Mechanical Engineering
Professor and Department Head
Anthony J. Petrella, Department Head
Professors
Alexandra Newman, Director of Operations Research with Engineering Program
Carl Frick, Professor and Dean of Graduate Studies
Cristian Ciobanu
Gregory Jackson
John Berger, Dean of Energy and Materials
Mohsen Asle Zaeem
Neal Sullivan
Robert Braun, University Distinguished Professor of Mechanical Engineering and Director of Mines/NREL Advanced Energy Systems Program
Robert Kee, George R. Brown Distinguished Professor
Associate Professors
Andrew Petruska
Anne Silverman
Anthony J. Petrella, Interim Department Head
Joy Gockel
Leslie Lamberson
Mark Deinert
Nils Tilton
Owen Hildreth
Paulo Cesar Tabares-Velasco
Ruichong "Ray" Zhang
Steven DeCaluwe, Director of Graduate Studies
Veronica Eliasson
Xiaoli Zhang
Assistant Professors
Aashutosh Mistry
Andrew Osborne
Denis Aslangil
Rajavasanth Rajasegar
Samantha "Sam" Webster
Frankie Zhu
Professors of Practice
Angel Abbud-Madrid, Director of Space Resources Program
Brian Gockel
Christopher Dreyer
Craig Brice, Director of Additive Manufacturing Program
George Sowers
Teaching Professors
Derrick Rodriguez
Kristine R. Csavina, Director of Capstone
Ventzi Karaivanov
Teaching Associate Professors
Daniel Blood, Director of Undergraduate Studies
Jeffrey Ackerman
Jeffrey Wheeler
Oyvind Nilsen
Teaching Assistant Professors
Adam Duran
Elijah Kuska
Gary Nave
Jim Wong
Kelly Rickey
Mathew Johnson
Polina Brodsky
Siby Thomas
Stephen Geer
Affiliate Professor of Mechanical Engineering
Mike Mooney
Research Associate Professors
Sandrine Ricote
Huayang Zhu
Research Assistant Professors
Omid Babaie-Rizvandi
Carolina Herradon Hernandez
Garrison Hommer
Research Professor
Brian Thomas
Emeriti Professors
Joan Gosink
Graham Mustoe
Robert King
Terry Parker
Emeriti Associate Professors
Dave Munoz
Joel Bach
John P.H. Steele
Program Details
The Mechanical Engineering Department offers the degrees Master of Science and Doctor of Philosophy in Mechanical Engineering. The master's program is designed to prepare candidates for careers in industry or government or for further study at the PhD level; both thesis and non-thesis options are available. The PhD degree program is sufficiently flexible to prepare candidates for careers in industry, government, or academia. The following information provides details on these degrees.
Mines's Combined Undergraduate / Graduate Degree Program
Students enrolled in Mines’s combined undergraduate/graduate program may double count up to six credits of graduate coursework to fulfill requirements of both their undergraduate and graduate degree programs. See Graduate section of the Catalog under Combined Undergraduate/Graduate Degree Programs for specific details on what types of courses are allowed and under what conditions. These courses must have been passed with “B-” or better, must not be substitutes for required coursework, and must meet all other University, Department, and Program requirements for graduate credit.
Students are advised to consult with their undergraduate and graduate advisors for appropriate courses to double count upon admission to the combined program.
Program Restrictions
Transfer Courses: Graduate-level courses taken at other universities and passed with a grade equivalent of "B" or better will be considered for transfer credit into the Mechanical Engineering Department. Approval from the Advisor and/or Thesis Committee and ME Department Head will be required as appropriate.
Internships: The Mechanical Engineering Graduate Program does not accept Internships (such as SYGN: 598I) for Graduate Credit.
Master of Science Degree Requirements
The MS degree in Mechanical Engineering requires 30 credits. Requirements for the MS thesis option are 24 credits of coursework and 6 credits of thesis research. The MS non-thesis option requires 30 credits of coursework.
Advisor and Thesis Committee: Students must have an Advisor from the Mechanical Engineering Department Faculty to direct and monitor their academic plan, research, and independent studies. The MS graduate Thesis Committee must have at least three members, two of whom must be permanent faculty in the Mechanical Engineering Department.
MS Non-Thesis Degree
MEGN502 | ADVANCED ENGINEERING ANALYSIS | 3.0 |
ME CORE | Two courses from the Mechanical Engineering Core List | 6.0 |
ME ELECTIVES | Any 500-level or above MEGN, AMFG, or FEGN courses | 12.0 |
TECHNICAL ELECTIVES | Any 500-level or above courses | 9.0 |
Total Semester Hrs | 30.0 |
Time Limit: As stipulated by the Mines Graduate School, a candidate for a Masters degree must complete all requirements for the degree within five years of the date of admission into the degree program.
An online modality is also available for Masters Non-Thesis.
MS Thesis Degree
MEGN502 | ADVANCED ENGINEERING ANALYSIS | 3.0 |
MEGN503 | GRADUATE SEMINAR Enrollment required every Fall and Spring semester | 0.0 |
ME CORE | Courses from the Mechanical Engineering Core List | 6.0 |
ME ELECTIVES | Any 500-level or above MEGN, AMFG, or FEGN courses. | 9.0 |
TECHNICAL ELECTIVES | Any 500-level or above courses (Approved by Advisor/Thesis Committee) | 6.0 |
MEGN707 | GRADUATE THESIS / DISSERTATION RESEARCH CREDIT | 6.0 |
Total Semester Hrs | 30.0 |
Thesis Defense: At the conclusion of the MS Thesis Option, the student will be required to make a formal presentation and defense of their thesis research to their Advisor and Thesis Committee.
Doctor of Philosophy Degree Requirements
The PhD degree in Mechanical Engineering requires 72 credits of coursework + research credits. A minimum of 30 credits of course work and 30 credits of research credits must be completed. A minimum of 12 of the 30 credits of required coursework must be taken at Colorado School of Mines.
MEGN502 | ADVANCED ENGINEERING ANALYSIS | 3.0 |
MEGN503 | GRADUATE SEMINAR Enrollment required every Fall and Spring semester | 0.0 |
ME CORE | Courses from the Mechanical Engineering Core List | 6.0 |
TECHNICAL ELECTIVES | Technical Electives. Any 500-level or above courses approved by Advisor/Thesis Committee. | 21.0 |
MEGN707 | GRADUATE THESIS / DISSERTATION RESEARCH CREDIT | 30.0 |
TOTAL CREDITS | Remaining 12 credits can come from Research and/or Technical Electives | 72.0 |
MILESTONE | TIMELINE | |
Select a permanent advisor | Second semester | |
Complete the PhD qualifying examination | By the end of third semester | |
Complete all core curriculum course requirements | Fourth semester | |
Submit Degree Audit and Admission to Candidacy forms | By fifth semester | |
Establish a dissertation committee and present research proposal | By fifth semester | |
Present a preliminary defense | 12 months before dissertation defense | |
Present a dissertation defense |
Advisor and Thesis Committee: Students must have an Advisor from the Mechanical Engineering Department Faculty to direct and monitor their academic plan, research, and independent studies. The PhD graduate Thesis Committee must have at least four members; at least two members must be permanent faculty in the Mechanical Engineering Department, and at least one member must be from outside the department. This outside member must chair the committee. Students who choose to have a minor program must select a representative from the minor areas of study to serve on the Thesis Committee.
Qualifying Exam: Students enrolled in the Mechanical Engineering PhD program will be required to pass a Qualifying Exam. PhD students with a minimum graduate grade point average of 3.0 are eligible to take the qualifying exam. Students must have completed at least four 500-level courses before taking the qualifier.
The Qualifying Exam assesses some attributes expected of a successful PhD student, including:
- ability to review, synthesize and apply fundamental concepts;
- creative and technical ability of the student to solve open-ended and challenging problems;
- technical communication skills.
Exam results of Pass, Conditional Pass or Fail will be provided to the student in a timely manner by the Qualifying Exam Chair. A Conditional Pass will require the student to take a remedial plan. Students have two attempts to pass the exam. If the student fails the exam on their first attempt, they must retake the exam in the following semester. One-semester extensions may be granted by the Qualifying Exam Chair.
Research Proposal: After passing the Qualifying Examination, the PhD student will prepare a written Research Proposal for the Dissertation and present it formally to the Dissertation Committee, which is selected by the student and the student's advisor and approved by the Department Head. This Research Proposal gives the Committee an early chance to discuss the work and to help the student more clearly define the work and identify the salient aspects. The research proposal must be completed before admission to candidacy.
Degree Audit and Admission to Candidacy: PhD students must complete the Degree Audit form by the posted deadlines and the Admission to Candidacy form by the first day of classes of the semester in which they want to be considered PhD candidates.
Additionally, full-time PhD students must complete the following requirements within the first two calendar years after enrolling into the PhD program:
- have a Thesis Committee appointment form on file in the Graduate Office;
- complete all prerequisite and core curriculum course requirements;
- pass the qualifier; and
- be admitted into full candidacy for the degree.
Preliminary Defense: Prior to the final Dissertation Defense, the PhD student will make an oral presentation to the student’s Committee to summarize research accomplishments and remaining goals and work plan. This meeting serves as a final check to assess if the student's progress is on schedule for graduation. The student must give no more than a 45-minute presentation that summarizes the work already accomplished, including their relevant publication(s) and a proposed plan of the work needed to culminate in a formal defense and graduation. The Committee will provide feedback and, as necessary, revisions to the proposed work plan such that its completion should lead to a successful Dissertation Defense and publication record in a realistic time frame. The time period between the Research Proposal and the Preliminary Defense can span a few years, but the Preliminary Defense should take place 12 months and no less than 6 months prior to the date of Dissertation Defense.
Required Number of Publications and Presentations: The required and recommended journal publications for PhD students prior to graduation are listed below. Students wanting to defend before meeting these requirements must submit a one-page petition with a reasonable explanation to the ME Graduate Curriculum Committee.
Journal publications - Required: Minimum of one first-author paper accepted or published (DOI is required) in a peer-reviewed journal (recognized as high quality in the research field), before Dissertation Defense. Recommended: Three or more first-author papers accepted or published in peer-reviewed journals.
Presentations - Required: Minimum of one research presentation (poster or podium) at an external technical conference before the Dissertation Defense. Recommended: Two or more conference presentations (poster or podium), before the Dissertation Defense in which the student is the first author on these presentations.
Thesis Defense: At the conclusion of the student’s PhD program, the student will make a formal presentation and defense of her/his thesis research. A student must pass this defense to earn a PhD degree. The Dissertation document should be submitted to the Dissertation Committee at least 10 days prior to the Defense. The Committee will perform a post-presentation review of the Dissertation, technical contributions, and publications with the student. The Committee may request revisions to the Dissertation and additional work that requires subsequent review by the advisor and or the Committee.
Time Limit: As stipulated by the Mines Graduate School, a candidate for a doctoral degree must complete all requirements for the degree within nine years of the date of admission into the degree program.
MECHANICAL ENGINEERING CORE COURSES (ME CORE) | ||
MEGN505 | ADVANCED DYNAMICS | 3.0 |
MEGN514 | CONTINUUM MECHANICS | 3.0 |
MEGN551 | ADVANCED FLUID MECHANICS | 3.0 |
MEGN571 | ADVANCED HEAT TRANSFER | 3.0 |
Courses
MEGN501. ADVANCED ENGINEERING MEASUREMENTS. 3.0 Semester Hrs.
Equivalent with EGGN501,
Introduction to the fundamentals of measurements within the context of engineering systems. Topics that are covered include: errors and error analysis, modeling of measurement systems, basic electronics, noise and noise reduction, and data acquisition systems. Prerequisite: EGGN250, EENG281 or equivalent, and MATH201 or equivalent, Graduate student status.
MEGN502. ADVANCED ENGINEERING ANALYSIS. 3.0 Semester Hrs.
(I) Introduce advanced mathematical and numerical methods used to solve engineering problems. Analytic methods include series solutions, special functions, Sturm-Liouville theory, separation of variables, and integral transforms. Numerical methods for initial and boundary value problems include boundary, domain, and mixed methods, finite difference approaches for elliptic, parabolic, and hyperbolic equations, Crank-Nicolson methods, and strategies for nonlinear problems. The approaches are applied to solve typical engineering problems. The student must have a solid understanding of linear algebra, calculus, ordinary differential equations, and Fourier theory. 3 hours lecture.
MEGN503. GRADUATE SEMINAR. 0.0 Semester Hrs.
(I, II) This is a seminar forum for graduate students to present their research projects, critique
others’ presentations, understand the breadth of engineering projects both within their
specialty area and across the Division, hear from leaders of industry about contemporary
engineering as well as socio-economical and marketing issues facing today’s competitive
global environment. In order to improve communication skills, each student is required to
present a seminar in this course before his/her graduation from the Mechanical
Engineering graduate program. Prerequisite: Graduate standing. 1 hour per week; 0 semester hours. Course is repeatable, but no coursework credit is awarded.
MEGN505. ADVANCED DYNAMICS. 3.0 Semester Hrs.
This course will teach advanced methods for describing and analyzing equations of motion for mechanical systems. This class is intended for students who have a solid grasp of dynamics and differential equations. Course topics include: Lagrangian mechanics, Hamiltonian mechanics, constraints in mechanical systems, 3-D rigid body motion, stability and bifurcations of nonlinear systems, and dynamical systems theory. With these tools, students will have the capacity to model and analyze the dynamics of complex mechanical systems. The knowledge and skills from this class will help prepare students for potential careers in biomechanics, robotics, aerospace, and more.
MEGN510. THEORY OF ELASTICITY. 3.0 Semester Hrs.
This is a graduate course that builds upon the learning outcomes of Continuum Mechanics course to introduce students the fundamentals of Theory of Elasticity. Introduction is realized through theory development, application examples, and numerical solutions. Learning outcomes from this course would be essential to further studies in visco-elasticity and plasticity. Knowledge from this course will enable students to work on variety of engineering applications in Mechanical, Materials, Aerospace, Civil and related engineering fields. This course is cross-listed with MLGN517.
View Course Learning Outcomes
- 1. Recall definitions for indicial notation, transformation rules for tensors, and eigenvalue problems. Tensor algebra and tensor calculus.
- 2. Define, and apply, displacement-strain relationships. Strain measurements using strain gauges and rosettes. Calculate principal strains, maximum shear strain in 3D.
- 3. Establish the definitions, and use, stress tensor, traction vector, normal, and shear tractions. Find stresses at a point on a given plane, principal stresses and max shear stress.
- 4. State the general three-dimensional constitutive law for linear elastic materials. Define material symmetry and the engineering notation stiffness matrix for materials with monoclinic, orthotropic, transversely isotropic, cubic symmetry.
- 5. Define, and apply, the generalized form of Hooke’s Law for isotropic materials.
- 6. State, and apply, the field equations for linear isotropic elasticity.
- 7. Write clear and complete boundary condition statement.
- 8. Use the semi-inverse method to find solutions for two dimensional elasticity problems.
- 9. Use the Airy stress function to find solutions for two dimensional elasticity problems.
- 10. Define, and apply, yield theories (von Mises and Tresca) for isotropic solids.
- 11. Use the Prandtl stress function to find solutions for torsional elasticity problems.
MEGN511. FATIGUE AND FRACTURE. 3.0 Semester Hrs.
Equivalent with MTGN545,
(I) Basic fracture mechanics as applied to engineering materials, S-N curves, the Goodman diagram, stress concentrations, residual stress effects, effect of material properties on mechanisms of crack propagation. Fall semesters, odd numbered years.
MEGN512. ADVANCED ENGINEERING VIBRATION. 3.0 Semester Hrs.
Vibration theory as applied to single- and multi-degree-of freedom systems. Free and forced vibrations to different types of loading-harmonic, impulse, periodic and general. Natural frequencies. Role of Damping. Importance of resonance. Modal superposition method. Prerequisite: MEGN315, 3 hours lecture; 3 semester hours.
MEGN513. KINETIC PHENOMENA IN MATERIALS. 3.0 Semester Hrs.
Equivalent with MLGN511,
Linear irreversible thermodynamics, dorce-flux couplings, diffusion, crystalline materials, amorphous materials, defect kinetics in crystalline materials, interface kinetics, morphological evolution of interfaces, nucleation theory, crystal growth, coarsening phenomena and grain growth, solidification, spinodal decomposition. Prerequisites: MATH225: Differential equations (or equivalent), MTGN555/CBEN509: Thermodynamics (or its equivalent).
MEGN514. CONTINUUM MECHANICS. 3.0 Semester Hrs.
(I) This is a graduate course covering fundamentals of continuum mechanics and constitutive modeling. The goal of the course is to provide graduate students interested in fluid and solid mechanics with the foundation necessary to review and write papers in the field. Students will also gain experience interpreting, formulating, deriving, and implementing three-dimensional constitutive laws. The course explores six subjects: 1. Mathematical Preliminaries of Continuum Mechanics (Vectors, Tensors, Indicial Notation, Tensor Properties and Operations, Coordinate Transformations) 2. Stress (Traction, Invariants, Principal Values) 3. Motion and Deformation (Deformation Rates, Geometric Measures, Strain Tensors, Linearized Displacement Gradients) 4. Balance Laws (Conservation of Mass, Momentum, Energy) 5. Ideal Constitutive Relations (Frictionless & Linearly Viscous Fluids, Elasticity) 6. Constitutive Modeling (Formulation, Derivation, Implementation, Programming). 3 hours lecture, 3 semester hours.
View Course Learning Outcomes
- Students will learn vector calculus and index notation by solving problems sets and writing their own Matlab toolboxes of vector calculus operators
- Students will learn general formulations of stress, strain, motion and balance laws by solving problem sets
- Students will be introduced to constitutive modeling for both fluids and solids by solving problem sets and coding a model of their choice for the final project
MEGN515. COMPUTATIONAL MECHANICS. 3.0 Semester Hrs.
(I) A graduate course in computational mechanics with an emphasis on a studying the major numerical techniques used to solve problems that arise in mechanics and some related topical areas. Variational methods are applied throughout as a general approach in the development of many of these computational techniques. A wide range of problems are addressed in one- and two- dimensions which include linear and nonlinear elastic and elastoplastic steady state mechanics problems. Computational algorithms for time dependent problems such as transient dynamics and viscoplasticity are also addressed. In the latter part of the course an introduction to computational methods employing boundary integral equations, and particle methods for solving the mechanical behavior of multi-body systems are also given. Note all the software used in this course is written in MATLAB which has become a widely acceptable engineering programming tool. 3 lecture hours, 3 semester hours. Prerequisite: MEGN502.
View Course Learning Outcomes
- Understand and apply the variational approach to governing equations in the development of finite element algorithms.
- Develop, implement and apply computational algorithms to solve linear and nonlinear steady problems.
- Develop, implement and apply computational algorithms to solve transient problems.
- Perform extensive computer coding in MATLAB to develop and modify existing computational mechanics algorithms.
MEGN517. NONLINEAR MATERIAL BEHAVIOR. 3.0 Semester Hrs.
This course provides students with a foundational knowledge in the mechanics of solid materials displaying nonlinear deformation behavior. The course introduces general measures of deformation, such as deformation tensors, velocity gradients, stretch rate and spin tensors, as well as measures of stress, including Cauchy, Green, nominal and material stress. These concepts create a foundation on which are built in-depth descriptions of hypoelastic, hyperelastic, and viscoelastic materials, as well as plastic and viscoplastic material behaviors. For each material behavior addressed, students will put relevant mechanics theory into practice by solving problems from contemporary applications (e.g., additive manufacturing, biomechanics, battery mechanics, aerospace). A working knowledge of continuum mechanics or elasticity theory would be helpful but is not required.
View Course Learning Outcomes
- Explain and apply different measures of deformation, including displacement, different strain tensors, and corresponding compatibility equations.
- Explain, compare, and apply different stress tensors as well as different constitutive relationships between stress and strain tensors; analyze boundary conditions.
- Recall and apply different functional forms of the strain energy density, explain the differences between hypo and hyper-elastic stress-strain relations, and analyze the relevance of these materials in practical applications.
- Analyze the properties and deformation behaviors of polymers; calibrate or design the properties of polymers using scaling relationships.
- Explain and apply flow and hardening laws that govern the behavior of metals loaded beyond yield, and analyze incremental stress-strain relations and stability through the perspective of maximum plastic flow and Drucker’s postulate,
- Analyze creep behavior and viscoplastic materials in the small and high strain rate regimes.
MEGN520. BOUNDARY ELEMENT METHODS. 3.0 Semester Hrs.
(II) Development of the fundamental theory of the boundary element method with applications in elasticity, heat transfer, diffusion, and wave propagation. Derivation of indirect and direct boundary integral equations. Introduction to other Green’s function based methods of analysis. Computational experiments in primarily two dimensions. Prerequisite: MEGN502. 3 hours lecture; 3 semester hours Spring Semester, odd numbered years.
MEGN521. INTRODUCTION TO DISCRETE ELEMENT METHODS (DEMS). 3.0 Semester Hrs.
(I) Review of particle/rigid body dynamics, numerical DEM solution of equations of motion for a system of particles/rigid bodies, linear and nonlinear contact and impact laws dynamics, applications of DEM in mechanical engineering, materials processing and geo-mechanics. Prerequisites: CEEN311, MEGN315 and some scientific programming experience in C/C++ or Fortran. 3 hours lecture; 3 semester hours Spring semester of even numbered years.
MEGN531. PROSTHETIC AND IMPLANT ENGINEERING. 3.0 Semester Hrs.
Prosthetics and implants for the musculoskeletal and other systems of the human body are becoming increasingly sophisticated. From simple joint replacements to myoelectric limb replacements and functional electrical stimulation, the engineering opportunities continue to expand. This course builds on musculoskeletal biomechanics and other BELS courses to provide engineering students with an introduction to prosthetics and implants for the musculoskeletal system. At the end of the semester, students should have a working knowledge of the challenges and special considerations necessary to apply engineering principles to augmentation or replacement in the musculoskeletal system. Prerequisite: MEGN430.
MEGN532. EXPERIMENTAL METHODS IN BIOMECHANICS. 3.0 Semester Hrs.
(I) Introduction to experimental methods in biomechanical research. Topics include experimental design, hypothesis testing, motion capture, kinematic models, ground reaction force data collection, electromyography, inverse dynamics calculations, and applications. Strong emphasis on hands-on data collection and technical presentation of results. The course will culminate in individual projects combining multiple experimental measurement techniques. Prerequisite: Graduate Student Standing. 3 hours lecture; 3.0 semester hours.
MEGN535. MODELING AND SIMULATION OF HUMAN MOVEMENT. 3.0 Semester Hrs.
Introduction to modeling and simulation in biomechanics. The course includes a synthesis of musculoskeletal properties, interactions with the environment, and computational optimization to construct detailed computer models and simulations of human movement. Prerequisite: MEGN315 and MEGN330.
MEGN536. COMPUTATIONAL BIOMECHANICS. 3.0 Semester Hrs.
Computational Biomechanics provides an introduction to the application of computer simulation to solve fundamental problems in biomechanics and bioengineering. Musculoskeletal biomechanics, joint kinematics, medical image reconstruction, hard and soft tissue modeling, and medical device design are considered in the context of a semester-long project to develop and evaluate an artificial knee implant. Leading commercial software tools are introduced with hands-on exercises. An emphasis is placed on understanding the limitations of the computer model as a predictive tool and the need for rigorous verification and validation of all modeling tasks. Clinical application of biomechanical modeling tools is highlighted and impact on patient quality of life is discussed. Prerequisite: MEGN330, MEGN324.
MEGN537. PROBABILISTIC BIOMECHANICS. 3.0 Semester Hrs.
The course introduces the application of probabilistic analysis methods in biomechanical systems. All real engineering systems, and especially human systems, contain inherent uncertainty due to normal variations in dimensional parameters, material properties, motion profiles, and loading conditions. The purpose of this course is to examine methods for including these sources of variation in biomechanical computations. Concepts of basic probability will be reviewed and applied in the context of engineering reliability analysis. Probabilistic analysis methods will be introduced and examples specifically pertaining to musculoskeletal biomechanics will be studied. Prerequisite: MEGN436 or MEGN536.
MEGN540. MECHATRONICS. 3.0 Semester Hrs.
A course focusing on implementation aspects of mechatronic and control systems. Significant lab component involving embedded C programming on a mechatronics teaching platform, called a haptic paddle, a single degree-of-freedom force-feedback joystick.
View Course Learning Outcomes
- Become proficient in mechanical system modeling, system identification and simulations.
- Develop an understanding of how control theory is applied and implemented in practice.
- Learn fundamentals of and how to use semiconductor devices in mechatronic systems.
- Learn the basics of sensor and actuator theory, design, and application.
- Gain experience in embedded C programming for mechatronic systems.
- Gain experience in research article reading and technical presentations.
MEGN544. ROBOT MECHANICS: KINEMATICS, DYNAMICS, AND CONTROL. 3.0 Semester Hrs.
Mathematical representation of robot structures. Mechanical analysis including kinematics, dynamics, and design of robot manipulators. Representations for trajectories and path planning for robots. Fundamentals of robot control including, linear, nonlinear and force control methods. Introduction to off-line programming techniques and simulation. 3 hours lecture; 3 semester hours. Prerequisite: EENG307 and MEGN441.
View Course Learning Outcomes
- No change
MEGN545. ADVANCED ROBOT CONTROL. 3.0 Semester Hrs.
The goal of this course is to give the students an introduction to a fundamental working knowledge of the main techniques of intelligent learning-based control and their applications in robotics and autonomous systems. Specific topics include neural network based control, model predictive control, reinforcement learning based control, fuzzy logic control, and human-in-the-loop control.
View Course Learning Outcomes
- Obtain a basic understanding of a variety of intelligent control techniques and know how these techniques are applied to robotics engineering.
- Design robot control systems using neural network.
- Design robot control systems using reinforcement learning.
- Read and assess technical papers in intelligent robot control.
- Conduct class projects related to advanced robot control.
MEGN551. ADVANCED FLUID MECHANICS. 3.0 Semester Hrs.
(I) This first year graduate course covers the fundamentals of incompressible fluid mechanics with a focus on differential analysis and building a strong foundation in the prerequisite concepts required for subsequent study of computational fluid dynamics and turbulence. The course is roughly divided into four parts covering (i) the governing equations of fluid mechanics, (ii) Stokes flows and ideal-fluid flows, (iii) boundary layer flows, and (iv) hydrodynamic stability and transition to turbulence. 3 hours lecture; 3 semester hours.
View Course Learning Outcomes
- 1. Understand the conservation of mass, momentum, and energy in fluid mechanics from both a differential and control volume perspective.
- 2. Understand the competing roles of inertia, pressure, viscosity, body forces, and boundary conditions in diverse fluid flows.
- 3. Understand dimensional and order-of-magnitude analyses, and their applications to Stokes flows, ideal fluid flows, and boundary layer flows.
- 4. Understand the central importance of hydrodynamic stability to fluid mechanics.
MEGN552. VISCOUS FLOW AND BOUNDARY LAYERS. 3.0 Semester Hrs.
(I) This course establishes the theoretical underpinnings of fluid mechanics, including fluid kinematics, stress-strain relationships, and derivation of the fluid-mechanical conservation equations. These include the mass-continuity and Navier-Stokes equations as well as the multi-component energy and species-conservation equations. Fluid-mechanical boundary-layer theory is developed and applied to situations arising in chemically reacting flow applications including combustion, chemical processing, and thin-film materials processing. Prerequisite: MEGN451, or CBEN430. 3 hours lecture; 3 semester hours.
MEGN553. COMPUTATIONAL FLUID DYNAMICS. 3.0 Semester Hrs.
Introduction to Computational Fluid Dynamics (CFD) for graduate students with no prior knowledge of this topic. Basic techniques for the numerical analysis of fluid flows. Acquisition of hands-on experience in the development of numerical algorithms and codes for the numerical modeling and simulation of flows and transport phenomena of practical and fundamental interest. Capabilities and limitations of CFD. Prerequisite: MEGN451.
View Course Learning Outcomes
- Learn in-depth theoretical and mathematical development about the finite difference and finite volume methods for the numerical solution of the mass, momentum, energy, and species transport problems.
- Learn how to develop computer codes for solving the hyperbolic, parabolic, elliptic partial differential equations.
- Develop numerical codes for the solution of the 2D compressible Navier-Stokes equations.
- Learn how to validate and verify computer codes.
- Analyze and interpret the computed solutions of the governing conservation equations and to represent the computed numerical solution graphically using visualization techniques.
- Experience with the Ansys Fluent CFD code.
MEGN554. ORBITAL MECHANICS. 3.0 Semester Hrs.
Orbital Mechanics introduces students to the dynamics that govern motion of bodies in space and the utilization of these dynamics in spacecraft orbit and trajectory design. This course develops the mathematical foundation of propagating, describing, and manipulating the motion of a spacecraft in orbit. Throughout the semester students will script their own universe simulators to examine the various forces and geometries in orbit. Prerequisites: MEGN315.
MEGN560. DESIGN AND SIMULATION OF THERMAL SYSTEMS. 3.0 Semester Hrs.
In this course the principles of design, modeling, analysis, and optimization of processes, devices, and systems are introduced and applied to conventional and advanced energy conversion systems. It is intended to integrate conservation principles of thermodynamics (MEGN261) with the mechanism relations of fluid mechanics (MEGN351) and heat transfer (MEGN471). The course begins with general system design approaches and requirements and proceeds with mathematical modeling, simulation, analysis, and optimization methods. The design and simulation of energy systems is inherently computational and involves modeling of thermal equipment, system simulation using performance characteristics, thermodynamic properties, mechanistic relations, and optimization (typically with economic-based objective functions). Fundamental principles for steady-state and dynamic modeling are covered. Methods for system simulation which involves predicting performance with a given design (fixed geometry) are studied. Analysis methods that include Pinch Technology, Exergy Analysis, and Thermo-economics are examined and are considered complementary to achieving optimal designs. Optimization encompasses objective function formulation, systems analytical methods, and programming techniques. System optimization of the design and operating parameters of a configuration using various objective functions are explored through case studies and problem sets. Economics and optimization for analyses and design of advanced energy systems, such as Rankine and Brayton cycle power plants, combined.
MEGN561. ADVANCED ENGINEERING THERMODYNAMICS. 3.0 Semester Hrs.
First year graduate course in engineering thermodynamics that emphasizes a greater depth of study of undergraduate subject matter and an advancement to more complex analyses and topics. The course begins with fundamental concepts, 1st and 2nd Law analyses of processes, devices, and systems and advances to equations of state, property relations, ideal and non-ideal gas mixtures, chemically reacting systems, and phase equilibrium. Historical and modern contexts on the development and advancements of thermodynamic concepts are given. Fundamental concepts are explored through the analysis of advanced thermodynamic phenomena and use of computational tools to solve more realistic problems. 3 hours lecture; 3 semester hours. Prerequisite: MEGN261, MEGN351, and MEGN471.
View Course Learning Outcomes
- 1. Understand the fundamental theory of the 1st and 2nd Laws of Thermodynamics
- 2. Recognize critical assumptions, property relations, and approaches for different physical situations
- 3. Understand how thermodynamic problems are solved and solve them using available computational tools and techniques
- 4. Use engineering thermodynamics in their research work or applications
MEGN565. ELECTRIC VEHICLE POWERTRAIN SYSTEMS. 0-3 Semester Hr.
In the fast-evolving world of sustainable transportation, it is essential for engineers in the automotive industry to understand energy conversion, storage, utilization, and optimization of vehicle powertrains. Electric Vehicle Powertrain Systems (EVPS) is designed to provide students with a comprehensive understanding of the essential powertrain components in battery-electric vehicles (BEVs) including motors, controllers, and battery packs. Through a combination of theoretical modeling and hands-on projects, students will gain knowledge and skills in powertrain system design to achieve vehicle objectives, encompassing energy analysis, power requirements, and efficiency considerations. The course will also explore the state-of-the-art in safety measures, management strategies, control systems, charging/balancing techniques, and State of Charge (SOC)/State of Health (SOH) estimation for EV battery packs. Prerequisites: MEGN 300 or EENG282.
MEGN566. COMBUSTION. 3.0 Semester Hrs.
(I) An introduction to combustion. Course subjects include: the development of the Chapman-Jouget solutions for deflagration and detonation, a brief review of the fundamentals of kinetics and thermochemistry, development of solutions for diffusion flames and premixed flames, discussion of flame structure, pollutant formation, and combustion in practical systems. Prerequisite: MEGN451 or
CBEN430. 3 hours lecture; 3 semester hours.
MEGN567. PRINCIPLES OF BUILDING SCIENCE. 3.0 Semester Hrs.
First or second year graduate course that covers the fundamentals of building energy systems, moist air processes, heating, ventilation, and air conditioning (HVAC) systems and the use of numerical models for heat and mass transfer to analyze advanced building technologies such as phase change materials, green roofs or cross laminated timber. 3 hours lecture; 3 semester hours. Prerequisite: MEGN261, MEGN351, MEGN471.
View Course Learning Outcomes
- 1. Understand and apply fundamental principles to HVAC design
- 2. Describe components in HVAC systems
- 3. Understand how building HVAC loads are calculated and calculate building HVAC loads
- 4. Analyze advance building technologies using building energy simulations tools
- 5. Write technical report based on energy modeling results
MEGN569. FUEL CELL SCIENCE AND TECHNOLOGY. 3.0 Semester Hrs.
Equivalent with CBEN569,CHEN569,MLGN569,MTGN569,
(I) Investigate fundamentals of fuel-cell operation and electrochemistry from a chemical-thermodynamics and materials- science perspective. Review types of fuel cells, fuel-processing requirements and approaches, and fuel-cell system integration. Examine current topics in fuel-cell science and technology. Fabricate and test operational fuel cells in the Colorado Fuel Cell Center. 3 credit hours.
MEGN570. ELECTROCHEMICAL SYSTEMS ENGINEERING. 3.0 Semester Hrs.
In this course, students will gain fundamental, quantitative insight into the operation of electrochemical devices for engineering analysis across a range of length scales and applications. The course will use the development of numerical models as a lens through which to view electrochemical devices. However, the course will also deal extensively with "real world" systems and issues, including experimental characterization, system optimization and design, and the cyclical interplay between models and physical systems. The course begins by establishing the equations that govern device performance at the most fundamental level, describing chemical and electrochemical reactions, heat transfer, transport of charged and neutral species, and material properties in operating devices. Subsequently, these equations will be used to discuss and analyze engineering issues facing three basic types of electrochemical devices: fuel cells, batteries, and sensors. At each juncture will evaluate our equations to determine when simpler models may be more suitable. Throughout the semester, concepts will be applied in homework assignments, including an over-arching, semester-long project to build detailed numerical models for an application of each student's choosing. 3 hours lecture; 3 semester hours.
View Course Learning Outcomes
- 1. Apply conservation of mass, species and energy to model electrochemical processes and predict performance.
- 2. Use numerical simulations to design and optimize electrochemical systems.
- 3. Given multiple alternatives, students will choose an appropriate level of detail for charge transfer and mass transport models.
- 4. Interpret model simulation results to identify limiting physical processes in a given electrochemical device.
MEGN571. ADVANCED HEAT TRANSFER. 3.0 Semester Hrs.
An advanced course in heat transfer that supplements topics covered in MEGN471. Derivation and solution of governing heat transfer equations from conservation laws. Development of analytical and numerical models for conduction, convection, and radiation heat transfer, including transient, multidimensional, and multimode problems. Introduction to turbulence, boiling and condensation, and radiative transfer in participating media.
MEGN579. OPTIMIZATION MODELS IN MANUFACTURING. 3.0 Semester Hrs.
This course addresses the mathematical formulation and solution of optimization models relevant in manufacturing operations. The types of optimization models examined include: (i) network models; (ii) linear programs; (iii) integer programs; and (iv) nonlinear programs. Application areas include scheduling, blending, design, equipment replacement, logistics and transportation, among other topics. Students learn not only how to mathematically formulate the models, but also how to solve them with a state-of-the-art modeling language (AMPL) and appropriate solver (e.g. CPLEX or Minos). Algorithms for each problem class will be briefly discussed.
View Course Learning Outcomes
- Understand the concepts of optimization as applied in a manufacturing setting. See Syllaubs
MEGN583. ADDITIVE MANUFACTURING. 3.0 Semester Hrs.
Additive Manufacturing (AM), also known as 3D Printing in the popular press, is an emerging manufacturing technology that will see widespread adoption across a wide range of industries during your career. Subtractive Manufacturing (SM) technologies (CNCs, drill presses, lathes, etc.) have been an industry mainstay for over 100 years. The transition from SM to AM technologies, the blending of SM and AM technologies, and other developments in the manufacturing world has direct impact on how we design and manufacture products. This course will prepare students for the new design and manufacturing environment that AM is unlocking. The graduate section of this course differs from the undergraduate section in that graduate students perform AM-related research. While students complete quizzes and homework, they do not take a midterm or final exam. Prerequisites: MEGN200 and MEGN201 or equivalent project classes. 3 hours lecture; 3 semester hours.
View Course Learning Outcomes
- 1. Succinctly state differences between AM and SM, and cases where AM or SM is the better technology choice
- 2. Describe all major AM technologies and their applications (FFDM, SLS, etc…)
- 3. Use a software tool chain to bring an assembly from engineering concept to prototype production
- 4. Perform an engineering and economic analysis to determine if AM is appropriate for an engineered part, what AM process is appropriate, and where the economic break-over points are between using one AM technology versus another or SM.
- 5. Use a 3D scanner to obtain 3D data
- 6. Select post processing technique(s) to achieve desired part characteristics for AM part
- 7. Understand the various materials available for use in AM systems
- 8. Understand quality assurance requirements and the process for implementing AM parts into production articles
- 9. Understand qualification and certification methodology
- 10. Conducting research in Additive Manufacturing and Technology
MEGN584. MODELING MATERIALS PROCESSING. 3.0 Semester Hrs.
This course aims to enable students to examine a given materials processing operation or manufacturing problem, identify the important phenomena, develop simple quantitative models of those phenomena, and apply them to obtain reasonable solutions to practical design issues and problems. Phenomena involving fluid flow, heat transfer, solidification, diffusion, and thermal-mechanical behavior are related to terms in governing equations based on heat, mass, and momentum balances. These equations are simplified by formal estimation and scaling to create mechanistic process models, often selected from classic analytical solutions. Example applications to manufacturing processes for metals and polymers include controlled cooling, extrusion, casting, and welding. Prerequisite: Undergraduate degree in Mechanical Engineering or equivalent (that includes relevant courses of calculus, differential equations, materials and/or manufacturing, heat transer, fluid mechanics, and solid mechanics) or instructor consent.
View Course Learning Outcomes
- 1) Understand basic processes used in manufacturing materials. Examples presented in class include -controlled cooling -polymer processing (extrusion, molding) -metal casting (sand, metal-mold, continuous, crystal growth, welding) -other processes of interest to the class (based on first-day survey)
- 2) Identify basic phenomena important to specific materials processes -fluid flow (laminar and turbulent; Newtonian and non-Newtonian) -energy transport (transient heat conduction, advection / conduction, forced and natural convection, radiation, viscous dissipation) -solidification (including heat transfer, microstructure development and segregation) -diffusion (solid state and liquid state) -mechanical behavior (thermal stress)
- 3) Write the governing equations to quantify understanding of these phenomena in the context of a particular materials process. -balance equations (energy, mass, momentum) in both global and differential forms -how balance equations are modified to include phenomena such as solidification -choose and transform between Lagrangian and Eulerian reference frames as needed.
- 4) Understand the relationship between physical phenomena and corresponding terms in the governing equations
- 5) Apply formal estimation and scaling to the governing equations to derive appropriate dimensionless groups to evaluate the importance of particular phenomena to a given materials process or problem and to obtain initial estimates of important parameters.
- 6) Decide what phenomena/terms are important, and develop simple, but reasonable, mechanistic mathematical models of materials processes.
- 7) Make approximations to these equations to obtain solutions quickly to a given problem in materials processing: - derive particular analytical solutions by applying appropriate boundary conditions - select appropriate classic analytical solutions - solve to obtain quick quantitative solutions and - evaluate the significance of the solutions and make appropriate recommendations
MEGN585. NETWORK MODELS. 3.0 Semester Hrs.
We examine network flow models that arise in manufacturing, energy, mining, transportation and logistics: minimum cost flow models in transportation, shortest path problems in assigning inspection effort on a manufacturing line, and maximum flow models to allocate machine-hours to jobs. We also discuss an algorithm or two applicable to each problem class. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Offered every other year. 3 hours lecture; 3 semester hours.
View Course Learning Outcomes
- 1. Understand how to differentiate spanning tree, shortest path, maximum flow and minimum cost flow models.
- 2. Understand how to graphically depict and mathematically model spanning tree, shortest path, maximum flow and minimum cost flow models.
- 3. Understand algorithms that solve model spanning tree, shortest path, maximum flow and minimum cost flow models.
- 4. Understand the difference between network and non-network optimization models
MEGN586. LINEAR OPTIMIZATION. 3.0 Semester Hrs.
We address the formulation of linear programming models, linear programs in two dimensions, standard form, the Simplex method, duality theory, complementary slackness conditions, sensitivity analysis, and multi-objective programming. Applications of linear programming models include, but are not limited to, the areas of manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Offered every other year.
View Course Learning Outcomes
- Understand how to formulate linear optimization models
- Understand how to solve linear optimization models, both by hand and with the computer through an algebraic modeling language and a state-of-the-art solver.
- Understand the special structure underlying linear optimization models and how this affects their ability to be solved.
- Understand sensitivity and post-optimality analysis.
MEGN587. NONLINEAR OPTIMIZATION. 3.0 Semester Hrs.
Equivalent with MEGN487,
This course addresses both unconstrained and constrained nonlinear model formulation and corresponding algorithms (e.g., Gradient Search and Newton's Method, and Lagrange Multiplier Methods and Reduced Gradient Algorithms, respectively). Applications of state-of-the-art hardware and software will emphasize solving real-world engineering problems in areas such as manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with an algorithm such as MINOS) these optimization problems is introduced. Offered every other year. Prerequisite: MATH111.
View Course Learning Outcomes
- 1. Understand how to formulate nonlinear optimization models.
- 2. Understand how to solve nonlinear optimization models, both by hand and with the computer through an algebraic modeling language and a state-of-the-art solver.
- 3. Understand the special structure underlying nonlinear optimization models and how this affects their ability to be solved.
MEGN588. INTEGER OPTIMIZATION. 3.0 Semester Hrs.
Equivalent with MEGN488,
(I) This course addresses the formulation of integer programming models, the branch-and-bound algorithm, total unimodularity and the ease with which these models are solved, and then suggest methods to increase tractability, including cuts, strong formulations, and decomposition techniques, e.g., Lagrangian relaxation, Benders decomposition. Applications include manufacturing, energy, mining, transportation and logistics, and the military. Computer use for modeling (in a language such as AMPL) and solving (with software such as CPLEX) these optimization problems is introduced. Offered every other year. 3 hours lecture; 3 semester hours. Prerequisite: MATH111.
View Course Learning Outcomes
- 1. Understand how to formulate linear-integer optimization models.
- 2. Understand how to solve linear-integer optimization models, both by hand and with the computer through an algebraic modeling language and a state-of-the-art solver.
- 3. Understand the special structure underlying linear-integer optimization models and how this affects their ability to be solved.
- 4. Understand decomposition techniques to aid in solution.
MEGN592. RISK AND RELIABILITY ENGINEERING ANALYSIS AND DESIGN. 3.0 Semester Hrs.
The importance of understanding, assessing, communicating, and making decisions based in part upon risk, reliability, robustness, and uncertainty is rapidly increasing in a variety of industries (e.g.: petroleum, electric power production, etc.) and has been a focus of some industries for many decades (e.g.: nuclear power, aerospace, automotive, etc). This graduate class will provide the student with a technical understanding of and ability to use common risk assessment tools such as Reliability Block Diagrams (RBD), Failure Modes and Effects Analysis (FMEA), and Probabilistic Risk Assessment (PRA); and new tools being developed in universities including Function Failure Design Methods (FFDM), Function Failure Identification and Propagation (FFIP), and Uncoupled Failure Flow State Reasoning (UFFSR) among others. Students will also be provided with a high-level overview of what risk really means and how to contextualize risk information. Methods of communicating and making decisions based in part upon risk information will be discussed.
View Course Learning Outcomes
- Understand and be able to use probability statistics
- Understand and be able to use Bayesian statistical methods
- Demonstrate ability to use PRA software
- Demonstrate ability to model a complex engineered system using several (RBD, FMEA, PRA, FFDM, etc) risk and reliability methods
MEGN597. CASE STUDY - MATERIALS SCIENCE. 0.5-6 Semester Hr.
Individual research or special problem projects supervised by a faculty member.
MEGN598. SPECIAL TOPICS IN MECHANICAL ENGINEERING. 0-6 Semester Hr.
(I, II, S) Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once, but no more than twice for the same course content. Prerequisite: none. Variable credit: 0 to 6 credit hours. Repeatable for credit under different titles.
MEGN651. ADVANCED COMPUTATIONAL FLUID DYNAMICS. 3.0 Semester Hrs.
This course covers the fundamentals of computational fluid dynamics (CFD) for unsteady incompressible fluids flows, including examples of heat and mass transport. The course focuses on finite-difference methods, finite volume-methods, efficient projection methods for simulating unsteady flows, and recent advances in immersed boundary methods for complicated geometries. The course is entirely based on weekly homeworks, through which students will learn to how build and benchmark their own CFD codes. By the end of the course, students should have the required fundamentals to either build their own research codes, or use commercial and open source CFD codes intelligently. Prerequisites: MEGN502 and MEGN551 are recommended.
View Course Learning Outcomes
- 1)
- 2)
- 3)
- 4)
MEGN671. RADIATION HEAT TRANSFER. 3.0 Semester Hrs.
Accurate radiative transfer models are essential in many fields, including: combustion, propulsion, astronomy, solar technology, and climate science, to name only a few. The complex nature of radiative transfer can be intimidating, and calculations can be computationally expensive. In the first half of this course, we will study the role of material and surface properties on radiative transfer and develop and solve models for radiation exchange between surfaces (applicable to solar technology and high temperature systems). In the second half of the course, we will tackle radiation propagation through absorbing, scattering, and emitting media (gases, aerosols, semitransparent materials). We will model these systems using the Radiative Transfer Equation (RTE) and explore a few approaches to solving the RTE for select environments. Prerequisite: MEGN471.
View Course Learning Outcomes
- 1. Describe the spectral dependence (particularly blackbody spectral distributions) and directional dependence of radiation heat transfer.
- 2. Apply electromagnetic wave theory to model surface properties and radiation propagation through absorbing media.
- 3. Model and quantitatively calculate net radiation transfer between surfaces, including diffuse, specular, and non-gray surfaces.
- 4. Select methods for measuring radiative properties (e.g. spectral emissivity, absorption cross section), and describe the working principles of the instruments.
- 5. Calculate band absorption and emission for gases using spectral databases (e.g. HITRAN via SpectraPlot).
- 6. Use optical properties to calculate absorption and scattering by particulates.
- 7. Write the appropriate form of the Radiative Transfer Equation (RTE) required to model ra- diation propagating through absorbing, scattering, and emitting media (gases, liquids, and solids).
- 8. Apply select techniques to solve the RTE (including absorption, scattering, and emission) in planar and higher dimensional systems.
- 9. Successfully model a radiation heat transfer problem of your choosing, perform needed computations using appropriate computer software, and summarize your findings in written and oral reports.
MEGN686. ADVANCED LINEAR OPTIMIZATION. 3.0 Semester Hrs.
(II) As an advanced course in optimization, we expand upon topics in linear programming: advanced formulation, the dual simplex method, the interior point method, algorithmic tuning for linear programs (including numerical stability considerations), column generation, and Dantzig-Wolfe decomposition. Time permitting, dynamic programming is introduced. Applications of state-of-the-art hardware and software emphasize solving real-world problems in areas such as manufacturing, mining, energy, transportation and logistics, and the military. Computers are used for model formulation and solution. Offered every other year. Prerequisite: MEGN586. 3 hours lecture; 3 semester hours.
View Course Learning Outcomes
- Understand how to formulate complicated linear optimization models.
- Dual Simplex Method and Interior Point Method
- Algorithmic Tuning
- Column Generation and Dantzig-Wolfe Decomposition
MEGN688. ADVANCED INTEGER OPTIMIZATION. 3.0 Semester Hrs.
(II) As an advanced course in optimization, we expand upon topics in integer programming: advanced formulation, strong integer programming formulations (e.g., symmetry elimination, variable elimination, persistence), in-depth mixed integer programming cuts, rounding heuristics, constraint programming, and decompositions. Applications of state-of-the-art hardware and software emphasize solving real-world problems in areas such as manufacturing, mining, energy, transportation and logistics, and the military. Computers are used for model formulation and solution. Prerequisite: MEGN588. 3 hours lecture; 3 semester hours. Years to be Offered: Every Other Year.
View Course Learning Outcomes
- 1. Know how to formulate advanced integer optimization models 2. Be familiar with advanced algorithms to solve these models 3. Be able to use software, including scripting, to model and solve these models 4. Understand the theory behind and mathematical tenants of advanced integer optimization models
MEGN698. SPECIAL TOPICS. 0-6 Semester Hr.
(I, II, S) Pilot course or special topics course. Topics chosen from special interests of instructor(s) and student(s). Usually the course is offered only once, but no more than twice for the same course content. Prerequisite: none. Variable credit: 0 to 6 credit hours. Repeatable for credit under different titles.
MEGN699. INDEPENDENT STUDY. 0.5-6 Semester Hr.
(I, II, S) Individual research or special problem projects supervised by a faculty member, also, when a student and instructor agree on a subject matter, content, and credit hours. Prerequisite: “Independent Study” form must be completed and submitted to the Registrar. Variable credit: 0.5 to 6 credit hours. Repeatable for credit under different topics/experience and maximums vary by department. Contact the Department for credit limits toward the degree.
MEGN707. GRADUATE THESIS / DISSERTATION RESEARCH CREDIT. 1-15 Semester Hr.
(I, II, S) Research credit hours required for completion of a Masters-level thesis or Doctoral dissertation. Research must be carried out under the direct supervision of the student's faculty advisor. Variable class and semester hours. Repeatable for credit.