
to a function at a particular point for
some given information.
Use basic rules of differentiation,
including the chain rule, to find
derivatives.
Find higher order derivatives and
interpret the meaning of the derivative
for applications.
Use derivatives to determine intervals
for which a function is
increasing/decreasing, concave up or
concave down, local maxima and
minima, points of inflection and sketch
the graph of a function.
Throughout the semester, students will
achieve the following Gen Ed outcomes.
A specific course outcome may correlate
to one or more of the following Gen Ed
outcomes:
CT 1: Students gather knowledge, apply
it to a new situation, and draw
reasonable conclusions in ways that
demonstrate comprehension. Students
inquire into an unfamiliar situation given
a strategy or concept.
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 1: Students create a message using
various structures, claims, support,
credibility, etc., depending upon their
topic, purpose, and audience.
CO 2: Students effectively deliver a
message via various channels/modalities.
DI 1: Students are receptive to beliefs
Range of
Assessment
Methods
Throughout
the semester,
the following
assessment
methods will
be used to
measure the
course and
Gen Ed
learning
outcomes:
MyLabsPlus
Homework;
Quizzes;
Discussion
Postings;
Exams;
Projects
Use Riemann sums to estimate the total
change in a quantity and estimate
definite integrals.
Use the Fundamental Theorem of
Calculus to determine the value of a
function at a particular input-value.
Understand the relationship between the
definite integral and area.
Interpret the meaning of the definite
integral for applications.
Use the Fundamental Theorem of
Calculus to determine the value of a
function at a particular input value.
Evaluate and interpret multivariable
functions.
Interpret and determine partial
derivatives.
Determine the extrema of a
multivariable function.
Use Lagrange Multipliers to determine
the maxima and minima of a
multivariable function subject to a given
constraint.
Use properties of double integrals.
Evaluate a double integral as an iterated
integral.
Apply calculus ideas 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.
and values that differ from their own.
DI 3: Students reflect upon the
formation of their own perspectives,
beliefs, opinions, attitudes, ideals and
values.
PS 1: Students can solve problems
based on examples and frameworks
provided by instructor. Student can only
solve problems that they are shown first.
Student sees answers as only being right
or wrong. Student is highly dependent on
the instructor.
PS 2: Students identify the type of
problem and use a framework to solve
the problem. Students can solve
problems different from those shown.
Students recognize where the process
broke down when incorrect answers
result.
PS 3: Students identify the type of
problem and, from multiple problem
solving methods, chooses the best
method and solves the problem.
Students try to apply multiple strategies
to solve problems. Students show ability
to solve problems which have not been
previously demonstrated by the
instructor. Students are not as dependent
on instructor.
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.
Functions and their graphs
The Derivative
Techniques of differentiation
Applications and Interpretations of the Derivative
The Definite Integral
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 might include but are not limited to unit test(s), quiz(zes), homework,
project(s), and a comprehensive final exam.
GRADING SCALE:
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/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.