Engineering Analyses – Methods
and Models (ENM 503)
Lesson 0 - Course Introduction
A preliminary course in the mathematical
methods and models used in the formulation
and solution of problems found in engineering
management and operations research
Narrator: Charles Ebeling
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Course Description
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The necessary foundation in mathematics to complete
successfully the ENM and MSC core courses in probability
and statistics and operations research as well as the
quantitative elective program.
The mathematical techniques presented are motivated by
their use in solving real-world problems.
Not a concept-theory course but rather a course designed
to enhance your mathematical modeling and solution
method skills.
The models discussed have proven to be the most
useful and successful constructs in solving operations
research and engineering management problems.
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Who should take this course?
Those that have not previously studied in any depth or may have studied but
have forgotten nor never quite mastered the following:
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Set notation and set theory
Systems of linear equations and inequalities
Linear algebra (vectors and matrices)
Discrete mathematics (combinatorics)
Why didn’t I take the
Nonlinear systems of equations
503 course?
Differential and Integral Calculus
Classical optimization
Differential equations
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Course Objective
To be able to mathematically model engineering
management and management science problems and
to manipulate these models using the methods of
engineering, operations research, economics,
mathematics, computer science, probability and
statistics, and any other discipline or technique that
will solve the problem at hand.
Gosh, this is a
really great
objective.
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Specific Objectives
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Apply symbolic logic and set theory, Cartesian
graphs, and functions to describe real world
problems,
Formulate and solve algebraic models,
Use matrix algebra to define and solve linear
systems,
Find discrete solutions using counting methods,
random events, and discrete optimization,
Apply differential calculus to describe,
approximate, and optimize nonlinear functions, and
Use integral calculus to model stochastic
processes and dynamic systems.
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Methods and Models
The topics covered…
 May be well known to you
 May be something you once knew but forgot
 May be completely new to you
For the typical student, it is
very likely that all three
cases will be encountered.
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The Five Building Blocks
(consisting of 18 easy lessons)
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Block 1 - Algebraic Systems
 Sets (qualitative models)
 Algebraic equations and functions
Block 2 - Linear Systems
 Linear equations / inequalities and Matrices
Block 3 - Discrete Systems
 Combinatorics & Discrete Probability
Block 4 Nonlinear Systems
 Differentiation & Optimization
Block 5 Stochastic and Dynamic Systems
 Integration & Differential Equations
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The 18 Easy Lessons
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
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Course orientation
Methods and Models (An Introduction)
Ch 0
Block 1 – Algebraic Systems
The Algebra of Sets - Methods
Handout
Modeling using Sets
Algebraic Methods (Equations & Functions)
Ch 1.1-1.4, 2, 4, 5.1,5.2
Algebraic Models
Block 2 – Linear Systems
Linear Methods (Linear Equations and functions) Ch 3.1, 3.2, 3.4
Matrix Methods (General Linear Systems)
Ch 6.1 – 6.6
Linear Models (Linear Optimization)
Ch 7.1, 7.2
Block 3 – Discrete Systems
Methods of Discrete Counting
Ch 8.1, 8.2
Sequences & Series
Ch 1.5, 5.4
Discrete Probability Models
Ch 8.3, 8.4, 9.1
Discrete Models (Optimization)
Block 4 – Nonlinear Systems
Nonlinear Equation Methods
Ch 3.3, 3.5, 3.6
Methods of Differential Calculus
Ch 11, 12, 17.1 -17.2
Nonlinear Models (Classical Optimization )
Ch 13, 17.5-17.7
Block 5 –Dynamic and Stochastic Systems
Methods of Integral Calculus
Ch 14, 15.1 15.3- 15.4, 15.7
Stochastic Models (Continuous Random
Ch 16.1
Variables)
Differential Equations – Methods and Models
Ch 15.5, 15.6
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Course material
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For each Block and each lesson, there are
 Recorded class lectures
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Adobe Media player
Presentation slides
Textbook references
Problems with solutions
In some cases, additional handout material
Optional Lab session
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Prerequisites
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An undergraduate sequence in calculus
y
g ( y )   f ( x)dx
a
L( x, y,  ) f ( x, y )
g ( x, y )


0
x
x
x
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Textbook(s) – check the
syllabus for the current text
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Haeussler, Ernest; Richard Paul , & Richard Wood,
Introductory Mathematical Analysis, 12th ed.,
Prentice Hall, Upper Saddle River, NJ,
2008. ISBN: 0-13-113948-7
For those needing more practice with the mathematics,
either of the following texts is also recommended:
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1. Jeffrey, Alan, Mathematics for Engineers and
Scientists, 6th ed., Chapman & Hall/CRC, NY, 2005,
ISBN: 1-58488-488-6
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2. Stroud, K. A. , Engineering Mathematics, 6th
ed., Industrial Press, Inc., NY, 2007
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Modeling References
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Meyer, Walter J. Concepts of Mathematical Modeling, Dover
Publications, Inc., Mineola, NY, 2004.
Bender, Edward A., An Introduction to Mathematical Modeling,
Dover Publications, Inc., Mineola, NY, 2000.
Dym, Clive L., Principles of Mathematical Modeling, 2nd Ed., Elsevier
Academic Press, 2004.
Mooney, Douglas and Randall Swift, A Course in Mathematical
Modeling, The Mathematical Association of America, 1999.
Saaty and Alexander, Thinking with Models, Pergamon Press, 1981
Starfield, A., Smith, K., and Bleloch, A., How to Model It, McGrawHill, Inc., 1990
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Software
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MS Excel with VBA and Solver
Internet calculators
You should find the
computer to be
quite helpful in
solving some of the
problems.
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Grading
Exams
5 Block Exams@20 % each
Grade
90-100
85-89
80-84
75-79
70-74
60-69
A
AB+
B
BC
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Scheduled Exam Dates
Exam
Schedule
Pretest
Block 1
Block 2
Block 3
Block 4
Block 5
Topic
Test date
Basic Algebra
Algebraic Models
Linear Models
Discrete Models
Nonlinear Models
Dynamic & Stochastic Models
no later than Thursday Sept. 3
Tuesday September 15
Tuesday October 6
Tuesday October 27
Tuesday November 17
Tuesday December 15
All exams are open book.
Calculators, computers and
laptops may (should) be used.
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An Arranged Course
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Self study
Optional discussion/problem solving sessions
Must adhere to exam Schedule
Instructor available for help
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Contact by email, phone, fax, or office visits
Course material available via internet
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Planned Dates for Optional Lab
Thursday August 27 - course introduction and overview
Thursday September 10 - Block 1
Thursday October 1 - Block 2
Thursday October 22 - Block 3
Thursday November 12 - Block 4
Thursday December 10 - Block 5
Class times are 11:30 am to 12:45 pm
Campus: Room 405
Internet: https://udayton.webex.com/udayton/meet/Ebeling
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About Webex
Website: https://udayton.webex.com/udayton/meet/Ebeling
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Sessions are not password protected
Enter name and an email address to login
Minimal software downloaded the first time you log-in
Will need speakers and mike or a headset (VOIP)
To play a WebEx recording you will need to first
download the WebEx player
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Player can be downloaded from the course Website
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Course Website
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Make good use of it
Check the bulletin board page frequently
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Any changes to the course and course website will
be identified here
Update contact form as necessary
All course material is available on this site
Exam scores will be posted once everyone
has completed a block exam.
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Taking Exams
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Exams are 90 minutes in length and open book.
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Exams will be given at the scheduled time and date
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Computers can be used and may be required
Campus students will take exam in the assigned classroom
Internet exams will be emailed; answers emailed or faxed back
Scores along with the solutions will be posted on the course
Website
Late exams will result in lost points unless prior approval
has been received
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Exams taken after the scheduled completion date will include
additional questions
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Our Very First Assignments
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Go to the course Website, complete, and then submit the
form on the contact page.
Complete the pretest this week
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the link is on the syllabus page under Examinations
The pretest is not part of your course grade
submit your solutions either by fax (937 229-2698) or by
emailing the pretest answer page
Review the first chapter in the text and work as many
problem exercises as needed. Solutions to odd numbered
problems are in the back of the book.
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Contact Information
Last Name: First Name:
Student ID:
email address:
Primary phone number:
Alternate phone (optional):
Alternate email (optional):
Fax (optional):
Internet student? check if yes
(otherwise will attend classes and take exams on campus)
Comments:
Test and homework scores may be posted on this Website using your
student ID as reference. This information may be resubmitted if
changes occur.
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On to the academics…
They are sold on
this methods and
models course!
Let’s get
started!
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