UCC/UGC/ECCC
Proposal for New Course
Fall 2016
Please attach proposed Syllabus in approved university format.
1. Course subject and number:
ME 556
2. Units:
See upper and lower division undergraduate course definitions.
3. College:
CEFNS
4. Academic Unit:
3
Mechanical Engineering
5. Student Learning Outcomes of the new course. (Resources & Examples for Developing Course
Learning Outcomes)
LO1. Demonstrate the ability to apply graduate level critical thinking skills to formulate and
solve advanced mechanical engineering problems:
Acquire knowledge on advanced contemporary engineering topics and computational tools
specific to the emphasis area.
Develop the ability to identify, formulate, and solve advanced engineering problems relevant
to the emphasis area.
c Develop the ability to synthesize, explain, verify, and justify solutions to complex
engineering problems specific to the emphasis area.
LO2. Demonstrate the ability to independently and creatively design and conduct research
studies:
Assess the state of the art in their field of study, including a thorough literature review
Design a research study of personal or professional interest and importance including:
planning, organizing, scheduling, and executing the project with the guidance and input of
their thesis advisor.
Apply independently and creatively appropriate engineering theories and tools towards
finding a viable solution to the thesis topic.
Perform and interpret complex quantitative analyses specific to the thesis.
LO3. Demonstrate the ability to communicate effectively the results of a comprehensive
research study/project through oral presentations and publications:
Create a publishable paper reflecting the integration of knowledge acquired through the thesis
study.
Evaluate the effectiveness of the project and the implications of the resulting data
Synthesize and present the relevance of the research study in both technical and nontechnical terms.
Effective Fall 2015
Deliver an oral presentation to peers summarizing the work performed on the research study
and its outcomes.
Conduct a thesis defense to a community of engineering faculty and peers
Via the following specific steps:
(i) Concepts and methods to enable students to analyze and develop physical models of
nonlinear engineering systems hence allowing them to select nonlinear systems as design
options,
(ii) Concepts and methods to enable students to analyze and develop mathematical models of
nonlinear engineering systems hence allowing them to select nonlinear systems as design
options,
(iii) Application of physical and analytical methods in the solution of engineering problems.
(iv) An ability to adopt the concepts and applications of the physical and analytical methods
listed above at an independent analytical level, and an ability to draw conclusions from the
analysis and apply critical thinking in adopting follow-up decisions.
(v) An ability to read, digest and interpret scientific articles and apply the methods presented
in such articles in similar but different problems.
(scientific articles will be selected at each instant to represent the contemporary
developments in the filed at the time of the course offering, e.g. Journal of Porous Media, Vol.
18 (11), pp. 1075-1089, 2015.)
6. Justification for new course, including how the course contributes to degree program outcomes,
or other university requirements / student learning outcomes. (Resources, Examples & Tools for
Developing Effective Program Student Learning Outcomes)
This course will expand our graduate course offerings to give our M.Eng., M.S., and Ph.D.
students more choices in classes. It is aimed at preparing our graduate students for applying
the concepts and methods taught to analyze and develop physical and mathematical models
of engineering nonlinear systems, and eventually using these as design options. In particular
the graduate students will develop an ability to adopt the concepts and applications of the
physical and analytical methods mentioned above at an independent analytical level, and will
develop an ability to draw conclusions from the analysis and apply critical thinking in
adopting follow-up decisions.
7. Course Title:
ENGINEERING MODELING OF NONLINEAR SYSTEMS
(max 100 characters including spaces)
8. Catalog course description (max. 60 words, excluding requisites):
Introducing modeling. Using dimensional analysis and similarity, and their application to
experimental design leading to physical modeling, Deriving governing equations from first
principles leading to mathematical modeling. Analyzing one, two, three and multi-dimensional
systems in engineering, the presentation of the solutions on a phase diagram. Investigating
bifurcations, linear stability, and numerical solutions.
9. Will this course be part of any plan (major, minor or certificate) or sub plan (emphasis)?
Yes
If yes, list and include the appropriate plan proposal.
MSE / MEng Elective – no related plan change is needed.
Effective Fall 2015
No
10. Does this course duplicate content of existing courses?
Yes
No
If yes, list the courses with duplicate material. If the duplication is greater than 20%, explain why
NAU should establish this course, and include applicable support/correspondence.
11. Grading option:
Letter grade
Pass/Fail
Both
12. Proposed Co-convene with:
ME 456
14a. UGC approval date*:
See co-convening policy.
*Must be approved by UGC before UCC submission, and both course syllabi must be presented.
13. Proposed Cross-list with:
See cross listing policy.
14. May course be repeated for additional units?
14a. If yes, maximum units allowed?
14b. If yes, may course be repeated for additional units in the same term?
Yes
No
Yes
No
ME 252, ME 395, MAT
239 and MAT 362 with
15. Proposed Prerequisites:
grades of C or better.
If prerequisites, include the rationale for the prerequisites.
Topics from these courses will be used directly in ME 556. In particular the mathematical tools
from Differential Equations (MAT 239) and Numerical Analysis (MAT 362) are used in the
analytical part of the course, the topics from dynamics (ME 252) and fluid dynamics (ME 395)
are expanded in this course and the applications to engineering design are particularly dealt
with.
16. Proposed Co requisites:
If co requisites, include the rationale for the co requisites.
17. Does this course include combined lecture and lab components?
Yes
If yes, include the units specific to each component in the course description above.
No
18. Does this course include an experiential learning component?
No
19. Class Instruction Mode:
In-person
If In-person or Blended, where will the course be offered?
20. Which terms will the course be offered?
Fall
Winter
Other
Effective Fall 2015
Online
FLGMTN
Yes
Blended
Other
Spring
Summer
(Fall/Even Yrs, Spring/Odd Yrs, Intermittent, etc.)
21. Do you anticipate this course will be scheduled outside the regular term?
Yes
No
If yes, please refer to: http://nau.edu/Registrar/Faculty-Resources/Schedule-of-Classes-Maintenance/
22. Will there be a course fee?
If yes, please refer to: http://nau.edu/Registrar/Faculty-Resources/Course-Fees/
Yes
No
23. Is this course being proposed for Liberal Studies designation?
Yes
No
24. Is this course being proposed for Diversity designation?
Yes
No
Answer 23-24 for UCC/ECCC only:
FLAGSTAFF MOUNTAIN CAMPUS
Scott Galland
Reviewed by Curriculum Process Associate
2/1/2016
Date
Approvals:
F. Ernesto Penado
Department Chair/Unit Head (if appropriate)
12/7/2015
Date
Chair of college curriculum committee
Date
Dean of college
Date
For Committee use only:
UCC/UGC Approval
Date
EXTENDED CAMPUSES
Reviewed by Curriculum Process Associate
Date
Approvals:
Academic Unit Head
Effective Fall 2015
Date
Division Curriculum Committee (Yuma, Yavapai, or Personalized Learning)
Date
Division Administrator in Extended Campuses (Yuma, Yavapai, or Personalized
Learning)
Date
Faculty Chair of Extended Campuses Curriculum Committee (Yuma, Yavapai, or
Personalized Learning)
Date
UGC Approval (Graduate-Level Courses Only)
Date
Chief Academic Officer; Extended Campuses (or Designee)
Date
From: F Ernesto Penado
Sent: Monday, December 07, 2015 2:18 PM
To: Stuart S Galland <Stuart.Galland@nau.edu>
Subject: ME 456/556
Hi Scott,
Attached are the proposal forms for ME 456/556 with my electronic approval.
Thanks,
-Ernesto
----------------F. Ernesto Penado, Ph.D.
Professor and Chair
Department of Mechanical Engineering
Northern Arizona University
ME 556 (3 cr. hrs.) : Engineering Modeling of Nonlinear Systems
Syllabus & Course Information
1. ME 556 (3 cr. hrs.) : Engineering Modeling of Nonlinear Systems
2. Syllabus & Course Outline: Problem Formulation, The Problem: Schematic Figure, Effects and Phenomena, The Question,
Governing Equations, Modeling Principles, Optimization Problems. Modeling Principles, Physical Modeling versus Mathematical
Modeling, Dimensional Analysis and Similarity, Application of similarity to experimental design – Physical Modeling, Deriving
governing equations from first principles – Mathematical Modeling, One-dimensional systems in engineering, the Phase Diagram,
Bifurcations, Linear Stability, Superconducting Josephson Junctions, Two-dimensional systems, Limit Cycles, Pendulum, Duffing
and van derPol oscillators, Bifurcations extended, Natural Convection and the Lorenz System, Engineering Projects to design,
manufacture and test simple nonlinear engineering systems that manifest chaotic behavior, OR to model, analyze and solve
numerically more complex engineering systems that manifest chaotic behavior.
3. Pre-requisites: MAT 239 (DiffEq), ME 252 (Dyn), ME 395 (FlMech), MAT 362 (IntNumAnal).
4. Textbook(s) and/or other required material:
Recommended Textbooks:
Effective Fall 2015

Strogatz, S.H.,: Nonlinear Dynamics and Chaos, Perseus Books Publ., 1994.

Frank M. White “Fluid Mechanics” 7th edition, McGraw Hill 2011.

Schaum’s series: Spiegel, Murray R., Mathematical Handbook.
Scientific Articles for reading, digesting, and applying their methods in similar problems:
Journal of Porous Media, Vol. 18 (11), pp. 1075-1089, 2015
International Journal of Heat and Mass Transfer, Vol. 43 (5), pp.705-724, 1999
Transport in Porous Media, Vol. 37 (2), pp.213-245, 1999
Journal of Fluid Mechanics, Vol. 376, pp. 351-375, 1998
5. Course objectives:
 to teach concepts and methods that enables students to analyze and develop physical models of nonlinear engineering systems
hence allowing them to select nonlinear systems as design options. LO1*, LO2*
 to teach concepts and methods that enables students to analyze and develop mathematical models of nonlinear engineering
systems hence allowing them to select nonlinear systems as design options. LO1*, LO2*
 Application of physical and analytical methods in the solution of engineering problems. LO1*, LO2*
 Graduate students will have more challenging assignments and Projects than undergraduate students. Project deliverables
will include presentations to the class on progress, a final project presentation, and a formal Project Report. LO3*
 Graduate students are expected to set the standards for class participation, and to produce high-quality deliverables. LO3*
 Graduate students are assessed in part on their use of scientific articles published in technical journals. LO3*
6. Class: 3 hrs. Lecture
7. Contribution of course to meeting the professional component: Engineering Science: 100%
8. *Graduate Learning Outcomes
(LO1). Demonstrate the ability to apply graduate level critical thinking skills to formulate and solve advanced mechanical
engineering problems:
Acquires knowledge on advanced contemporary engineering topics and computational tools specific to mechanical
engineering.
Develops the ability to identify, formulate, and solve relevant advanced mechanical engineering problems.
Develops the ability to synthesize, explain, verify, and justify solutions to complex mechanical engineering problems.
(LO2). Demonstrate the ability to independently and creatively design and conduct research studies:
Assess the state of the art in their field of study, including a thorough literature review
Design a research study of personal or professional interest and importance including: planning, organizing, scheduling, and
executing the project with the guidance and input of their thesis advisor.
Apply independently and creatively appropriate engineering theories and tools towards finding a viable solution to the thesis
topic.
Perform and interpret complex quantitative analyses specific to the thesis.
(LO3). Demonstrate the ability to communicate effectively the results of a comprehensive research project through oral presentations
and publications.
Creates a report reflecting the integration of knowledge acquired through the project.
Delivers an oral presentation to peers summarizing the work performed on the project and its outcomes.
Synthesizes and presents the relevance of the engineering project in both technical and non-technical terms.
9. Instructor:
Dr. Peter Vadasz, Room 260, Engineering Bldg.
Ph. 523-5843, e-mail: peter.vadasz@nau.edu
Office Hours: Tu & Th 9:15 am – 11:10 am & 12:25 pm – 12:35 pm. and any other time by scheduled appointment (send an email to
request an appointment to: Peter.Vadasz@nau.edu ).
10. Assignments: to be submitted as hard copy in MSWord to the instructor in class.
Typed in MS Word, Font “Times” or “Times New Roman”, size 12 points, using Equation Editor/MathType within Word for equations
as well as symbols in text. Symbols and equations in Italics, Vectors in Bold Italics. Number equations consecutively.
11. Project Final Report (Formal Report): to be submitted electronically in MSWord via email to the instructor’s email (see below).
Typed in MS Word, Font “Times” or “Times New Roman”, size 12 points, using Equation Editor/MathType within Word for equations
as well as symbols in text. Symbols and equations in Italics, Vectors in Bold Italics. Number equations consecutively. Include a
Nomenclature, Abstract, Introduction, Problem Formulation, Methods, Results, Discussion, Conclusion, References, Appendices.
Effective Fall 2015
Figures and Tables to be inserted near the text that refers to them. Tables captions above the table. Figures captions below the Figures.
Number Tables and Figures separately.
12. Final Grade Distribution: Test 40%, Homework Assignments 20%, Project 40% (part of it are the progress presentations).
13. Person(s) who prepared this description and date of preparation: Dr. Peter Vadasz, August 25, 2014.
TENTATIVE LECTURE SCHEDULE:
Tentative Lecture Schedule (Revision 0 – Sep. 2015)
No.
1.
2.
3.
4.
5.
6.
Date
Sep. 1
Sep. 3
Sep. 8
Sep. 10
Sep. 15
Sep. 17
7.
8.
9.
Sep. 22
Sep. 24
Sep. 29
10.
11.
12.
13.
14.
15.
16.
17.
Oct. 1
Oct. 6
Oct. 8
Oct. 13
Oct. 15
Oct. 20
Oct. 22
Oct. 27
18.
Oct. 29
19.
20.
Nov. 3
Nov. 5
Introduction to Bifurcations and Applications
Introduction to Bifurcations and Applications
Two Dimensional Linear Systems
Two Dimensional Linear Systems
Two Dimensional Linear Systems
Phase Diagram – Nonlinear Systems
Bifurcations and Applications
Limit Cycles and Applications: van der Pol
oscillator, Duffing oscillator
TEST
Lorenz System for Natural Convection
Project Kickoff Meeting
Project Progress Report Meeting
20.
Nov. 10
Project Progress Report Meeting
Project Progress Report
21.
22.
Nov. 12
Nov. 17
Project Progress Report Meeting
Project Progress Report Meeting
Project Progress Report
Project Progress Report
23.
24.
Nov. 19
Nov. 24
Nov. 26
25.
26.
Dec. 1
Dec. 3
27.
Dec. 8
28.
30.
Dec. 10
Dec. 15
Effective Fall 2015
Topic
Introduction
Dimensionless Analysis and Similarity
Application of Similarity to Experimental Design
Physical Modeling
Physical Modeling
Deriving governing equations from first
principles - Mathematical Modeling
One dimensional systems. Phase Plane
One dimensional systems. Phase Plane
One dimensional systems. Phase Plane
Project Progress Report Meeting
Project Progress Report Meeting
THANKSGIVING HOLIDAY
Project Progress Report Meeting
Project Progress Report Meeting
Project Progress Report Meeting
Submission of Draft Project Final Report
FINAL Report due Tuesday Dec 15, 2015, at
2:30 pm
Homework Due
Assignment 1
Assignment 2
Assignment 3
Assignment 4
Assignment 5
Assignment 6
Proposed Project Topics Assignment 7
Allocation of Project Topics to Groups &
Assignment 8
Assignment 9
Assignment 10
Assignment 11
Assignment 12
Assignment 13
Assignment 14
Assignment 15
Assignment 16
Project Progress Report
Project Progress Report
Project Progress Report
Project Progress Report
Project Progress Report
Project Progress Report
Project Draft Final Report
Project Final Report
FINAL REPORT due: to be submitted electronically to: Peter.Vadasz@nau.edu
Dr. Peter Vadasz, Room 260, Engineering Bldg.
Ph. 523-5843, e-mail: peter.vadasz@nau.edu
Office Hours: Tu & Th 9:10 am – 11:10 am & 12:25 pm – 12:45 pm.
and any other time by scheduled appointment (send an email to request an appointment to: Peter.Vadasz@nau.edu ).
Evaluation is based on a differential assessment, which for the graduate group focuses on using the conceptual principles to making
engineering decisions, while using techniques and their application in the solution of engineering problems. The graduate group is also
assessed on its use of scientific articles published in scientific journals (as listed above), and has to demonstrate critical thinking in
addressing the corresponding engineering problems.
NORTHERN ARIZONA UNIVERSITY
POLICY STATEMENTS FOR COURSE SYLLABI
SAFE ENVIRONMENT POLICY
NAU’s Safe Working and Learning Environment Policy prohibits sexual harassment and assault, and discrimination and
harassment on the basis of sex, race, color, age, national origin, religion, sexual orientation, gender, gender identity,
disability, or veteran status by anyone at this university. Retaliation of any kind as a result of making a complaint under the
policy or participating in an investigation is also prohibited. The Director of the Equity and Access Office (EAO) serves as
the university’s compliance officer for affirmative action, civil rights, and Title IX, and is the ADA/504 Coordinator. EAO also
assists with religious accommodations. You may obtain a copy of this policy from the college dean’s office or from NAU’s
Equity and Access Office website nau.edu/diversity/. If you have questions or concerns about this policy, it is important that
you contact the departmental chair, dean’s office, the Office of Student Life (928-523-5181), or NAU’s Equity and Access
Office (928) 523-3312 (voice), (928) 523-9977 (fax), (928) 523-1006 (TTD) or equityandaccess@nau.edu.
STUDENTS WITH DISABILITIES
If you have a documented disability, you can arrange for accommodations by contacting Disability Resources (DR) at 5238773 (voice) or 523-6906 (TTY), dr@nau.edu (e-mail) or 928-523-8747 (fax). Students needing academic accommodations
are required to register with DR and provide required disability related documentation. Although you may request an
accommodation at any time, in order for DR to best meet your individual needs, you are urged to register and submit
necessary documentation (www.nau.edu/dr) 8 weeks prior to the time you wish to receive accommodations. DR is strongly
committed to the needs of student with disabilities and the promotion of Universal Design. Concerns or questions related to
the accessibility of programs and facilities at NAU may be brought to the attention of DR or the Office of Affirmative Action
and Equal Opportunity (523-3312).
ACADEMIC CONTACT HOUR POLICY
Based on the Arizona Board of Regents Academic Contact Hour Policy (ABOR Handbook, 2-224), for every unit of credit,
a student should expect, on average, to do a minimum of three hours of work per week, including but not limited to class
time, preparation, homework, studying.
ACADEMIC INTEGRITY
Integrity is expected of every member of the NAU community in all academic undertakings. Integrity entails a firm
adherence to a set of values, and the values most essential to an academic community are grounded in honesty with
respect to all intellectual efforts of oneself and others. Academic integrity is expected not only in formal coursework
situations, but in all University relationships and interactions connected to the educational process, including the use of
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All outside assistance should be acknowledged, and the student’s academic contribution truthfully reported at all times. In
addition, NAU students have a right to expect academic integrity from each of their peers.
Individual students and faculty members are responsible for identifying potential violations of the university’s academic
integrity policy. Instances of potential violations are adjudicated using the process found in the university Academic
Integrity Policy.
RESEARCH INTEGRITY
Effective Fall 2015
The Responsible Conduct of Research policy is intended to ensure that NAU personnel including NAU students engaged
in research are adequately trained in the basic principles of ethics in research. Additionally, this policy assists NAU in
meeting the RCR training and compliance requirements of the National Science Foundation (NSF)-The America
COMPETES Act (Creating Opportunities to Meaningfully Promote Excellence in Technology, Education and Science); 42
U.S.C 18620-1, Section 7009, and the National Institutes of Health (NIH) policy on the instruction of the RCR (NOT-OD-10019; “Update on the Requirement for Instruction in the Responsible Conduct of Research”). For more information on the
policy and the training activities required for personnel and students conducting research, at NAU,
visit: http://nau.edu/Research/Compliance/Research-Integrity/
SENSITIVE COURSE MATERIALS
University education aims to expand student understanding and awareness. Thus, it necessarily involves engagement with
a wide range of information, ideas, and creative representations. In the course of college studies, students can expect to
encounter—and critically appraise—materials that may differ from and perhaps challenge familiar understandings, ideas,
and beliefs. Students are encouraged to discuss these matters with faculty.
CLASSROOM DISRUPTION POLICY
Membership in the academic community places a special obligation on all participants to preserve an atmosphere
conducive to a safe and positive learning environment. Part of that obligation implies the responsibility of each member of
the NAU community to maintain an environment in which the behavior of any individual is not disruptive. Instructors have
the authority and the responsibility to manage their classes in accordance with University regulations. Instructors have the
right and obligation to confront disruptive behavior thereby promoting and enforcing standards of behavior necessary for
maintaining an atmosphere conducive to teaching and learning. Instructors are responsible for establishing,
communicating, and enforcing reasonable expectations and rules of classroom behavior. These expectations are to be
communicated to students in the syllabus and in class discussions and activities at the outset of the course. Each student
is responsible for behaving in a manner that supports a positive learning environment and that does not interrupt nor
disrupt the delivery of education by instructors or receipt of education by students, within or outside a class. The complete
classroom disruption policy is in Appendices of NAU’s Student Handbook.
August 25, 2015
Effective Fall 2015