N. D. Ebrahimi


UNM is offering this course as an "online" course. As such, except for three (3) exams, there are no live (synchronous) class meetings.

Office Hours

Since this course is offered through the Extended University, traditional office hours are not set. I may be contacted by e-mail, however. Additionally, students who may have questions on the homeworks are offered a "Flipped Classroom" session on most Friday afternoons (12:00-1:00 PM) throughout the semester.


Course updates, announcements, etc. will be sent to you via your UNM e-mail account. For this reason, it is important that you check your UNM e-mail Inbox on a very regular basis. If you prefer to receive e-mail through other accounts (addresses), you can update your UNM preferred e-mail account at


Homeworks will be assigned regularly.


Important note: Working diligently on assignments constitutes the best path toward doing well in exams (and, therefore, receiving a good grade in the course). It is the responsibility of the students to make sure that they gain a high level of competency with the subject through homeworks.


Topical prerequisites: Undergraduate Vibrations (ME 357 at UNM) and Controls (ME 380 at UNM); Ordinary Differential Equations (MATH 316 at UNM); Introductory Linear Algebra (MATH 314 or 321 at UNM)

A high level of proficiency is required in the above subjects. Students who feel deficient should review their previous (undergraduate) Vibrations, Controls, Ordinary Differential Equations, and Linear Algebra textbooks.

Additional Information Regarding Prerequisites: Students who have received their BSME degree at UNM automatically satisfy the first three prerequisites mentioned above (ME 357, 380, MATH 316), since all three of these courses are required for the BSME.

UNM Registrar's Office, however, does not check/enforce the prerequisites for graduate courses (such as ME 580); the registered graduate students are held responsible for self-enforcement of the prerequisites.

If, at any point, it is discovered that a student does not have the correct prerequisites, the instructor reserves the right to disenroll the student from the class. (This is a campus-wide academic policy/practice.)

Students who have never taken Linear Algebra should first complete MATH 314 or 321 before taking ME 480/580. Both of these courses can count as acceptable graduate courses for the MSME or as a Math Elective towards the BSME. The knowledge of this subject is necessary in a large majority of graduate and upper level undergraduate ME courses. 

In relation to Math background, the following topics are of particular importance to ME 480/580: 

  • Solving Constant-Coefficient, Linear, Ordinary Differential Equations

  • Partial Fraction Expansion

  • Laplace Transform

  • Matrix Operations/Arithmetic (Add, Subtract, Multiply, Inverse)

  • Solving Systems of Linear Algebraic Equations

  • Matrix Determinants

  • Eigenvalues and Eigenvectors

  • Matrix Rank and Linear Independence

Course                     Objective

To improve students’ understanding of linear dynamic systems (with a focus on state-space techniques). To put it simply, if you took ME 357 and ME 380 and you enjoyed the subjects [but you would want to gain a deeper understanding of the fundamentals] you may consider taking ME 480/580.


Grades will be curved.

  • 15%: Home-works (subject to availability of funds and qualified personnel for grading)

  • 85%: Three (3) Semester Exams (equally weighted)

Note to ME 480 students: this course is one of the options of the ME Graduate Core courses at UNM. As such, it is intended mainly as a Graduate course. Undergraduate students who choose to take this course are treated the same way as graduate students.

Exams Logistics

1. Quantitative as well as concept-type.

2. Range of coverage: all home works (and their supporting material) that are due before the day of exam.
3. Closed-book/closed-notes; one sheet of notes (8.5 × 11.0 in., only one side) and calculators are allowed, however.

4. Cell phones, electronic tablets, Laptops as well as all other similar electronic devices are not allowed.

                                                                                                  Computational      Software

It is very appropriate (and in many cases, necessary) to make use of your scientific calculator and/or commercially available software (such as Matlab) in carrying out complex or tedious calculations. Examples of this type of calculations include (but not limited to): Plots, Eigen-problems, Matrix Inversions, Systems of Algebraic Equations, Differential Equations, Integration, etc. Matlab is available at UNM computer pods as well as ME Department's computer room. For a tutorial on Matlab please visit The MathWorks.

Course Material &
Web-based Instructional Support

No textbook is required. Lecture notes will be made available (in electronic form) to all registered students.  Other e-handouts, including example as well as homework problems, are also provided. Access will be provided at the beginning of the semester (open your UNM e-mail “Inbox” on the first day of the).

Outline of Contents

Writing Differential Equations for Engineering Systems such as Mechanical, Hydraulic, Electric, Electromechanical, and Thermal Systems.

2.      Standard Signals: Unit Step, Unit Ramp, and Unit Parabola. Mathematical Descriptions of Continuous-Time Systems: Input-Output Descriptions of Single Variable Systems; Computation of the Impulse Response; Transfer Functions; “Simulation” Diagrams; Concept of State; Continuous Dynamical Systems; Deriving State-Space Descriptions; Linear Transformation of State Variables; Obtaining the Transfer Function from the State-Space Description.

3.      Analysis of the State Equations for Continuous-Time Systems: Time-Varying Homogeneous Case, State Transition Matrix; Time-Invariant Homogeneous Case; Time-Invariant Forced Case; System Modes.

4.      System Controllability and Observability: Controllability and Observability of Time-Invariant Systems with Distinct Eigenvalues; Direct Criteria.

5.      System Stability: Equilibrium States; Stability Concepts; Stability Criteria for Zero-Input and Nonzero-Input Systems; Total Stability; Lyapunov's Direct Method.

Learn about UNM Learn

Activities of this class will be conducted via the UNM Learning Management System (LMS) referred to as "UNM Learn."

Extensive information about how to use the Learn system is available to you through the following page:

Please make sure that you are familiar with this system before starting your actual (academic) course activities.