Courses

Course Planning Aids

The Vergil course planning tool and Course Bulletin are useful resources when searching for classes. For convenience, Mechanical Engineering courses are listed below.

Mechanical Engineering Courses

MECE E1001 Mechanical engineering: micromachines to jumbo jets. 3 points.

Lect: 3. Not offered during this academic year.

Corequisites: MATH UN1101

This introductory course explores the role of Mechanical Engineering in developing many of the fundamental technological advances on which today's society depends.  Students will be exposed to several mature and emerging technologies through a series of case studies. Topics include: airplanes, automobiles, robots, modern manufacturing methods as well as the emerging fields of micro-electro-mechanical machines (MEMS) and nanotechnology.  The physical concepts that govern the operation of these technologies will be developed from basic principles and then applied in simple design problems.  Students will also be exposed to state-of-the art innovations in each case study.

MECE E1008 Introduction to Machining. 1 point.

Introduction to the manual machine operation, CNC fabrication and usage of basic hand tools, band/hack saws, drill presses, grinders and sanders. 

MECE E1304 Naval Ship Systems, I. 3 points.

Students are strongly advised to consult with the ME Department prior to registering for this course. A study of ship characteristics and types including ship design, hydrodynamic forces, stability, compartmentation, propulsion, electrical and auxiliary systems, interior communications, ship control, and damage control; theory and design of steam, gas turbine, and nuclear propulsion; shipboard safety and firefighting. This course is part of the Naval ROTC program at Columbia but will be taught at SUNY Maritime. Enrollment may be limited; priority is given to students participating in Naval ROTC. This course will not count as a technical elective. Students should see a faculty adviser as well as Columbia NROTC staff (nrotc@ columbia.edu) for more information.

MECE E3018 Mechanical engineering laboratory, I. 3 points.

Lect: 3.

Experiments in instrumentation and measurement: optical, pressure, fluid flow, temperature, stress, and electricity; viscometry, cantilever beam, digital data acquisition. Probability theory: distribution, functions of random variables, tests of significance, correlation, ANOVA, linear regression. A lab fee of $50.00 is collected.

MECE E3028 Mechanical engineering laboratory, II. 3 points.

Lect: 3.

Experiments in engineering and physical phenomena: aerofoil lift and drag in wind tunnels, laser doppler anemometry in immersed fluidic channels, supersonic flow and shock waves, Rankine thermodynamical cycle for power generation, and structural truss mechanics and analysis.. A lab fee of $50.00 is collected.

MECE E3038 Mechanical engineering laboratory, III. 3 points.

Lect: 3. Not offered during this academic year.

Mechatronic control of mechanical and electromechanical systems. Control of various thermodynamic cycles, including internal combustion engine (Otto cycle). Reverse engineering of an electromechanical product. A lab fee of $50.00 is collected.

MECE E3100 Introduction to mechanics of fluids. 3 points.

Lect: 3.

Prerequisites: (ENME E3105) ENME E3105.

Basic continuum concepts. Liquids and gases in static equilibrium. Continuity equation. Two-dimensional kinematics. Equation of motion. Bernoulli's equation and applications. Equations of energy and angular momentum. Dimensional analysis. Two-dimensional laminar flow. Pipe flow, laminar,and turbulent. Elements of compressible flow.

MECE E3301 Thermodynamics. 3 points.

Lect: 3.

Classical thermodynamics. Basic properties and concepts, thermodynamic properties of pure substances, equation of state, work, heat, the first and second laws for flow and nonflow processes, energy equations, entropy, and irreversibility. Introduction to power and refrigeration cycles.

MECE E3311 Heat transfer. 3 points.

Lect: 3.

Steady and unsteady heat conduction. Radiative heat transfer. Internal and external forced and free convective heat transfer. Change of phase. Heat exchangers.

MECE E3401 Mechanics of machines. 3 points.

Lect: 3.

Prerequisites: (ENME E3105) and (MECE E3408) 

Introduction to mechanisms and machines, analytical and graphical synthesis of mechanism, displacement analysis, velocity analysis, acceleration analysis of linkages, dynamics of mechanism, cam design, gear and gear trains, and computer-aided mechanism design.

MECE E3408 Computer graphics and design. 3 points.

Lect: 3.

Introduction to drafting, engineering graphics, computer graphics, solid modeling, and mechanical engineering design. Interactive computer graphics and numerical methods applied to the solution of mechanical engineering design problems. A laboratory fee of $175 is collected.

MECE E3409 Machine design. 3 points.

Lect: 3.

Prerequisites: (MECE E3408) MECE E3408

Computer-aided analysis of general loading states and deformation of machine components using singularity functions and energy methods.Theoretical introduction to static failure theories, fractre mechanics, and fatigue failure theories.  Introduction to conceptual design and design optimization problems.  Design of machine components such as springs, shafts, fasteners, lead screws, rivets, welds.  Modeling, analysis, and testing of machine assemblies for prescribed design problems.  Problems will be drawn from statics, kinematics, dynamics, solid modeling, stress analysis, and design optimization.

MECE E3411 Fundamentals of engineering. 1 point.

Lect: 3.

Prerequisites: Senior Standing.

Review of core courses in mechanical engineering, including mechanics, strength of materials, fluid mechanics, thermodynamics, heat transfer, materials and processing, control, and mechanical design and analysis.  Review of additional topics, including engineering economics and ethics in engineering.  The course culminates with a comprehensive examination, similar to the Fundamentals of Engineering examination.

This course meets the first 4.5 weeks only.

MECE E3420 Engineering concept and design. 1 point.

Prerequisites: Senior standing.
Corequisites: MECE E3409.

A preliminary design for an original project is a pre-requisite for the Capstone Design course.  This course will focus on the steps required for generating a preliminary design concept. Included will be a brainstorming concept geration phase, a literature search, and the production of a layout drawing of the proposed capstone design project in a Computer Aided Design (CAD) software package (i.e. ProEngineer)

MECE E3430 Engineering Design. 3 points.

Prerequisites: (MECE E3420) MECE E3409 Machine Design

Elements of the design process: concept formulation, systems synthesis, design analysis optimization.  Selection and execution of a project involving the design of an actual engineering device or system. A labortatory fee of $125 is collected.

MECE E3450 Computer Aided Design. 3 points.

Lect: 3.

Prerequisites: (ENME E3105) and (ENME E3113) and (MECE E3408) and (MECE E3311) 

Introduction to numerical methods and their applications to rigid body mechanics for mechanisms and linkages. Introduction to finite element stress analysis for deformable bodies. Computer-aided mechanical engineering design using established software tools and verifications against analytical and finite difference solutions

MECE E3610 Materials and Processes in Manufacturing. 3 points.

Lect: 3.

Prerequisites: (ENME E3113) OR EQUIVALENT

Introduction to microstructures and properties of metals, polymers, ceramics and composites; typical manufacturing processes: material removal, shaping, joining, and property alteration; behavior of engineering materials in the manufacturing processes.

MECE E3900 Honors tutorial in mechanical engineering. 3 points.

Lect: 3.

Prerequisites: 3.2 or higher GPA

Individual study; may be selected after the first term of the junior year by students maintaining a 3.2 grade-point average. Normally not to be taken in a student's final semester. Course format may vary from individual tutorial to laboratory work to seminar instruction under faculty supervision. Written application must be made prior to registration outlining proposed study program. Projects requiring machine-shop use must be approved by the laboratory supervisor. Students may count up to 6 points toward degree requirements. Students must submit both a project outline prior to registration and a final project write up at the end of the semester. 

 

MECE E3901 Honors tutorial in mechanical engineering. 3 points.

Lect: 3.

Prerequisites: 3.2 or higher GPA.

Individual study; may be selected after the first term of the junior year by students maintaining a 3.2 grade-point average. Normally not to be taken in a student's final semester. Course format may vary from individual tutorial to laboratory work to seminar instruction under faculty supervision. Written application must be made prior to registration outlining proposed study program. Projects requiring machine-shop use must be approved by the laboratory supervisor. Students may count up to 6 points toward degree requirements. Students must submit both a project outline prior to registration and a final project write up at the end of the semester. 

MECE E3998 Projects in mechanical engineering. 1-3 points.

Prerequisites: Approval by faculty member who agrees to supervise the work.

Normally not to be taken in a student's final semester. Independent project involving theoretical, computational, experimental or engineering design work. May be repeated, but no more than 3 points may be counted toward degree requirements. Projects requiring machine-shop use must be approved by the laboratory supervisor. Students must submit both a project outline prior to registration and a final project write-up at the end of the semester. 

MECE E3999 Fieldwork. 1 point.

Prerequisites: Obtained internship and approval from faculty advisor. 

May be repeated for credit, but no more than 3 total points may be used toward the 128-credit degree requirement. Only for MECE undergraduate students who include relevant on-campus and off-campus work experience as part of their approved program of study. Final report and letter of evaluation required. Fieldwork credits may not count toward any major core, technical, elective, and non-technical requirements. May not be taken for pass/fail credit or audited.

MECE E4058 Mechatronics and embedded microcomputer control. 3 points.

Lect: 3.

Prerequisites: (ELEN E1201) ELEN E1201.

Recommended: ELEN E3000. Enrollment limited to 12 students. Mechatronics is the application of electronics and microcomputers to control mechanical systems. Systems explored include on/off systems, solenoids, stepper motors, dc motors, thermal systems, magnetic levitation. Use of analog and digital electronics and various sensors for control. Programming microcomputers in Assembly and C. A lab fee of $75.00 is collected.

MECE E4100 Mechanics of fluids. 3 points.

Lect: 3.

Prerequisites: (MECE E3100) MECE E3100 or equivalent.

Fluid dynamics and analyses for mechanical engineering and aerospace applications: boundary layers and lubrication, stability and turbulence, and compressible flow. Turbomachinery as well as additional selected topics.

MECE E4210 Energy Infrastructure Planning. 3 points.

Lect. 3.

Prerequisites: One year each of college level Physics, Chemistry, and Mathematics

Energy infrastructure planning with specific focus on countries with rapidly growing infrastructure needs. Spatiotemporal characteristics, scale, and environmental footprints of energy resources, power generation and storage, modeling demand growth, technology choices and learning for planning. Computer-assisted decision support and network design/optimization tools. Similarities, differences and interactions among electricity, gas, information, transportation and water distribution networks. Penetration of renewable and/or decentralized technologies into existing or new infrastructure. Special guest lectures on infrastructure finance, regulation and public-private partnerships.

MECE E4211 Energy: sources and conversion. 3 points.

Lect: 3.

Prerequisites: (MECE E3301) MECE E3301.

Energy sources such as oil, gas, coal, gas hydrates, hydrogen, solar, and wind.  Energy conversion systems for electrical power generation, automobiles, propulsion and refrigeration. Engines, steam and gas turbines, wind turbines; devices such as fuel cells, thermoelectric converters, and photovoltaic cells. Specialized topics may include carbon-dioxide sequestration, cogeneration, hybrid vehicles and energy storage devices.

MECE E4212 Microelectromechanical systems. 3 points.

Lect: 1.5. Lab: 3.

MEMS markets and applications; Scaling laws; Silicon as a mechanical material; Sensors and actuators; micromechanical analysis and design; substrate (bulk) and surface micromachining; computer aided design; packaging; testing and characterization; microfluidics.

MECE E4213 Bio-microelectromechanical systems (BioMEMS): design, fabrication and analysis. 3 points.

Lect: 3.

Prerequisites: (MECE E3100) and (MECE E3311) A course in transport phenomena, or by instructor's permission

Silicon and polymer micro/nanofabrication techniques; hydrodynamic microfluidic control; electrokinetic microfluidic control; microfluidic separation and detection; sample preparation; micro bioreactors and temperature control; implantable MEMS, including sensors, actuators and drug delivery devices.  

MECE E4302 Advanced thermodynamics. 3 points.

Lect: 3.

Prerequisites: (MECE E3301) 

Advanced classical thermodynamics. Availability, irreversibility, generalized behavior, equations of state for nonideal gases, mixtures and solutions, phase and chemical behavior, combustion. Thermodynamic properties of ideal gases. Applications to automotive and aircraft engines, refrigeration and air conditioning, and biological systems.

MECE E4304 Turbomachinery. 3 points.

This course will introduce you to the basics of theory, design, selection and applications of turbomachinery. Turbomachines are widely used in many engineering applications such as energy conversion, power plants, air-conditioning, pumping, refrigeration and vehicle engines, as there are pumps, blowers, compressors, gas turbines, jet engines, wind turbines etc. Applications are drawn from energy conversion technologies, HVAC and propulsion. The course will provide you with a basic understanding of the different kinds of turbomachines.

MECE E4305 Mechanics and thermodynamics of propulsion. 3 points.

Lect: 3.

Prerequisites: (MECE E3301) and (MECE E3311) and (MECE E4304) or MECE E3301x Thermodynamics, and MECE E3311y Heat Transfer; MECE E4304x Turbomachinery (or instructor approval).

Principles of propulsion. Thermodynamic cycles of air breathing propulsion systems including ramjet, scramjet, turbojet, and turbofan engine and rocket propulsion system concepts. Turbine engine and rocket performance characteristics. Component and cycle analysis of jet engines and turbomachinery. Advanced propulsion systems. 

MECE E4306 Introduction to Aerodynamics. 3 points.

Prerequisites: MECE E3100, or ENME E3161, or the equivalent

Principles of flight, imcompressible flows, compressible regimes.  Inviscid compressible aerodynamic in nozzles (wind tunnels, jet engines), around wings (aircraft, space shuttle) and around blunt bodies (rockets, reentry vehicles). Physics of normal shock waves, oblique shock waves, and explosion waves.

MECE E4312 Solar thermal engineering. 3 points.

Lect: 3.

Prerequisites: (MECE E3311) 

Fundamentals of solar energy transport: radiation heat transfer, convention, conduction and phase change processes.  Heat exchangers and solar collectors: basic methods of thermal design, flow arrangements, effects of variable conditions, rating procedures.  Solar energy concentration.  Piping Systems: series and parallel arrangements, fluid movers.  Thermal response and management of photovoltaic energy conversion.  Solar energy storage.  Solar cooling, solar thermal power and cogeneration.  Applications to the design of solar thermal engineering systems. 

MECE E4314 Energy dynamics of green buildings. 3 points.

Lect: 3.

Prerequisites: (MECE E3301) and (MECE E3311) 

Introduction to analysis and design of heating, ventilating and air-conditioning systems. Heating and cooling loads. Humidity control. Solar gain and passive solar design. Global energy implications. Green buildings. Building-integrated photovoltaics. Roof-mounted gardens and greenhouses. Financial assessment tools and case studies. Open to Mechanical Engineering graduate students only

MECE E4330 Thermofluid Systems Design. 3 points.

Lect: 3.

Prerequisites: (MECE E3100) and (MECE E3301) and (MECE E3311) 

Theoretical and practical considerations, and design principles, for modern thermofluids systems. Topics include boiling, condensation, phase change heat transfer, multimode heat transfer, heat exchangers, and modeling of thermal transport systems. Emphasis on applications of thermodynamics, heat transfer, and fluid mechanics to modeling actual physical systems. Term project on conceptual design and presentation of a thermofluid system that meets specified criteria.

MECE E4400 Computer laboratory access. 0 points.

0 pts.

Sign up for this class to obtain a computer account and access to the Department of Mechanical Engineering Computer Laboratory. 

MECE E4404 Tribology: Friction, Lubrication and Wear. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (MECE E3100) and (MECE E3311) and (ENME E3113) or permission of the instructor

Friction, lubrication and wear between sliding surfaces. Surface metrology, contact mechanics, and sliding friction.  Deformation, wear, and temperature rise of non-lubricated, liquid lubricated, and solid-lubricated rolling and sliding materials. The theories of boundary, elastohydrodynamic, hydrodynamic, hydrostatic, and solid-phase lubrication.  Lubricant flow and load-carrying capacity in bearings. Special applications such as geartrains, cam/tappets, and micro and nano-scale tribological interfaces.

MECE E4430 Automotive dynamics. 3 points.

Lect: 3.

Prerequisites: (ENME E3105) or (ENME E3106) or ENME 3105 or equivalent, recommended: ENME 3106 or equivalent

Automobile dynamic behavior is divided into three subjects: vehicle subsystems, ride, and handling. Vehicle subsystems include: tire, steering, mechanisms, suspensions, gearbox, engine, clutch, etc.  Regarding ride, vibrations and ride comfort are analyzed, and suspension optimization of a quarter car model is treated.  Regarding handling, vehicle dynamic behavior on the road is analyzed, with emphasis on numerical simulations using planar as well as roll models.

MECE E4431 Space vehicle dynamics and control. 3 points.

Lect: 3.

Prerequisites: (MECE E3105) or (ENME E3105) and (ENME E4202) ENME E4202 recommended

Space vehicle dynamics and control, rocket equations, satellite orbits, initial trajectory designs from earth to other planets, satellite attitude dynamics, gravity gradient stabilization of satellites, spin-stabilized satellites, dual-spin satellites, satellite attitude control, modeling, dynamics, and control of large flexible spacecraft.

MECE E4501 Geometrical modeling. 3 points.

Lect: 3.

Prerequisites: (COMS W1005) 

Relationship between 3D geometry and CAD/CAM; representations of solids; geometry as the basis of analysis, design, and manufacturing; constructive solid geometry and the CSG tree; octree representation and applications; surface representations and intersections; boundary representation and boundary evaluation; applied computational geometry; analysis of geometrical algorithms and associated data structures; applications of geometrical modeling in vision and robotics.

MECE E4502 Computational geometry for CAD/CAM. 3 points.

Lect: 3.

Prerequisites: (COMS W1005) FORTRAN or PASCAL.

Analysis of geometric problems and the design of efficient methodologies to obtain solutions to these problems. Algorithms to be studied include geometric searching, convex hulls, triangulations, Voronoi diagrams, intersections, hidden surfaces. Emphasis will be on practical aspects of these algorithms, and on applications of the solutions in computer-aided product design and manufacturing.

MECE E4510 Evolutionary Computation & Design Automation. 3 points

Lect: 3. Not offered during this academic year.

Prerequisites:  Basic programming in any language.

This course will dover fundamental and advanced topics in evolutionary algorithms and their application to open-ended optimization and computational design.  Covers generic algorithms, genetic programming, and evolutionary strategies, as well as governing dynamics of co-evolution and symbiosis.  Includes discussion of problem representations and applications to design problems in a variety of domains including software, electronics, and mechanics.

MECE E4602 Introduction to robotics. 3 points.

Lect: 3.

Overview of robot applications and capabilities. Linear algebra, kinematics, statics, and dynamics of robot manipulators. Survey of sensor technology: force, proximity, vision, compliant manipulators. Motion planning and artificial intelligence; manipulator programming requirements and languages.

MECE E4604 Product design for manufacturability. 3 points.

Lect: 3.

Prerequisites: Manufacturing process, computer graphics, engineering design, mechanical design.

General review of product development process; market analysis and product system design; principles of design for manufacturing; strategy for material selection and manufacturing process choice; component design for machining; casting; molding; sheet metal working and inspection; general assembly processes; product design for manual assembly; design for robotic and automatic assembly; case studies of product design and improvement.

MECE E4606 Digital Manufacturing. 3 points.

Prerequisites: Basic programming experience in any language

Additive manufacturing processes, CNC, Sheet cutting processes, Numerical control, Generative and algorithmic design. Social, economic, legal and business implications.Course involves both theoretical exercises and a hands-on project.

MECE E4609 Computer-aided manufacturing. 3 points.

Lect: 3.

Prerequisites: An introductory course on Manufacturing Processes, and knowledge of Computer Aided Design, and Mechanical Design or the Instructor's permission.

Computer aided design, free-form surface modeling, tooling and fixturing, computer numeric control, rapid prototyping, process engineering, fixed and programmable automation, industrial robotics.

MECE E4610 Advanced manufacturing processes. 3 points.

Lect: 3.

Prerequisites: Introductory course on manufacturing processes, and heat transfer, knowledge of engineering materials, or the Instructor's permission.

Principles of nontraditional manufacturing, nontraditional transport and media.  Emphasis on laser assisted materials processing, laser material interactions with applications to laser material removal, forming, and surface modification.  Introduction to electrochemical machining, electrical discharge machining and abrasive water jet machining.

MECE E4990 Special topics in mechanical engineering. 3 points.

Lect: 3.

Prerequisites: Permission of the Instructor

Topics and Instructors change from year to year. For advanced undergraduate students and graduate students in engineering, physical sciences, and other fields.

MECE E4999 Curricular practical training. 1 point.

Prerequisites: Instructor's written approval.

Only for ME graduate students who need relevant off-campus work experience as part of their program of study as determined by the instructor. Written application must be made prior to registration outlining proposed study program. Final reports required. May not be taken for pass/fail credit or audited. International students must consult with the International Students and Scholars Office.

MECE E6100 Advanced mechanics of fluids. 3 points.

Lect: 3.

Prerequisites: (MATH UN2030) and (MECE E3100) MATH V2030 and MECE E3100.

Eulerian and Lagrangian descriptions of motion. Stress and strain rate tensors, vorticity, integral and differentialequations of mass, momentum, and energy conservation. Potential flow.

MECE E6102 Computational heat transfer and fluid flow. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (MECE E3100) and (MECE E3311) and (COMS W1005) COMS W1005 FORTRAN.

Mathematical description of pertinent physical phenomena. Basics of finite-difference methods of discretization, explicit and implicit schemes, grid sizes, stability, and convergence. Solution of algebraic equations, relaxation. Heat conduction. Incompressible fluid flow, stream function-vorticity formulation. Forced and natural convection. Use of primitive variables, turbulence modeling, and coordinate transformations.

MECE E6103 Compressible Flow. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (APMA E4200) and (MECE E3100) and (MECE E3301) 

Fundamental analysis of compressible flows and its applications for various sonic/ supersonic elements including supersonic airfoils/ projectiles, nozzles, and shock tubes. Steady and unsteady shock/expansion waves, oblique shock waves. Shock reflections, methods of characteristic.

MECE E6104 Case studies in computational fluid dynamics. 3 points.

Lect: 3.

Prerequisites: (APMA E4200) and (MECE E6100) APAM E4200 and MECE E6100
Corequisites: APAM E4300 and MECE E4400

Hands-on case studies in computational fluid dynamics, including steady and transient flows, heat and mass transfer, turbulence, compressible flow and multiphase flow. Identifying assumptions, computational domain selection, model creation and setup, boundary conditions, choice of convergence criteria, visualization and interpretation of computed results. Taught in the Mechanical Engineering Computer Laboratory with Computational Fluid Dynamics software.

MECE E6105 Transport phenomena in the presence of interfaces. 3 points.

Lect: 3. Not offered this academic year.

Prerequisites: (MECE E3301) and (MECE E3311) and (MECE E4100) and (CHEE E4252) MECE E4100 Mechanics of Fluids, or the equivalent or the instructor's permission; CHEE E4252, Introduction to Surface and Colloid Chemistry, or the equivalent, or the instructor's permission.

Surface energy and capillary phenomena. Wetting and spreading of liquids, wetting line pinning and hysteresis, dynamics of wetting. Surfactants. Bubbles: nucleation, stability, dynamics, microstreaming. Jets and Drops: generation, dynamics, stabiligy and impact with surfaces. Measurement of transport phenomena involving interfaces. Interfacial transport phenomena involvng thermal, chemical or electrical gradients. Applications in microfluidic systems.

MECE E6200 Turbulence. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (MECE E6100) 

Introductory concepts and statistical description. Kinematics of random velocity fields, dynamics of vorticity, and scalar quantities. Transport processes in a turbulent medium. Turbulent shear flows: deterministic and random structures. Experimental techniques, prediction methods, and simulation.

MECE E6313 Advanced heat transfer. 3 points.

Lect: 3.

Prerequisites: MECE E3311.
Corequisites: MECE E6100.

Application of analytical techniques to the solution of multi-dimensional steady and transient problems in heat conduction and convection. Lumped, integral, and differential formulations. Topics include use of sources and sinks, laminar/turbulent forced convection, and natural convection in internal and external geometries.

MECE E6400 Advanced machine dynamics. 3 points.

Lect: 3.

Prerequisites: (MECE E3401) MECE E3401.

Review of classical dynamics, including Lagrange's equations. Analysis of dynamic response of high-speed machine elements and systems, including mass-spring systems, cam-follower systems, and gearing; shock isolation; introduction to gyrodynamics.

MECE E6422 Introduction to the theory of elasticity, I and II. 3 points.

Lect: 3.

Corequisites: APMA E4200.

Analysis of stress and strain. Formulation of the problem of elastic equilibrium. Torsion and flexure of prismatic bars. Problems in stress concentration, rotating disks, shrink fits, and curved beams; pressure vessels, contact and impact of elastic bodies, thermal stresses, propagation of elastic waves.

MECE E6423 Introduction to the theory of elasticity, I and II. 3 points.

Lect: 3.

Corequisites: APMA E4200.

Analysis of stress and strain. Formulation of the problem of elastic equilibrium. Torsion and flexure of prismatic bars. Problems in stress concentration, rotating disks, shrink fits, and curved beams; pressure vessels, contact and impact of elastic bodies, thermal stresses, propagation of elastic waves.

MECE E6424 Vibrations in machines, I. 3 points.

Lect: 3.

Prerequisites: MECE E3401

Review of vibration analysis of systems and mechanisms with one degree of freedom. Natural frequencies. Forced vibrations. Effects of dry and vicious friction. Energy methods of Rayleigh and Ritz. Suppression and elimination of vibration. Vibration isolation. Measuring instruments. Critical speeds in machinery. Synchronous whirl. Half-frequency whirl. Influence of bearing characteristics on critical speeds. Effect of gyroscopic moments. Systems with multiple degrees of freedom. Dynamic vibration absorbers. Self-tuning absorbers of pendulum and roller types. Lagrangian equations of motion as applied in vibrating systems. General equations for transverse critical speeds of shafts. Surging of helical springs.

MECE E6614 Advanced topics in robotics and mechanism synthesis. 3 points.

Lect: 3.

Prerequisites: (APMA E2101) and (APMA E3101) and (MECE E4602) or (COMS W4733) 
Corequisites: MECE E3401

Kinematic modeling methods for serial, parallel, redundant, wire-actuated robots and multifingered hands with discussion of open research problems. Introduction to screw theory and line geometry tools for kinematics.  Applications of homotropy continuation methods and symbolic-numerical methods for direct kinematics of parallel robots and synthesis of mechanisms.  Course uses textbook materials as well as a collection of recent research papers.

MECE E6620 Applied signal recognition and classification. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (MATH UN2030) and (APMA E3101) or knowledge of a programming language, or permission of instructor.

Applied recognition and classification of signals using a selection of tools borrowed from different disciplines. Applications include human biometrics, imaging, geophysics, machinery, electronics, networking, languages, communications, and finance. Practical algorithms are covered in signal generation, modeling, feature extraction, metrics for comparison and classification, parameter estimation, supervised, unsupervised and hierarchical clustering and learning, optimization, scaling and alignment, signals as codes emitted from natural sources, information, and extremely large-scale search techniques.

MECE E6700 Carbon nanotube science and technology. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (PHYS G4018) or (APPH E6081) or (MSAE E3103) or Knowledge of introductory solid state physics or instructor's permission.

Basic science of solid state systems. Crystal structure, electronic and phonon bandstructures of nanotubes. Synthesis of nanotubes and other nanomaterials. Experimental determination of nanotube structures and techniques for nanoscale imaging. Theory and measurement of mechanical, thermal, and electronic properties of nanotubes and nanomaterials. Nanofabrication and nanoelectronic devices. Applications of nanotubes.

MECE E6710 Nanofabrication laboratory. 3 points.

Lect: 3.

Prerequisites: ELEN E6945 or Instructor's permission.

Laboratory in techniques for fabrication at the nanometer scale.  Electron-beam lithography.  Plasma etching and 3D nanofabrication.  Thin film deposition.  Self-assembly and 'bottom up' nanofabrication.  Fabrication of and testing of complete nanodevices.  A lab fee of $300 is required.  

MECE E6720 Nano/microscale thermal transport process. 3 points.

Lect: 3. Not offered during this academic year.

Nano and microscale origins of thermal transport phenomena by molecules, electrons, phonons, and photons.  Quantum mechanics and statistical physics.  Density of states.  Kinetic theory of  gases.  Boltzmann transport equation (BTE), classical and quantum size effects.  Landauer formalism for transport via nanostructures.  Macroscopic constitutive equations from BTE.  Application to electronics cooling, thermoelectric and thermophotovoltaic decices, and energy conversion.

MECE E8020 Master's thesis.

Research in an area of Mechanical Engineering culminating in a verbal presentation and a written thesis document approved by the thesis advisor. Must  obtain permission from a thesis advisor to enroll.  Recommended enrollment for two terms, one of which can be the summer. A maximum of 6 points of master's thesis may count towards an MS degree , and additional research points cannot be counted. On completion of all master's thesis credits, the thesis advisor will assign a single grade. Students must use a department recommended format for thesis writing. 

MECE E8021 Master's thesis. 3 points.

3-6 pts.

Research in an area of Mechanical Engineering culminating in a verbal presentation and a written thesis document approved by the thesis advisor. A student enrolling in this course must obtain permission from a thesis advisor. Students are recommended to enroll in M.S. thesis for two terms, one of which can be the summer. Students may count a maximum of 6 points of Master's Thesis towards an MS degree and cannot count additional research points. On completion of all Master's Thesis credits, the thesis advisor will assign a single grade. Additional MS Thesis guidelines: • Students must use a department recommended format for thesis writing. A copy of the thesis will be uploaded on an electronic archive accessible through the Mechanical Engineering department website.

MECE E8100 Advanced topics in fluid mechanics. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: MECE E6100 MECE E6100.

This course may be taken more than once, since its content has minimal overlap between consecutive years. Selected topics from viscous flow, turbulence, compressible flow, rarefied gas dynamics, computational methods, and dynamical systems theory, non-Newtonian fluids, etc.

MECE E8501 Advanced Continuum Biomechanics. 3 points.

Prerequisites: Instructor Permission

The essentials of finite deformation theory of solids and fluids needed to describe mechanical behavior of biological tissue: kinematics of finite deformations, balance laws, principle of material objectivity, theory of constitutive equations, concept of simple solids and simple fluids, approximate constitutive equations, some boundary-value problems. Topics include one- and two-point tensor components with respect to generalized coordinates; finite deformation tensors, such as right and left Cauchy-Green tensors; rate of deformation tensors, such as Rivlin-Ericksen tensors; various forms of objective time derivatives, such as co-rotational and convected derivatives of tensors; viscometric flows of simple fluids; examples of rate and integral type of constitutive equations.

MECE E8990 Special topics in mechanical engineering. 3 points.

Lect: 3.

Prerequisites: Instructor's permission.

This course may be taken for credit more than once. The instructor from the Mechanical Engineering Department and the topics covered in the course will vary from year to year.  This course is intended for students with graduate standing in Mechanical Engineering and other engineering and applied sciences.  

MECE E9000 Graduate research and study. 1-3 points.

Theoretical or experimental study or research in graduate areas in mechanical engineering and engineering science.

MECE E9001 Graduate research and study. 1-3 points.

Theoretical or experimental study or research in graduate areas in mechanical engineering and engineering science.

MECE E9500 Graduate seminar. 0 points.

0 pts.

Pass/fail only. All doctoral students are required to successfully complete four semesters of the mechanical engineering seminar MECE E9500.

MECE E9800 Doctoral research instruction. 0 points.

3, 6, 9 or 12 pts.

A candidate for the Eng.Sc.D. degree in mechanical engineering must register for 12 points of doctoral research instruction. Registration in MECE E9800 may not be used to satisfy the minimum residence requirement for the degree.

MECE E9900 Doctoral dissertation. 0 points.

0 pts.

A candidate for the doctorate may be required to register for this course every term after his/her course work has been completed and until the dissertation has been accepted.

MEBM E4439 Modeling and identification of dynamic systems. 3 points.

Prerequisites: (APMA E2101) and (ELEN E3801) or instructor's permission.
Corequisites: EEME E3601

Generalized dynamic system modeling and simulation. Fluid, thermal, mechanical, diffusive, electrical, and hybrid systems are considered. Nonlinear and high order systems. System identification problem and Linear Least Squares method. State-space and noise representation. Kalman filter. Parameter estimation via prediction-error and subspace approaches. Iterative and bootstrap methods. Fit criteria. Wide applicability: medical, energy, others. MATLAB and Simulink environments.

MEBM E4702 Advanced musculoskeletal biomechanics. 3 points.

Lect: 3.

Advanced analysis and modeling of the musculoskeletal system. Topics include advanced concepts of 3-D segmental kinematics, musculoskeletal dynamics, experimental measurements of joints kinematics and anatomy, modeling of muscles and locomotion, multibody joint modeling, introduction to musculoskeletal surgical simulations.

MEBM E4703 Molecular mechanics in biology. 3 points.

Lect: 3.

Prerequisites: (ENME E3105) and (APMA E2101) or instructor's permission.

Mechanical understanding of biological structures including proteins, DNA and RNA in cells and tissues. Force response of proteins and DNA, mechanics of membranes, biophysics of molecular motors, mechanics of protein-protein interactions.  Introduction to modeling and simulation techniques, and modern biophysical techniques such as single molecule FRET, optical traps, AFM, and super-resolution imaging, for understanding molecular mechanics and dynamics.

MEBM E4710 Morphogenesis: Shape and structure in biological materials.

Prerequisites: Courses in mechanics, thermodynamics, and ordinary differential equations (for example, ENME E3113, MECE E3301 and MATH UN3027) at the undergraduate level or instructor's permission. 

Introduction to how shape and structure are generated in biological materials using an engineering approach that emphasizes the application of fundamental physical concepts to a diverse set of problems. Mechanisms of pattern formation, self-assembly, and self-organization in biological materials, including intracellular structures, cells, tissues, and developing embryos. Structure, mechanical properties, and dynamic behavior of these materials. Discussion of experimental approaches and modeling. Course uses textbook materials as well as a collection of research papers.

MEBM E6310 Mixture theories for biological tissues, I. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (MECE E6422) and (APMA E4200) or equivalent.

Development of governing equations for mixtures with solid matrix, interstitial fluid, and ion constituents. Formulation of constitutive models for biological tissues. Linear and nonlinear models of fibrillar and viscoelastic porous matrices. Solutions to special problems, such as confined and unconfined compression, permeation, indentation and contact, and swelling experiments.

MEBM E6311 Mixture theories for biological tissues, II. 3 points.

Lect: 3.

Prerequisites: (MECE E6422) and (APMA E4200) or equivalent.

Development of governing equations for mixtures with solid matrix, interstitial fluid, and ion constituents. Formulation of constitutive models for biological tissues. Linear and nonlinear models of fibrillar and viscoelastic porous matrices. Solutions to special problems, such as confined and unconfined compression, permeation, indentation and contact, and swelling experiments.

MECH E4320 Introduction to Combustion. 3 points.

Prerequisites: Course in introductory thermodynamics, fluid mechanics, and heat transfer at the undergraduate level or instructor's permission

Thermodynamics and kinetics of reacting flows; chemical kinetic mechanisms for fuel oxidation and pollutant formation; transport phenomena; conservation equations for reacting flows; laminar non-premixed flames (including droplet vaporization and burning); laminar premixed flames; flame stabilization, quenching, ignition, extinction, and other limit phenomena; detonations; flame aerodynamics and turbulent flames.

MECS E4510 Evolutionary Computation and Design Automation. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: Basic programming experience in any language.

This course will cover fundamental and advanced topics in evolutionary algorithms and their application to open-ended optimization and computational design. Covers genetic algorithms, genetic programming, and evolutionary strategies, as well as governing dynamics of co-evolution and symbiosis. Includes discussions of problem representations and applications to design problems in a variety of domains including software, electronics, and mechanics.

MECS E4603 Applied Robotics: Algorithms and Software. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: Fundamental programming skills (e.g. COMS W1002 or COMS W1004 or COMS W1005 or ENGI E1006 or equivalent).

The science and systems aspects of Robotics taught from an applied perspective, focusing on algorithms and software tools. Spatial reasoning; tools for manipulating and visualizing spatial relationships. Analysis of robotic manipulators; numerical methods for kinematic analysis. Motion planning, search-based and stochastic approaches. Applications for force and impedance control. Grading based on a combination of exams and projects implemented using the Robot Operating System (ROS) software framework and executed on real and simulated robotic manipulators. Note: This course can be taken individually or simultaneously with MECE E4602 (Introduction to Robotics). This course can also be used to satisfy the requirements of the Robotics and Control concentration of the Mechanical Engineering Master of Science program.

MECS E6615 Robotic Manipulation: Sensing, Planning, Design and Execution. 3 points.

Lect: 3. 

Prerequisites: (MECE E4602) or (COMS W4733) 

Theory and mechanisms of robotic manipulation, from sensor data,reasoning and planning to implementation and execution. Grasp quality measures andoptimization; planning and execution for manipulation primitives; sensor modalities: vision, touch and proprioception; simulation for manipulation planning; design of robot manipulators. Grading based on a combination of class presentations of novel research results in the field, participation in discussions, and course projects combining simulation, processing of sensor data, planning for manipulation, design and implementation on real robot hands.

MEEM E6432 Small-Scale Mechanical Behavior. 3 points.

Prerequisites: ENME E3113 or equivalent; APMA E4200 or equivalent

Mechanics of small scale materials and structures that require nonlinear kinematics or nonlinear stress vs. strain constitutive relations to predict mechanical behavior. Topics include: variational calculus, deformation and vibration beam, strings, plates, and membranes;fracture, delamination, bulging, buckling of thin films, among others. Thermodynamics of solids will be reviewed to provide the basis for a detailed discussion of nonlinear elastic behavior as well as the study of the equilibrium and stability of surfaces.

MEIE E4810 Introduction to Human Spaceflight. 0 points.

Prerequisites: Department permission and knowledge of MATLAB or equivalent

Introduction to human spaceflight from a systems engineering perspective. Historical and current space programs and spacecraft. Motivation, cost and rationale for human space exploration. Overview of space environment needed to sustain human life and health, including physiological and psychological concerns in space habitat. Astronaut selection and training processes, spacewalking, robotics, mission operations, and future program directions. Systems integration for successful operation of a spacecraft. Highlights from current events and space research, Space Shuttle, Hubble Space Telescope, and International Space Station (ISS). Includes a design project to assist International Space Station astronauts. 

IEME E4200 Human Centered Design. 1 point.

Lect: 4.5.Not offered during this academic year.

Prerequisites: By application and instructor approval.

Fast-paced introduction to human centered design. Students learn the vocabulary of design methods, understanding of design process. Small group projects to create prototypes. Design of simple product, more complex systems of products and services, and design of business.

IEME E4310 The Manufacturing Enterprise. 3 points.

Lect: 3.

The strategies and technologies of global manufacturing and service enterprises. Connections between the needs of a global enterprise, the technology and methodology needed for manufacturing and product development, and strategic planning as currently practiced in industry.  

EEME E3601 Classical control systems. 3 points.

Lect: 3.

Prerequisites: (MATH UN2030) MATH V2030.

Analysis and design of feedback control systems. Transfer functions; block diagrams; proportional, rate, and integral controllers; hardware, implementation. Routh stability criterion, root locus, Bode and Nyquist plots, compensation techniques.

EEME E4601 Digital control systems. 3 points.

Lect: 3.

Prerequisites: (EEME E3601) or (ELEN E3201) 

Real-time control using digital computers. Solving scalar and state-space difference equations. Discrete equivalents of continuous systems fed by holds. Z-transer functions. Creating closed-loop difference equation models by Z-transform and state variable approaches. The Nyquist frequency and sample rate selection. Classical and modern based digital control laws. Digital system identification

EEME E6601 Introduction to control theory. 3 points.

Lect: 3.

Prerequisites: (MATH UN2030) 

A graduate-level introduction to classical and modern feedback control that does not presume an undergraduate background in control. Scalar and matrix differential equation models and solutions in terms of state transition matrices. Transfer functions and transfer function matrices, block diagram manipulations, closed loop response. Proportional, rate, and integral controllers, and compensators. Design by root locus and frequency response. Controllability and observability. Luenberger observers, pole placement, and linear-quadratic cost controllers.

EEME E6602 Modern control theory. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (EEME E6601) or (EEME E4601) or (ELEN E6201) or or the instructor's permission.

Singular value decomposition. ARX model and state space model system identification. Recursive least squares filters and Kalman filters. LQR, H∞, linear robust control, predictive control, adaptive control. Liapunov and Popov stability. Nonlinear adaptive control, nonlinear robust control, sliding mode control.

EEME E6610 Optimal control theory. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (EEME E6601) or (EEME E4601) or instructor's permission.

Covers topics in calculus of variations, Pontryagin maximum principle, quadratic cost optimal control, predictive control, dynamic programming for optimal control, Kalman filtering, numerical methods for solution. Some applications discussed include: minimum energy subway operation (our solution saved 11% in tests on the Flushing Line, and the method was adopted by the transit authority, saving many millions of dollars per year), minimum time robot optimal control allowing one to run assembly lines faster for increased productivity.

EEME E8601 Advanced topics in control theory. 3 points.

Lect: 3. Not offered during this academic year.

Prerequisites: (EEME E6601) and (EEME E4601) or instructor's permission.

This course may be taken more than once, since the content changes from year to year, electing different topics from control theory such as learning and repetitive control, adaptive control, system identification, Kalman filtering, etc.

 

BMME E4702 Advanced musculoskeletal biomechanics. 3 points.

Lect: 2.5. Lab: 0.5.Not offered during this academic year.

 

Advanced analysis and modeling of the musculoskeletal system. Topics include advanced concepts of 3-D segmental kinematics, musculoskeletal dynamics, experimental measurements of joint kinematics and anatomy, modeling of muscles and locomotion, multibody joint modeling, introduction to musculoskeletal surgical simulations.

 

"We want every mechanical engineer to 

        be a good engineer,

                 a solidly trained engineer,

        but also a solidly trained human being."

                     -Professor James Hone


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