# Introduction to Mathematical Modeling

**Textbook: **Explorations In College Algebra, 4^{th}
Edition, by Kime, Clark and Michael, John Wiley & Sons.

ISBN: 9780470281482. The 4^{th}
Edition comes with a code for WileyPlus
registration which is needed.

**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 precalculus 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. 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. and 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.

**Your course grade will be determined as follows:**

5. COURSE EVALUATION.

5. COURSE EVALUATION.

a. Three midterm tests (closed book/notes): 45% (15% each)

b. WileyPlus online homework and quizzes: 20%

c. Excel Projects: 10%

d. Final Exam (closed book/notes, cumulative): 25%

e. Bonus points: For example, the Pre-QL and Post-QL carry bonus points.

**Example of Course Grade Computation:**

Test Grades: T1 = 88, T2 = 72, T3 = 68; WileyPlus online homework and quizzes = 85;

Excel Project average = 90; Final Exam = 76; Bonus: 1.5.

Then the overall course score is 0.15*(88+72+68) + 0.20*85 + 0.10*90 + 0.25*76 + 1.5 = 80.7

**6. GRADING SCALE.**We will use the following grading scale (C- not available):

F: Less than 60

For example, the above score of 80.7 would make a letter
grade of B- for the course.

**7. Makeup Policy: **No make-up exams will be given unless in some extreme and
documented 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.

**8. CALCULATOR Policy.** You are recommended to have a scientific calculator or a
graphing calculator.

If you are not strong in mathematics, I strongly recommend
you obtain a graphing calculator. You are not

allowed to share calculator with
any other party in your class during any in class quiz or exam, unless

permitted
by your instructor.

**9. Academic assistance at GSU:**

1. Attend academic assistance session, MW 12:00-1:15pm, 120 Kell Hall.

2. Visit the Math Assistance Complex (MAC), Kell Hall 122 (phone: 404-413-6462).

3. Visit the Counseling Center for Learning assistance,
Test anxiety classes, and Student support

services (phone: 404-413-1641)

4. African American Student Services (phone: 404-413-1530)

5. A private tutor list is available at Math Assistance Complex and Math
Department

**10. ACADEMIC HONESTY:** Cheating/plagiarism will not be tolerated on any work. A
first occurrence

will result in a grade of 0 on the assignment for all concerned
parties as well as an Academic Dishonesty

form being filed with the Dean of
Students. A second occurrence will result in a grade of F for the course

for the
concerned parties and a second Academic Dishonesty form being filed. During
in-class quizzes,

tests, and the final exam you will be instructed to do your
own work, talk to nobody, and not share

calculators. Violations of these
instructions constitute dishonesty and will be handled in accordance with

University policy. The instructor has the option of withholding or denying
credit for answers not

adequately supported by you.

**11. Inclement Weather Policy:** If the University is closed due to inclement
weather, any exam that may

have been scheduled for that date will be
administered on the next available class date. If an assignment is

due that day
it will be due the next class.

**12. Attendance Policy:** Attending class is of utmost importance and is your
responsibility and yours alone.

(Attendance will be taken daily). During class
the instructor can clarify important or complex points for

you, observe you
working problems, and answer your questions. However, much, and perhaps most, of

what you learn during the course will occur outside of class; approximately two
hours preparation for each

hour in class over is the norm.

**13. Conduct Policy:** Turn off all pagers and cell phones before entering the
classroom – having these

items “go off” in class is considered disruptive
behavior and can result in your being administratively

dropped from the course.
In fact, any type of inappropriate conduct may result in your being

administratively dropped from the course.

**14. Withdrawal Policy: **You cannot withdraw from the course simply by ceasing to
attend class; you must

formally withdraw. If you intend to withdraw, do so
before **midpoint (Thursday, October 15th)** to be able

to **possibly** avoid a grade of
“F” or “WF.” **If you do not attend class during the first two weeks you will
be
administratively withdrawn.**

**15. ASSIGNMENTS.**Although we will basically follow the attached schedule, deviations might be

necessary. I will assume that you have read the corresponding lesson prior to arriving in class and do the

homework assignments posted on the ULEARN after attending class.

**The dates of the 3 tests are tentative. Make-up tests may be granted only for extreme**

16. EXAM DATES.

16. EXAM DATES.

emergencies (such as medical emergencies) that must be documented.

Test 1: | Thursday, September 10th, 1:00 – 2:15pm | In class | Chapter 1, 2 |

Test 2: | Tuesday, October 20th, 1:00 – 2:15pm | In class | Chapter 3, 4, 5 |

Test 3: | Thursday, November 19th, 1:00 – 2:15pm | In class | Chapter 6, 8 |

Final Exam: | Thursday, December 8th, 12:30 – 2:30pm | 625 GCB | Cumulative |

**17. OTHER IMPORTANT DATES.**

Last day to drop a class with full refund: Friday, August 21.

Last day to withdraw from term length classes and **possibly receive a W: **Thursday, October 15.

Welcome aboard!

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