Introduction to Mathematical Modeling

Course Location & Time: Classroom South 107, MWF 10:00-10:50

Textbook: Explorations In College Algebra, 4^th Edition, by Kime, Clark and Michael, John Wiley & sons.
ISBN: 9780470281482, and Wiley Plus.

Note: This course syllabus provides a general plan for the course; deviations may be necessary.

1. COURSE DESCRIPTION. Mathematical modeling uses graphical, numerical, symbolic, and verbal
techniques to describe and explore real-world data and phenomena. Emphasis is on the use of elementary
functions to investigate and analyze applied problems and questions, on the use of appropriate supporting
technology, and on the effective communication of quantitative concepts and results. THIS COURSE IS
NOT AN APPROPRIATE PREREQUISITE FOR PRECALCULUS OR CALCULUS. Students who must
take pre-calculus must understand the implications of taking MATH 1101 (See the instructor immediately
if you have any questions).

2. PREREQUISITE. Knowledge of high school algebra II, or equivalent, is expected. This includes
algebraic expressions , first degree equations and inequalities, exponents, radicals , solving and graphing
linear equations, factoring quadratic expressions, and other topics.

3. COURSE OBJECTIVES.

Algebra. Students will demonstrate the ability to:

a. Graph points.
b. Graph linear, piecewise linear, exponential, logarithmic, and quadratic equations and
functions, as well as identify horizontal asymptotes.
c. Determine the equation of a line given two points or one point and the slope .
d. Determine the absolute value of a quantity.
e. Solve and estimate solutions to linear, quadratic, exponential, and logarithmic equations ,
including use of the properties of exponents and common and natural logarithms.
f. Solve linear systems of two equations by substitution and elimination , including systems
that have a unique solution, no solution, or many solutions.
g. Simplify expressions using the laws of exponents and logarithms.
h. Calculate average rate of change of any function.
i. Perform arithmetic calculations to answer questions regarding two-variable data
presented in tabular, graphical, or equation form.
j. Express and compare very large and very small numbers using scientific notation and
orders of magnitude .
k. Factor quadratic expressions.
l. Complete the square of quadratic expressions.
m. Express the square root of negative numbers in terms of the imaginary unit, i.
n. Given conversion factors, convert units of measure.
o. Use the quadratic formula to solve quadratic equations

Functions. Students will demonstrate:

a. The understanding of the definitions of function, domain, range, independent and
dependent variables, and input and output.
b. The ability to determine if tables, graphs, and equations represent functions.
c. The ability to determine the domain and range of functions as mathematical abstractions
or in a physical context.
d. The ability to determine from the graph of a function the values of the independent
variable for which the function increases, decreases, or remains constant.

Linear and piecewise linear functions. Students will demonstrate the ability to:

a. Determine when two real-world variables are related by a linear or piecewise linear
function.
b. Calculate, and interpret average rate of change as slope .
c. Model the behavior of two real-world variables that are directly proportional or are
related by a linear or piecewise linear function using tables, graphs, equations.
d. Evaluate linear and piecewise linear functions.
e. Use a linear function to approximate the value of a non-linear function.
f. Interpret the intersection of the graphs of linear functions as equilibrium points.
Exponential Functions. Students will demonstrate the ability to:
a. Determine when two real-world variables are related by an exponential function.
b. Model the behavior of two real-world variables that are related by an exponential
function using tables, graphs, equations, or combinations thereof including such
applications as population growth and decay, radioactive decay, simple and compound
interest, inflation, the Malthusian dilemma, musical pitch, and the Rule of 70.
c. Change the base of an exponential function to determine rate of growth/decay,
growth/decay factor, and effective and nominal interest rate.
d. Express continuous growth/decay in terms of the number e.
e. Evaluate exponential functions.
f. Determine the exponential equation model from the table or graphical model.
g. Compare linear to exponential growth.

Logarithmic Functions. Students will demonstrate:

a. The ability to determine when two real-world variables are related by a logarithmic
function.
b. The ability to model the behavior of two real-world variables that are related by a
logarithmic function using tables, graphs, equations, or combinations thereof including
such applications as pH and the decibel system.
c. The understanding of the natural logarithm.
d. The ability to graph logarithmic functions.

Quadratic Functions. Students will demonstrate the ability to:

a. Estimate horizontal intercepts of quadratic functions from their graphs.
b. Determine the horizontal intercepts of quadratic functions in factored form.
c. Determine the vertex, axis of symmetry, and horizontal and vertical intercepts of
quadratic functions in either the a-b-c or a-h-k forms.
d. Convert quadratic functions from the a-b-c form to the a-h-k form and vice versa.
e. Determine when two real-world variables are related by a quadratic function by
calculating the average rate of change of the average rates of change.
f. Model the behavior of two real-world variables that are related by a quadratic function
using tables, graphs, equations, or combinations thereof including such applications as
maximum area for fixed perimeter, minimum perimeter for fixed area, free fall,
maximum profit, and break-even analysis.

4. COURSE COVERAGE. We will cover the following sections from the text:

Chapter 1 Making Sense of Data and Function (1.1 - 1.5)
Chapter 2 Rates of Change and Linear Functions (2.1 - 2.8)
Chapter 3 When Lines Meet: Linear Systems (3.1 - 3.2, 3.4)
Chapter 4 The Laws of Exponents and Logarithms: Measuring the Universe (4.1 - 4.7)
Chapter 5 Growth and Decay: An Introduction to Exponential Functions (5.1 - 5.6)
Chapter 6 Logarithmic Links: Logarithmic and Exponential Functions (6.1 - 6.5)
Chapter 8 Quadratic and Other Polynomial Functions (8.1 - 8.4)

IMPORTANT NOTE: Georgia State University and its faculty are not responsible for outcomes due to
individual technical issues, nor scheduled WileyPlus downtimes. It is expected that the students will be
responsible for completing their work in a timely fashion as to alleviate any pressures these scheduled
downtimes occur. All students will be notified of these downtimes by WileyPlus through the
announcements page of the course.

5. COURSE EVALUATION. Your course grade will be determined as follows:

a. Tests (Three close book, close notes tests) 45%

b. WileyPlus online homework and quizzes 15%

c. Excel Projects 10%

d. In Class Activities 5%

e. Final Exam (Comprehensive, close book, close notes final exam) 25%

Example of Course Grade Computation:
Test Grades: T1 = 88, T2 = 72, T3 = 68,
WileyPlus online homeworks and quizzes average = 85
Excel Project average = 90
In Class Activities =80
Final Exam=76
Course Grade: 0.15*(88+72+68) +0.15*85+ 0.10*90 + 0.05*80+0.25*76 = 79

6. GRADING SCALE. We will use the following grading scale:

A: 90 - 100, B+: 87 - 89, B: 80 -86, C+: 77 - 79, C: 70 - 76, D: 60 - 69, F: Below 60

7. Makeup Policy: No make-up exams will be given unless in some extreme situations. Absence from the
final exam will result in a grade of F for the course unless arrangements are made PRIOR (at least one
week before the final exam) to its administration.

MATH 1101 Homework Assignments
Kime, Clark and Michael 4^th Edition