Courses-Mechanical Engineering - Carnegie Mellon University

Course Descriptions

24-614 Microelectromechanical Systems
Fall: 12 units

This course introduces fabrication and design fundamentals for Microelectromechanical Systems (MEMS): on-chip sensor and actuator systems having micron-scale dimensions.  Basic principles covered include microstructure fabrication, mechanics of silicon and thin-film materials, electrostatic force, capacitive motion detection, fluidic damping, piezoelectricity, piezoresistivity, and thermal micromechanics.  Applications covered include pressure sensors, micromirror displays, accelerometers, and gas microsensors.  Grades are based on exams and homework assignments.
4 hrs lec.  Prerequisite for undergraduates: 18-321 or 24-351  Prerequisite course for: 18-724/24-724.  Crosslisted 18-614.

24-615 Microfluidics
Intermittent: 12 units

This course offers an introduction to the emerging field of microfluidics with an emphasis on chemical and life sciences applications.  During this course students will examine the fluid dynamical phenomena underlying key components of "lab on a chip" devices. Students will have the opportunity to learn practical aspects of microfluidic device operation through hands-on laboratory experience, computer simulations of microscale flows, and reviews of recent literature in the field.  Throughout the course, students will consider ways of optimizing device performance based on knowledge of the fundamental fluid mechanics. Students will explore selected topics in more detail through a semester project.  Major course topics include pressure-driven and electrokinetically-driven flows in microchannels, surface effects, micro-fabrication methods, micro/nanoparticles for biotechnology, biochemical reactions and assays, mixing and separation, two-phase flows, and integration and design of microfluidic chips.  Students are assumed to have an undergraduate level of knowledge in fluid mechanics (comparable to 24-231). Compared to the undergraduate course, graduate students will conduct an additional project, more extensive homework and attend an extra hour of recitation. 3 hrs lec., 1 hr recitation  Prerequisites: Instructor permission.

24-616 Tribology - Friction, Lubrication and Wear
Intermittent: 12 units

Covers the science of surfaces interacting via dry, lubricated, and mixed (i.e., dry + lubricated) contact. Fundamental aspects include the Reynolds Equation, thermal-tribology, friction, and wear. Applied topics include bearings, surface analysis, nanomanufacturing, and biotribology. The course will conclude with a team project which will require computer programming. 4 hrs lec.  Prerequisite: None.

24-617 Special Topics in Mechanics of Complex Fluids
Intermittent: 12 units

In this course we use the techniques of modern continuum mechanics to study the flow of complex fluids. Specifically, we present the various constitutive relations used in industry, such as the traditional non-Newtonian fluid models, electro-rheological fluids, granular materials, coal-slurries, drilling fluids, polymers, blood, mixtures of fluids and particles, etc. These fluids which have complex rheological characteristics are not only encountered in nature, for example mud slides and avalanches, but also in many chemical, biological, food, pharmaceutical and personal care processing industries. The course begins with a review of vector and tensor analysis, before discussing various measures of deformation and stress formulations. The development of appropriate constitutive models for particular problems is also considered. Both analytical and experimental results are presented through additional readings from journal articles and the relevance of these results to the solution of unsolved problems is highlighted. The importance of solving boundary value problems is also emphasized. 3 hrs lec. Pre-requisites: Differential Equations and Undergraduate Fluid Mechanics or permission of instructor.

24-619 Biological Fluid Mechanics
Rarely: 12 units

Fluid dynamics and transport phenomena applied to the biological and biomedical problems are studied through selected topics from cardiovascular fluid dynamics, swimming/flying in nature and biomimetics. Objectives: (1) to equip students with the fluid dynamics tools in order to design and perform contemporary research in physiological and biological and biomedical fluid mechanics. (2) Review and understand emerging biomimetic engineering, emphasizing the quantitative understanding and fundamental engineering concepts. Computational and experimental techniques (CFD, flow visualization, PIV, LDV, POD, confocal microscopy) will be studied with hands on research projects based on student's interest. Principles of interdisciplinary (biology/clinician/engineer) collaboration are emphasized. Applications include time permitting: bio-inspired fluid dynamic systems, cardiovascular fluid dynamics, multi-phase, microcirculation, aquatic locomotion and propulsion in cellular (planktons, bacteria) and larger scale systems (avian, fish, squid, insects), flocks/school dynamics. Prerequisites:  Familiarity with elementary fluid mechanics and introductory matlab programming. 

24-623 Molecular Simulation of Materials
Intermittent: 12 units

The purpose of this course is to expose engineering students to the theory and implementation of numerical techniques for modeling atomic-level behavior. The main focus is on molecular dynamics and Monte Carlo simulations. Students will write their own simulation computer codes, and learn how to perform calculations in different thermodynamic ensembles. Consideration will be given to heat transfer, mass transfer, fluid mechanics, mechanics, and materials science applications.  The course assumes some knowledge of thermodynamics and computer programming. 4 hrs lec.  Prerequisite: None

24-626 Air Quality Engineering
Intermittent: 12 units

Problems and methodologies for studies of environmental management, with an emphasis on air pollution. Key topics include sources of pollutants, focusing on combustion chemistry for a hydrocarbon fuel; behavior of gaseous and particulate pollutants in the atmosphere including the role of meteorology and the use of dispersion equations; effects of pollutants on human health and global climate; and procedures by which air pollution standards are developed and enforced by regulatory agencies. Statistical treatment of data is included at several places in the course. 

24-627 Special Topics in Nanophotonics:  Fundamentals and Applications
Intermittent: 12 units

This course introduces basic concepts and applications of nanophotonics, aiming at a fundamental understanding of principles for manipulating lights at the nanoscale. Topics include fundamentals of electromagnetics (Maxwell's equations, polarization, dipole antenna, etc.), optical properties of solids, localized and propagating surface plasmons, nanoscale thermal radiation by surface phonon polaritons, electromagnetic metamaterials with negative refraction, photonic crystals and band gap, with their applications in nanotechnology. 4 hrs lec. Prerequisites: None

24-628 Energy Transport and Conversion at the Nanoscale
Spring: 12 units

Energy transport and conversion processes occur at the nanoscale due to interactions between molecules, electrons, phonons, and photons. Understanding these processes is critical to the design of heat transfer equipment, thermoelectric materials, electronics, light emitting diodes, and photovoltaics. The objective of this course is to describe the science that underlies these processes and to introduce the contemporary experimental and theoretical tools used to understand them.

24-642 Fuel Cell Systems
Fall: 12 units

Fuel cells are devices that convert chemical potential energy directly into electrical energy. Existing fuel cell applications range from the small scale, such as portable cell phone chargers, to the large scale, such as MW-scale power plants. Depending on the application, fuel cell systems offer unique advantages and disadvantages compared with competing technologies. For vehicle applications, they offer efficiency and environmental advantages compared with traditional combustion engines. In the first half of the course, the focus is on understanding the thermodynamics and electrochemistry of the various types of fuel cells, such as calculating the open circuit voltage and the sources of voltage loss due to irreversible processes for the main fuel cells types: PEM/SOFC/MCFC. The design and operation of several real fuel cells are then compared against this theoretical background.  The second half of the course focuses on the balance-of-plant requirements of fuel cell systems, such as heat exchangers, pumps, fuel processors, compressors, as well as focusing on capital cost estimating. Applying the material learned from the first and second halves of the class into a final project, students will complete an energy & economic analysis of a fuel cell system of their choice.

24-652 Special Topics in Experimental Micro and Nano-Mechanics
Rarely: 12 units

The objective of this course is to become adept at modeling, testing and analyzing the mechanics of micro- and nanostructures. Methods to design, analyze, and characterize micro- and nanostructures will be presented in the lectures. Computer-aided design, using AutoCAD software, will be employed to learn layout of micromechanical components. Course participants will enter a competition in which they design micromechanical structures. These structures will be fabricated at Sandia National Labs (Albuquerque, NM), and may be used in students' own subsequent research. Actuation methods (electrostatic, thermal, piezoelectric) will be discussed in detail. Homeworks will emphasize analytical, programming (MATLAB) and finite element (ANSYS) approaches to modeling micro- and nanomechanical structures. Four laboratories (design, resonance, comb drive actuation and levitation, and Hertzian/JKR mechanics) will be conducted. Experimental analysis techniques will include laser-doppler velocimetry, interferometry, and optical pattern matching. 4 hrs lec. Senior or graduate level standing Basic knowledge of statics (e.g., 24-261), stress analysis (24-262), and familiarity with resonance phenomena. Good working knowledge of MATLAB. Prerequisite: None

24-655 Cellular Biomechanics
Intermittent: 9 units

This course discusses how mechanical quantities and processes such as force, motion, and deformation influence cell behavior and function, with a focus on the connection between mechanics and biochemistry. Specific topics include: (1) the role of stresses in the cytoskeleton dynamics as related to cell growth, spreading, motility, and adhesion; (2) the generation of force and motion by moot molecules; (3) stretch-activated ion channels; (4) protein and DNA deformation; (5) mechanochemical coupling in signal transduction. If time permits, we will also cover protein trafficking and secretion and the effects of mechanical forces on gene expression. Emphasis is placed on the biomechanics issues at the cellular and molecular levels; their clinical and engineering implications are elucidated. 3 hrs. lec.  Crosslisted 42-645.  Prerequisite:  Instructor permission.

24-656 Advanced Manufacturing
Intermittent: 12 units

This course focuses on modeling of material removal processes, including the turning, milling, boring, and drilling processes. The course also includes introduction on economics of material removal, non-traditional material removal processes, stability of machining processes, tool wear and tool life, dimensional and surface metrology, and experimental methods in manufacturing. A term project that may involve experimentations is an integral part of the course. 4 hrs lec.  Prerequisite:  Senior or Graduate Standing

24-657 Molecular Biomechanics
Intermittent: 9 units

This class is designed to present concepts of molecular biology, cellular biology and biophysics at the molecular level together with applications. Emphasis will be placed both on the biology of the system and on the fundamental physics, chemistry and mechanics which describe the molecular level phenomena within context. In addition to studying the structure, mechanics and energetics of biological systems at the nano-scale, we will also study and conceptually design biomimetic molecules and structures. Fundamentals of DNA, globular and structured proteins, lips and assemblies thereof will be covered Prerequisites Thermodynamics (06-221 or 24-221) or permission from the instructor.

24-658 Computational Bio-modeling and Visualization
Spring: 12 units

Biomedical modeling and visualization play an important role in mathematical modeling and computer simulation of real/artificial life for improved medical diagnosis and treatment. This course integrates mechanical engineering, biomedical engineering, computer science, and mathematics together.  Topics to be studied include medical imaging, image processing, geometric modeling, visualization,computational mechanics, and biomedical applications. The techniques introduced are applied to examples of multi-scale biomodeling and simulations at the molecular, cellular, tissue, and organ level scales.  4 hrs lec./lab

24-659 Introduction to Continuum Biomechanics
Intermittent: 12 units 

This course provides a general survey of the application of continuum mechanics to biomechanics. The objective of this course is to provide the basic ideas of continuum mechanics for engineering and science students with little or no background in biomechanics, with particular emphasis on the application of quantitative and system perspectives to fluid and solid mechanics problems. The course begins with a historical review of the subject followed by a review of vector and tensor analysis, before discussing various measures of deformation and stress formulations. The development and understanding of appropriate constitutive models for particular problems are emphasized. Both analytical and experimental results are presented through readings from recent literature and the relevance of these results to the solution of unsolved problems is highlighted. The course encourages class participation and discussion in a seminar fashion and includes individually-crafted research projects that will be discussed in class.

24-661  Vibration of Linear and Dynamic Systems
Intermittent: 12 units

The subject area for this course is mechanical vibration, at a level appropriate for first-year graduate students. Classical techniques in mechanical vibration are developed for the modeling and analysis of discrete and continuous linear systems. Continuous systems are described within the broader context of operator theory to emphasize the physical and mathematical analogies with discrete systems. Specific topics include: Discrete systems. Equations of motion for multiple degree of freedom systems through Lagrange's method; linearization about equilibrium; symmetry and definiteness properties; free vibration; matrix eigenvalue problems; orthogonality; Rayleigh quotient; generalized coordinates; transient and forced response through modal analysis; Continuous systems; Classical rod, shaft, string, beam, membrane and plate models; Hamilton's principle; equations of motion and boundary conditions through variational methods; essentials of functional analysis; exact solution of eigenvalue problems; response through modal analysis and Green's function methods; global discretization; Galerkin's method; essential and suppressible boundary conditions; Kamke quotient; introduction to elastic wave propagation.  4 hrs lec.

24-671 Special Topics in Practical Control and Automation
Fall: 12 units

This course provides a broad overview of topics relevant to the practice of control and automation, and aims to provide the broad set of skills required to actually implement full control systems, from theory to hardware.  The course focuses on the applications of basic theory to real-world problems, advanced frequency-domain techniques, best practices, and practical knowledge of hardware implementation.  Topics include: Fundamental limitaions and the Bode integral theorem.  Design tradeoffs- sensitivity/robustness, cost, performance.  Control implementation: Electrical circuits and schematics, A/D and D/A conversion, sampline, delays, shielding, grounding, noise.  Automation: actuators, motors, drives, servos, PLCs, power supply, etc.  4 hrs lec. Prerequisite: An undergraduate course in classical control engineering or consent of the instructor.  Beneficial but not required: 24-771 Linear Systems.

24-673 Soft Robots - Mechanics, Design and Modeling
Spring: 12 units

Soft, elastically-deformable machines and electronics will dramatically improve the functionality, versatility, and biological compatibility of future robotic systems.  In contrast to conventional robots and machines, these “soft robots” will be composed of elastomers, gels, fluids, gas, and other non-rigid matter.  We will explore emerging paradigms in soft robotics and study their design principles using classical theories in solid mechanics, thermodynamics, and electrostatics.  Specific topics include artificial muscles, peristaltic robotics, soft pneumatic robotics, fluid-embedded elastomers, and particle jamming.  This course will include a final project in which students may work individually or as a team.  For the project, students are expected to design and simulate and/or build all or part (eg. sensors, actuators, grippers, etc.) of a soft robots.

24-674 Design of Biomechatronic Systems for Humans
Fall: 12 units

This course explores methods for the design of electromechanical devices that physically interface with humans to improve biomechanical performance, such as robotic prostheses and exoskeletons. Students will learn about common physical disabilities and methods for generating and evaluating potential interventions. Students will learn about state-of-the-art actuation and sensing systems, and design selected types to meet dynamic performance criteria. We will cover technology for interfacing these devices with humans, and implications for the resulting biomechatronic systems. Students will learn experimental methods for evaluating intervention effectiveness, including inverse dynamics and metabolics analyses. Students will complete a final project that involves introduction of novel elements to a biomechatronic system. Students need a foundation in machine design and numerical tools such as Matlab, and will benefit from knowledge of dynamics and biomechanics.

24-675 Micro/Nano Robotics
Spring: 12 units

This course focuses on the design, modeling, fabrication, and control of miniature mobile robot and micro/nano-manipulation systems for graduate and upper level undergraduate students.  It provides an overview of the state-of-the-art micro- and nanoscale sensors, actuators, manipulators, energy sources, robot design, and control methods.  It requires active student participation, interaction, and in-class discussions.  In addition to the basic background, it includes many case studies of current miniature robots and micro/nano-systems, challenges and future trends, and potential applications.  The course requires a final project involving novel theoretical and/or experimental ideas for micro/nano-robotic systems with a team of students.  Depending on the equipment availability, these projects can also involve hands-on experience and experimental demonstrations.  4 hrs lec.  Prerequisites: Instructor permission

24-676  Bio-Inspired Robotics
Fall: 12 Units

This course will explore design and control of biologically inspired robots. Locomotion principles of many agile animals such as lizards, snakes, insects, fishes, and birds will be studied with corresponding bio-inspired robotic platforms. Required bio-inspired robotic mechanisms, materials, actuators, sensors, and power sources to enable similar locomotion principles will be taught. Besides the basic background knowledge, it will include the current trends in literature, detailed case studies and discussions, and guest lecturer talks. Course projects will involve theoretical and hands-on topics on design, manufacturing and control of bio-inspired robots. 4 hrs lec.  Crosslisted 42-641.

24-681 Computer Aided Design
Intermittent: 12 units

This course is the first section of the two-semester sequence on computational engineering.  Students will learn how computation and information technologies are rapidly changing the way engineering design is practiced in industry.  The course covers the theories and applications of the measurement, representation, modeling, and simulation of three-dimensional geometric data used in the engineering designed process. Students taking this course are assumed to have knowledge of the first course in computer programming. 4 hrs lecture, 2 hrs computer cluster  Prerequisites: None

24-682 Computer Aided Engineering
Intermittent: 12 units

This course is the second in the two-semester sequence on computational engineering.  Students will learn how computation and information technologies are rapidly changing the way engineering analysis is practiced in industry.  The course covers the theories and applications of finite element methods, finite element mesh generation, robot manipulator kinematics, and inverse kinematics, and manufacturing process optimization.  Students taking this course are assumed to have knowledge of the first course in computer programming.   4 hrs lecture, 2 hrs computer cluster    Prerequisites: None

24-683  Design for Manufacturing and the Environment
Fall: 12 units

Design for Manufacture and the Environment examines influences of manufacturing and other traditionally downstream issues on the overall design process.  Manufacturing is one facet that will be examined.  Other downstream influences studied include:  manufacturing processes, material choices, assembly, robustness and quality, platform design, maintenance and safety, economics and costing, lean manufacturing and globalization.  In additional, a core part of the course will focus on environment-based design issues. The class will study basic fundamentals in each of these areas and how they affect design decisions. Senior standing in mechanical engineering, standing in Master of Product Development or permission of instructor.   4 hrs lec. 

24-685 Engineering Design Fundamentals

This course will teach the basic principles and philosophies of engineering design (with emphasis on mechanical engineering). Topics include stress analysis and fracture, heat transfer, kinematics, and systems packaging. Students will learn the issues engineers must consider during design of commonly produced products. Class includes lectures and labs. This course is required for Masters in Product Development students who do not have an engineering background. 24-685 course prerequisites: Standing in Masters of Product Development or permission of instructor. Mini course. 4 hrs lec.

24-687 Special Topics in Grand Challenges: Technology Identification and Product Design
Intermittent: 12 units

There are many challenges to society that must be solved over the next century. The National Academy of Engineers have laid out 14 “Grand Challenges” for engineering to solve. However, in addition to the technology that must be identified or invented, the technology must be incorporated within a product (physical, system, infrastructure, service) that delivers value to society through its use. This class is a combination of design research and creation. Students will investigate the technological issues of a Grand Challenge in regards to product needs, then design products that meets short term and long term needs and capabilities to help solve the Grand Challenge. This is a graduate level class, also open to outstanding seniors by permission of instructor.

24-688 Introduction to CAD and CAE Tools
Fall: 12 units 

This course offers the hands-on training on how to apply modern CAD and CAE software tools to engineering design, analysis and manufacturing. In the first section, students will learn through 7 hands-on projects how to model complex free-form 3D objects using commercial CAD tools. In the second section, students will learn through 7 hands-on projects how to simulate complex multi-physics phenomena using commercial CAE tools. 

24-700  Special Topics in Mechanical Engineering

24-701 Mathematical Techniques in Engineering
Fall: 12 units

This course explores methods of solving ordinary differential equations and introduction to partial differential equations; reviews elementary concepts, series solutions, Fourier, Bessel and Legrendre functions, boundary value problems, and eigenfunction expansions; and addresses calculus of variations. Solutions of classical partial differential equations of mathematical physics, including Laplace transformation and the method of separation of variables, will be covered in this course. 4 hrs lec.  Crosslisted 12-701

24-703 Numerical Methods in Engineering
Spring: 12 units

This course emphasizes numerical methods to solve differential equations that are important in Mechanical Engineering. Procedures will be presented for solving systems of ordinary differential equations and boundary value problems in partial differential equations. Students will be required to develop computer algorithms and employ them in a variety of engineering applications. Comparison with analytical results from 24-701 will be made whenever possible. 4 hrs lec.  Prerequisite: Some computer programming experience.  Crosslisted 12-703

24-704 Probability and Estimation Methods for Engineering Systems
Intermittent Fall: 12 units

Overview of rules of probability, random variables, probability distribution functions, and random processes.  Techniques for estimating the parameters of probability models and related statistical inference.  Application to the analysis and design of engineered systems under conditions of variability and uncertainty.  Prerequisite(s) 26-211, or 36-220 or equivalent.   Crosslisted CEE 12-704

24-711 Fluid Mechanics
Fall: 12 units

This course focuses on development and application of control volume forms of mass, momentum and energy conservation laws, differential forms of these laws in Eulerian and Lagrangian coordinates, and Navier-Stokes equations. Students also explore applications to problems in incompressible and compressible laminar flows, boundary layers, hydrodynamic lubrication, transient and periodic flows, thermal boundary layers, convective heat transfer, and aerodynamic heating. 4 hrs lec.  Prerequisites: 24-701 or permission of the instructor.

24-712 Turbulent Flow
Intermittent: 12 units

Course content emphasizes basic equations of turbulent flow, Reynolds stresses, semi-empirical and phenomenological theories of turbulence, similarity theory, and eddy viscosity as well as turbulence production, dissipation, and scaling laws. In addition, applications to confined flows, boundary layers, convective heat transfer and jet mixing, and introduction to more complex closure schemes and statistical methods in turbulence are explored. 4 hrs lec.  Prerequisite: 24-711.

24-718 Computational Fluid Dynamics
Intermittent Fall or Spring: 12 units

This course focuses on numerical techniques for solving partial differential equations including the full incompressible Navier-Stokes equations. Several spatial-temporal discretization methods will be taught, namely the finite difference method, finite volume method and briefly, the finite element method. Explicit and implicit approaches, in addition to methods to solve linear equations are employed to study fluid flows. A review of various finite difference methods which will be used to analyze elliptic, hyperbolic, and parabolic partial differential equations and the concepts of stability, consistency and convergence are presented at the beginning of the course to familiarize the students with general numerical methods. 4 hrs lec.

24-719 Advanced Fluid Mechanics
Intermittent: 12 units

Kinematics and mechanics of continua; continuity equation; linear and angular momentum equations; Navier-Stokes equation; non-inertial reference frames; and exact and approximate solutions, including Stokes and Oseen flows, ideal and potential flows, and laminar boundary layer theory. 

24-721 Advanced Thermodynamics
Intermittent: 12 units

The course covers advanced macroscopic thermodynamics and introduces statistical thermodynamics.  Review of first and second laws.  Axiomatic formulation of macroscopic equilibrium thermodynamics and property relationships.  Criteria for thermodynamic equilibrium with application to multiphase and multi-component systems. Thermodynamic stability of multiphase systems.  Elementary kinetic theory of gases and evaluation of transport properties.  Statistical-mechanical evaluation of thermodynamic properties of gases, liquids, and solids.  Students are expected to have an undergraduate level of understanding of Thermodynamics (comparable to 24-221).  4 hrs lec.  Prerequisites: None

24-722 Energy System Modeling
Intermittent: 12 units

This course focuses on the thermodynamic modeling of energy systems with emphasis on exergy/availability analysis techniques.  These techniques are developed and applied to both established and emerging energy technologies, such as internal combustion engines, gas- and coal-fired power plants, solar and wind energy systems, thermochemical hydrogen production cycles, and fuel cells.  The course will also consider the integration of components such as reformers and electrolyzers. Modern computational tools are used throughout the course. The course culminates with a group project that requires developing sophisticated, quantitative models of an integrated energy system. 4 hrs lec.  Pre-requisite: 24-221 or 06-221 or 27-215, or equivalent. 

24-724 Microelectromechanical System Design
12 units

This course covers advanced design of integrated MicroElectroMechanical Systems (MEMS) as the basis for futuristic sensor and actuator systems on chip. The course starts with design of low-level device details and builds to design of "VLSI MEMS." Topics include layout vs. process design; analysis and modeling of micromechanics, thermomechanics, capacitive sensing, and coupled electromechanics; noise; test structures and characterization; modulation and switched-capacitor interface circuits; and system design. Homework and projects will make intensive use of MEMS schematic design; behavioral modeling with analog hardware description languages; layout generation and synthesis tools; visualization tools; and MEMS design rules and extraction. Assigned readings of recent advances in MEMS design are actively discussed. A final project centers on a complete microsystem design within a post-CMOS micromachined process. Possible systems include sensor/actuator arrays for inertial, ultrasonic, RF, micropositioning, acoustic, optic or fluidic applications. Crosslisted as 18-724.  Prerequisites: 18-614/24-614 or equivalent by petition of instructor and senior or graduate standing.

24-727 Special Topics in Aerosol Measurement Technology
Intermittent: 12 units 

This course explores modern methods and instrumentation used to characterize key physical and chemical properties of aerosol particles, and the fundamental principles underlying the technology. Topics include particle sampling and collection (aerosol inlets, impactors, cyclones, virtual impactors, collection on substrates, electrostatic precipitation), aerosol charging and neutralization, particle size measurements (electrical mobility, optically, and aerodynamically based), particle detection (optical and electrical), aerosol optical properties, and the characterization of particle chemical composition (online mass spectrometry, in particular). Methods for analyzing both individual and ensembles of aerosol particles are discussed and compared. Recent advances reported in the literature are explored through student-led presentations. Students write a term paper describing and justifying their choice of techniques to solve a realistic aerosol measurement need. While the focus is on atmospheric aerosol particles, industrial applications such as particle synthesis and characterization are also discussed.

24-730 Advanced Heat Transfer
Fall: 12 units

This course is open to students from all areas of engineering, although an undergraduate background in heat transfer is assumed. This class is an appropriate preparation for the doctoral qualifying exam.Topics to be covered include: mathematical formulation of heat transfer problems, heat conduction, thermal radiation, hydraulic boundary layers, and laminar and turbulent convection. Problems and examples will include theory and applications drawn from a spectrum of engineering design problems.  Prerequisite: Undergraduate Heat Transfer 24-322 or equivalent.

24-731 Conductive Heat Transfer
Intermittent: 6 units

This course is open to students from all areas of engineering, although a graduate background in heat transfer is assumed, such as the material covered in Advanced Heat Transfer.  This course focuses on application of exact and approximate analytical methods to problems of conduction heat transfer. This course also covers numerical techniques in heat conduction. Covered topics include steady periodic problems, melting and solidification, enthalpy formulation, parametric estimation, and the Boltzmann Transport Equation. Examples will be drawn from a spectrum of engineering application.  4 hrs lecture - 7 weeks
Prerequisite: Advanced Heat Transfer (24-730) or instructor's permission.

24-732 Convective Heat Transfer
Intermittent: 6 units

This course is open to students from all areas of engineering, although a graduate background in heat transfer is assumed, such as the material covered in Advanced Heat Transfer (24-730).  This course focuses on the fundamentals of convective heat transfer. Topics covered in this course are: laminar and turbulent heat transfer, high speed flow, natural convection, and experimental techniques. Examples will be drawn from a spectrum of engineering application. 4 hrs lec.  Prerequisite: Advanced Heat Transfer (24-730) or instructor's permission.

24-733 Radiative Heat Transfer
Intermittent: 6 units

This course is open to students from all areas of engineering, although a graduate background in heat transfer is assumed, such as the material covered in Advanced Heat Transfer (24-730).  This course focuses on the fundamentals of radiative heat transfer. Topics covered in this course are: surface radiation, radiation through participating media, and combined heat transfer problems of radiation with convection and/or conduction. This course also covers analytical and numerical techniques in heat radiation. Examples will be drawn from a spectrum of engineering applications. 4hrs lec.
Prerequisite: Advanced Heat Transfer (24-730) or instructor's permission.

24-734 Small Scale Heat Transfer
Intermittent: 6 units

This course is open to students from all areas of engineering, although a graduate level background in heat transfer is assumed, such as the material covered in Advanced Heat Transfer (24-730).  This course focuses on the unique heat transfer effects in micro and nano scales. This course includes mathematical modeling of small scale heat transfer, review of microfabrication techniques, thermometry, electrical and optical techniques for thermal conductivity measurements, and thermophysical properties of gasses and solids. Examples will be drawn from a spectrum of thermal engineering applications in microelectronics and instrumentation. 4 hrs lec. Prerequisite - Advanced Heat Transfer (24-730) or instructor's permission.

24-735 Heat Transfer in Biology and Medicine
Intermittent: 6 units

Course objectives include: studying applications of heat transfer to biological systems, reviewing biomedical instrumentation related to thermal therapy, and developing mathematical techniques for bioheat transfer analyses. Syllabus includes: introduction to heat transfer in biological systems, mathematical modeling of bioheat transfer, cryopreservation, cryosurgery, hyperthermia and thermal ablation, thermal regulation in the human body, and measurements of thermophysical properties of biomaterials.  4 hrs lec - 7 weeks.
Prerequisites:  24-731 or instructor permission.

24-736 Two-Phase Flow and Heat Transfer
Intermittent: 12 units

Fundamentals of liquid-gas flow and heat transfer will be studied for applications in petrochemical processes, steam generators, heat exchangers, rocket nozzle cooling, nuclear reactor and other applications.  The dynamics and heat transfer of liquid sprays will also be discussed for spray systems including the coating, cooling and combustion applications. Reviews of various current research topics will also be addressed. Lectures will be provided, but students shall work on selected assignments on specific subjects from their particular areas of interest. Each student will eventually write up and present a subject as a review. The goal is to make students ready for research in their area of interest. Students taking this course are assumed to have knowledge of graduate-level fluid mechanics (24-711) and graduate-level heat transfer (24-730).   4 hrs lec. Prerequisite: None

24-739 Special Topics in Thermal Fluid Sciences
Intermittent: 12 units

24-740 Combustion and Air Pollution Control
12 units

This course examines the generation and control of air pollution from combustion systems. The course's first part provides a brief treatment of combustion fundamentals, including thermochemical equilibrium, flame temperature, chemical kinetics, hydrocarbon chemistry, mass transfer, and flame structure. This foundation forms the basis for exploring the formation of gaseous (oxides of nitrogen, carbon monoxide, hydrocarbons, and sulfur dioxide) and particulate pollutants in combustion systems. The course then describes combustion modifications for pollutant control and theories for pollutant removal from effluent streams. The internal combustion engine and utility boilers serve as prototypical combustion systems for discussion. The course also addresses the relationship between technology and the formulation of rational regional, national, and global air pollution control strategies.

24-744 Applied Combustion
Intermittent: 12 units

Course provides a sound understanding of the physics of combustion and discusses applications of combustion in practical devices such as engines, combustors, gas turbines, gasifiers etc. Emphasis will be given on applying the fundamental combustion concepts to understand the design and operation of combustion devices. After taking this course, students will be able to understand how combustion systems are designed and modified to maximize efficiency and reduce formation of pollutants.

Basic topics that will be covered include thermochemistry, temperature calculations, laminar premixed and diffusion flames, first law of thermodynamics for reacting systems. Advanced topics that will be covered are kinetics of alternative fuels, low-temperature combustion, regimes of turbulent combustion, formation and mitigation of pollutants. Applications that will be discussed are spark and compression ignited engines, furnace combustion, gas turbine combustors, solid fuel combustors, gasifies, and micro engines. 4 hrs lec. Prerequisites:  24-221 Thermodynamics and 24-231 Fluid Mechanics or equivalent.

24-751 Introduction to Solid Mechanics I
Fall: 12 units

This is the first course in a two-part professionally oriented course sequence covering a variety of important problems in solid mechanics. Topics covered typically include torsion of non-circular cross sections, the field equations of elasticity and boundary conditions, and a number of classical plane stress/plane strain solutions in rectangular and polar coordinates. Emphasis is placed on not only elasticity theory and how classical elasticity solutions are derived, but also on their use in constructing and interpreting the results from finite element simulations of applied engineering problems. Where applicable, comparisons are also made between solutions derived via the full theory of elasticity and simplified solutions developed in strength of materials courses. 4 hrs lec. Crosslisted 12-775  Co-requisite for 24-751: 24-701 or permission of the instructor.  

24-752 Introduction to Solid Mechanics II
Intermittent: 12 units

This is the second course in a two-part professionally oriented course sequence covering a variety of important problems in solid mechanics. Topics covered typically include anisotropy, energy methods and finite elements, contact problems, fracture mechanics and plasticity. As in the first course in the sequence, emphasis is placed on not only mechanics theory and classical solutions, but also on their application in finite element modeling of applied engineering problems. This course builds on concepts from the first course, so that it or a similar course on elasticity theory is a prerequisite. 4 hrs lec.  Prerequisite: 24-751 and 24-701, or permission of the instructor.  Crosslisted  12-776 

24-754 Continuum Mechanics of Materials
Intermittent: 12 units

This course deals with the application of continuum mechanics to the mechanical behavior of materials. The topics that shall be covered are (1) An overview of Cartesian tensors, (2) Kinematics and Deformation, (3) Conservation Principles, (4) Constitutive Relations for Fluids and Solids and Boundary Value Problems, and (5) Dynamics of Continuum Systems. Crosslisted CEE 12-769

24-755 Finite Element Method in Mechanics I
Fall intermittent:  12 units

The basic theory and applications of the finite element method in mechanics are presented.  Development of the FEM as a Galerkin method for numerical solution of boundary value problems.  Applications to second-order steady problems, including heat conduction, elasticity, convective transport, viscous flow and others.  Introduction to advanced topics, including fourth-order equations, time dependence and nonlinear problems.
Prerequisite(s):  Graduate standing or consent of instructor  Cross listed 12-755

24-756 Special Topics in Advanced Multiscale Modeling & Computation Engineering Materials
Intermittent: 12 units

This course will deal with advanced topics in multi-scale modeling. Specific topics will vary depending on student and instructor interest, but will be in the general area of theoretical analysis of multi-scale problems, and application of the theoretical analysis to develop efficient numerical methods for such problems. The material presented will be at a level that assumes that students have a strong grounding in graduate level finite element methods, solid mechanics, continuum mechanics, and engineering mathematics. CEE course 12-784 crosslisted 12 units Prerequisites: 12769 AND (12755 OR 24751)

24-767 Mechanics of Fracture and Fatigue
Intermittent: 12 units

The main topics of this course relate to the analysis of elastic and elastic-plastic fracture mechanics problems.  Basic concepts of linear elastic fracture mechanics are covered, including the nature of near-crack-tip fields and energetic approaches to fracture problems.  Test methods are discussed, with particular emphasis on their theoretical basis.  Other topics addressed include path independent integrals, mixed-mode fracture, interfacial fracture and applications to thin films.  Emphasis is placed on a theoretical understanding of crack growth under cyclic and sustained loading and how this understanding can be applied to component design. 4 hrs lec.  Prequisite:   24-751 or equivalent

24-769 Inelasticity:  Theory and Computation
Intermittent:  12 units

The first part of the course focuses on a theoretical framework for describing the macroscopic inelastic response of common materials like metals, polymers, and soils.  The second part deals with computational approximation of such a framework within the finite element method.  Topics:  Theory- Physical origin of plasticity, stress-strain curve, yielding, work-hardening. Small and Finite deformation theory- constitutive structure, normality; Hill's method of "principal axes",work-conjugate stress measures corresponding to arbitrary strain measures, formulation of the boundary value problem of incremental equilibrium and analysis of uniqueness for rate-(in)dependent materials. Computational Algorithms- isotropic hyperelasticity and hypoelasticity; rate-(in)dependent plasticity within the additive and multiplicative decompositions; linear and nonlinear viscoelasticity-material updates with exact/second-order accurate linearizations; incremental objectivity for hypoelasticity and finite plasticity under additive decomposition; element formulation to deal with near incompressibility.  Prerequisites:  first course in elasticity, graduate-level course in continuum mechanics, first course in finite element methods.  This course is offered every third year.  Crosslisted 12-772 3 hrs lec.

24-771 Linear Systems
Fall: 12 units

Topics include review of classical feedback control; solution of differential and difference equations; Laplace and Z-transforms, matrix algebra, and convolution; state variable modeling of dynamic continuous and discrete processes; linearization of nonlinear processes; state variable differential and difference equations; computer-aided analysis techniques for control system design; state variable control principles of controllability, observability, stability, and performance specifications; trade-offs between state variable and transfer function control engineering design techniques; and design problems chosen from chemical, electrical, and mechanical processes. 4 hrs lec.  Crosslisted 18-771  Prerequisite: An undergraduate course in classical control engineering or consent of the instructor.

24-776 Nonlinear Controls

The course provides an introduction to the analysis and design of nonlinear control systems. Analysis of nonlinear systems: phase plane analysis of second order systems, determination of limit cycles, describing functions, Lyapunov theory and Barbalat's Lemma, Input-Output stability. Control of nonlinear systems: design using Lyapunov theory, feedback linearization, sliding mode control, and introduction to adaptive control. The course will begin with a description of some properties of nonlinear system followed by phase plane analysis for second order systems. 4 hrs lec.  Crosslisted 18-776  Prerequisite: 24-771. 

24-777 Complex Large-Scale Dynamic Systems
Intermittent: 12 units

This course is motivated by the ever-growing complexity of man-made dynamic systems and the need for flexible monitoring, operations and design techniques for such systems. Of particular interest are systematic model-based methods for relating the key real-life problems for such systems and the state-of-the-art techniques for large-scale dynamic systems. Examples of such real-life complex systems are critical man-made infrastructure systems (electric power systems, gas networks, transport industries, data networks, and their interdependencies) as well as large-scale systems on chips.
In this course we will first review the traditional large-scale methods for model simplification (aggregation), time scale separation of sub-processes and singular perturbation techniques to account for these, stability analysis, and estimation and control. In the second, novel part of this course, we recognize the highly interactive nature of the evolving complex systems, in which much monitoring, data gathering, and decision making is made at the lower, physical levels of the system, and some coordination exists at the higher system level at which physical layers interact. Several conceptual challenges are posed for minimal coordination of such decision makers under high uncertainties, in order to have predictable performance. These concepts will be illustrated using the same man-made network systems of interest introduced at the beginning of the course.
Requirements: Some background in dynamic systems is highly desirable. Students interested in large-scale real-life complex systems, their relation to the state-of-the-art methods available and new research challenges will gain from taking this course.  Prerequisites: senior or graduate standing.  Crosslisted 18-777

24-778 Mechatronic Design
Spring: 12 units

Mechatronics is the synergistic integration of mechanical mechanisms, electronics, and computer control to achieve a functional system. Because of the emphasis upon integration, this course will center around laboratory projects in which small teams of students will configure, design, and implement mechatronic systems. Lectures will complement the laboratory experience with operational principles and system design issues associated with the spectrum of mechanical, electrical, and microcontroller components. Class lectures will cover selected topics including mechatronic design methodologies, system modeling, mechanical components, sensor and I/O interfacing, motor control, and microcontroller basics.  Crosslisted 18-578, 16-778

24-780 Engineering Computation
Fall:  12 units


This course covers the practical programming and computational skills necessary for engineers. These include: (1)usage of modern CAD/CAE/CAM tools, (2)programming in scripting languages, (3)programming in MATLAB, and (4) programming in C++.  In addition to covering fundamentals of the engineering software packages and programming languages, the course offers intensive hands-on computational assignments for practice of common applications.  4 hrs lec.  Prerequisites:  None

24-781 Computational Engineering Project I
Fall: 12 units

This project course is the first section of the two-semester sequence of Computational Engineering Projects. The course provides the students with hands-on problem-solving experience by using commercial computational tools and/or developing their own custom software.  Each student, individually or along with other students, will work on a project under the guidance of Carnegie Mellon faculty members and/or senior engineers from industry.  Students may select a project topic from those presented by advising faculty members and/or industry engineers.  Alternatively, a student may propose and work on his/her own project topic if he/she can identify a sponsoring faculty member or industry engineer.

24-782 Computational Engineering Project II
Spring: 12/24 units

This project course is the second section of the two-semester sequence of Computational Engineering Projects.  The course provides the students with hands-on problem-solving experience by using commercial computational tools and/or developing custom software.  Each student, individually or along with other students, will work on a project under the guidance of Carnegie Mellon University faculty members and/or senior engineers from industry. Students may select a project topic from those presented by advising faculty members and/or industry engineers.  Pending instructor permission, a student may alternatively work on his/her own project under the guidance of a sponsoring faculty member or an industry engineer.
12/24 hrs lab  Prerequisite:  24-781

24-784 Decision Tools for Design and Entrepreneurship
Spring: 12 units

This course provides engineers with a multidisciplinary mathematical foundation for integrated modeling of engineering design and enterprise planning decisions in an uncertain, competitive market. Topics include economics in product design, manufacturing and operations modeling and accounting, consumer choice modeling, survey design, conjoint analysis, decision-tree analysis, optimization, game theory, model integration, and professional communication skills. Students will apply theory and methods to a team project for a new product or emerging technology of their choice, developing a business plan to defend technical and economic competitiveness. Students may choose to select emerging technologies from research at Carnegie Mellon for study in the course, and in some years venture capitalists and other industry leaders may take part in critiquing student projects. This course assumes fluency with calculus and some prior programming experience. Compared to the undergraduate course, graduate students will conduct an additional independent research project. 4 hrs lec.  Crosslisted 24-484, 19-484, 19-784

24-785 Engineering Optimization
Intermittent: 12 units

This course introduces students to 1) the process of formally representing an engineering design or decision-making problem as a mathematical problem and 2) the theory and numerical methods needed to understand and solve the mathematical problem. Theoretical topics focus on constrained nonlinear programming, including necessary and sufficient conditions for local and global optimality and numerical methods for solving nonlinear optimization problems. Additional topics such as linear programming, mixed integer programming, global optimization, and stochastic methods are briefly introduced. Model construction and interpretation are explored with metamodeling and model reformulation techniques, study of model boundedness, constraint activity, and sensitivity analysis. Matlab is used in homework assignments for visualization and algorithm development, and students apply theory and methods to a topic of interest in a course project. Fluency with multivariable calculus, linear algebra, and computer programming is expected. Students who are unfamiliar with Matlab are expected to learn independently using available tutorials and examples provided.

24-787 Artificial Intelligence and Machine Learning for Engineering Design
Intermittent: 12 units

This course will cover fundamental artificial intelligence and machine learning techniques useful for developing intelligent software tools to support engineering design and other engineering activities. The computational techniques covered include: search, constraint satisfaction, probability, data mining, pattern recognition, neural networks, optimization, and evolutionary computation. The course will examine both the theory behind these techniques and the issues related to their efficient implementation. The application of the techniques to engineering tasks, such as design representation and automation will be explored. In addition to regular homework sets, the course includes individual paper presentations and a substantial term project in which the student will develop an intelligent software tool to support an engineering task. A basic working knowledge of a scientific programming language (C/C++, Java, Matlab) is highly recommended.  4 hrs lec. Prerequisites: None

24-789 Special Topics in Design
Fall (variable units)

24-791/792  Graduate Seminar I & II
Fall and Spring

Graduate seminar speakers include faculty, students, and invited guests from industry and academia. Through seminars, students widen their perspectives and become more aware of other topics in mechanical engineering.

24-793 Supervised Reading
Fall and Spring: variable units

This independent study is designed to give students an opportunity to explore pertinent subjects through faculty directed reading. Variable hrs.
Prerequisite: permission of the instructor.

24-794 Master of Science Project
Fall and Spring: variable units

This course is designed to be a training opportunity in engineering research and associated professional activity. Content includes a series of investigations under the student's initiative culminating in comprehensive reports, with special emphasis on orderly presentation and effective English composition for Master of Science candidates. Variable hrs. Prerequisite: permission of the instructor.

24-795 CMU Mechanical Engineering Teaching Intern
Fall and Spring

Course description: A teaching assignment under the guidance of a faculty member for intermediate or terminal-level doctoral candidates. Typical activities include preparing and teaching recitations, preparing and teaching laboratory sessions, holding office hours, grading and preparation of quizzes, problem sets and other assignments, and assisting instructor with other activities associated with teaching a course. 24-795 is 12 units and offered in Fall and Spring. (P/F). All non-native English speakers should conform to the university regulation on the TA language requirements.

24-796 Qualifying Examinations for the Ph.D. Degree
Fall and Spring

24-797 Thesis Research for the Ph.D. Degree
Fall and Spring: variable units

This course is designed to give students enrolled in the Ph.D. program an opportunity to conduct extensive research over the course of their studies. Variable hrs.

24-798 Final Public Oral Examination for the Ph.D. Degree
Fall and Spring