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Modeling with Functions for Business
A. COURSE DESCRIPTION
1. Catalog Description:
This course will help students learn to mathematically
model realworld
applications, with emphasis on business applications, by developing algebraic
and
problem solving skills. Topics include linear and quadratic functions,
exponential
and logarithmic functions , trigonometric functions, polynomial and rational
functions, inverses and compositions of functions, and transformations of
functions and their graphs. In addition, the course will emphasize unit
analysis,
changing representations (graphical, tabular, formulaic, and verbal) of data,
estimation, and interpretation of solutions . Prerequisite: MATH 050 or
mathematics placement.
2. Course Outline for MATH 112Modeling with Functions for Business
I. Functions, Lines, and Change
A. Functions and Function Notation
1. Representations of functions by words
2. Representations of functions by graphs
3. Representations of functions by formulas
4. Representations of functions by tables of numbers
B. Functions and Rate of Change
C. Linear Functions
1. Constant Rate of Change
2. Formulas for Linear Functions
D. Geometric Properties of Linear Functions
1. Parallel Lines
2. Perpendicular Lines
E. Fitting Linear Functions to Data
II. Functions, Quadratics, and Concavity
A. Functions
1. Input and Output / Domain and Range
2. Piecewise Defined Functions
3. Inverse Functions
B. Concavity and Rates of Change
C. Quadratic Functions
A. Family of Exponential Functions
B. Comparing Exponential and Linear Functions
C. Graphs of Exponential Functions
D. Continuous Growth and the Number e
IV. Logarithmic Functions
A. Logarithms and their Properties
B. Modeling with exponential functions and logarithms
1. Logarithms and Exponential Models
2. The Logarithmic Function
C. Logarithmic Scales (optional)
V. Transformations of Functions and Their Graphs
A. Vertical and Horizontal Shifts
B. Reflections and Symmetry
C. Vertical Stretches and Compressions
D. Horizontal Stretches and Compressions
E. Applications of transformations to the Family of Quadratic Functions
VI. Trigonometric Functions
A. Introduction to Periodic Functions
1. The Sine and Cosine Functions
2. Radians
3. Graphs of the Sine and Cosine
4. Sinusoidal Functions
B. Inverse Trigonometric Functions
VII. Compositions, Inverses, and Combinations of Functions
A. Composition of Functions
B. Inverse Functions
C. Combinations of Functions
VIII. Polynomial and Rational Functions
A. Power Functions
B. Polynomial Functions
C. Rational Functions
D. Comparing Power, Exponential, and Log Functions
E. Fitting Exponentials and Polynomials to Data (optional)
Additional Topics Time Permitting
IV. Sequences and Series
A. Sequences
B. Defining Functions Using Sums : Arithmetic Series
C. Finite Geometric Series
D. Infinite Geometric Series
3. Instructional Methods Utilized
The basic method of instruction will be lecture,
discussion, problem sessions, and
group work . In addition, students will likely have access to online learning
resources available from most publishers of introductory mathematics texts and
have additional help available through the departmental tutoring program.
4. Course Requirements
Course requirements will include homework assignments,
quizzes, and exams.
Students may also be required to complete outside work using online learning
resources.
5. Course Materials
References: Functions Modeling Change: A Preparation for
Calculus (2^{nd} edition) by
Connally, HughesHallett, Gleason, et al., McGraw Hill (2004).
Functioning in the Real World : A Precalculus Experience
(2^{nd} edition) by
Gordon/Gordon/Fusaro/Siegel/Tucker, AddisonWesley (2004).
6. Bibliography
See above
RATIONALE
1. Representatives from the College of Business (Marzie Astani, Russ Smith, Mark
Young) requested a new Mathematics course to meet the needs of their majors
and
college. They want a course in Modeling with Precalculus that (a) provides a
consistent, common mathematical starting point for their majors, (b) is
specifically tailored to business applications, and (c) prepares their majors to
succeed if they go on to MATH 140, Applied Calculus. They also would like this
course specifically geared to their majors for the sake of assessing the
mathematical background and ability of the business students. The topics in
MATH
110 do not adequately prepare students for MATH 140. The
representatives said
they do not need their majors to be taught the topics currently
being covered in
MATH 110, Finite Math.
2. This course will be filling an obvious need in terms of
preparation for study of
higher mathematics for business majors as well as
serving as an excellent college
level mathematics experience.
3. No courses will
necessarily be dropped as a result of offering this course,
although the number
of sections offered of Finite Mathematics (MATH 110) will
be decreased.
C. Course Impact
1. The content of this course does not duplicate that taught in
other departments.
There is certainly some overlap between MATH 112 and the
current MATH 115
and MATH 120 sequence. However, the discussion of topics in the
MATH 115 /
MATH 120 sequence is intended for students preparing for Calculus
(MATH
160). The focus on topics in MATH 112 is to develop student’s
problem solving
skills with applications to businesses while also preparing for
MATH 140.
2. The number of credits required would stay the same for students who
enroll in
MATH 112 instead of MATH 110 to satisfy their mathematics requirement.
3. The Mathematics Department and Business College are currently working
together to adopt this change, and are encouraging Business students to enroll
in
MATH 112.
D. Proposal for University Studies Course
(see attached…)
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