Courses-Mechanical Engineering - Carnegie Mellon University

Graduate Course Descriptions

24-612 Cardiovascular Mechanics
Spring: 12 units          

The primary objective of the course is to learn to model blood flow and mechanical forces in the cardiovascular system. After a brief review of cardiovascular physiology and fluid mechanics, the students will progress from modeling blood flow in a.) small-scale steady flow applications to b.) small-scale pulsatile applications to c.) large-scale or complex pulsatile flow applications. The students will also learn how to calculate mechanical forces on cardiovascular tissue (blood vessels, the heart) and cardiovascular cells (endothelial cells, platelets, red and white blood cells), and the effects of those forces. Lastly, the students will learn various methods for modeling cardiac function. When applicable, students will apply these concepts to the design and function of selected medical devices (heart valves, ventricular assist devices, artificial lungs).


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. lecture Prerequisite for: 18-724/24-724


24-618 Special Topics: Computational Analysis of Transport Phenomena
Spring: 12 units          

In this course, students will develop basic understanding and skill sets to perform simulations of transport phenomena (mass, momentum, and energy transport) for engineering applications using a CAE tool, learn to analyze and compare simulation results with theory or available data, and develop ability to relate numerical predictions to behavior of governing equations and the underlying physical system. First 8 weeks of the course will include lectures and simulation-based homework assignments. During last 7 weeks, teams of students will work on self-proposed projects related to computational analysis of transport phenomena. In the project, students will learn to approach loosely defined problems through design of adequate computational mesh, choice of appropriate numerical scheme and boundary conditions, selection of suitable physical models, efficient utilization of available computational resources etc. Each team will communicate results of their project through multiple oral presentations and a final written report.


24-619 Special Topics in Bio-Fluid Mechanics
Intermittent: 12 units

Fluid dynamics associated with biological and biomedical problems including cardiovascular fluid dynamics, swimming/flying in nature and biomimetic engineering. We will study contemporary research findings in physiological,biological and biomedical fluid mechanics, and understand emerging biomimetic engineering methods, emphasizing quantitative understanding and fundamental engineering concepts. Computational and experimental techniques (CFD, flow visualization, PIV, LDV, POD, confocal microscopy) will be covered. This inter-diciplinary course is primarily intended for advanced undergraduate and entering graduate students. Familiarity with elementary fluid mechanics and introductory Matlab programming is beneficial. Students who have not previously taken a fluid dynamics class should consult with the instructor.


24-623 Molecular Simulation of Materials
Intermittent: 12 units 

24-623: Molecular Simulation of Materials Spring: 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

The course provides a quantitative introduction to the processes that control atmospheric pollutants and the use of mass balance models to predict pollutant concentrations. We survey major processes including emission rates, atmospheric dispersion, chemistry, and deposition. The course includes discussion of basic atmospheric science and meteorology to support understanding air pollution behavior. Concepts in this area include vertical structure of the atmosphere, atmospheric general circulation, atmospheric stability, and boundary layer turbulence. The course also discusses briefly the negative impacts of air pollution on society and the regulatory framework for controlling pollution in the United States. The principles taught are applicable to a wide variety of air pollutants but special focus is given to tropospheric ozone and particulate matter. The course is intended for graduate students as well as advanced undergraduates. It assumes a knowledge of mass balances, fluid mechanics, chemistry, and statistics typical of an undergraduate engineer but is open to students from other scientific disciplines. 12 units


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. The course includes a laboratory that gives the students experience with modern transport measurement instrumentation and data analysis. Integrated literature reviews and a final project require students to apply learned fundamentals to understand state-of-the-art research and technology. 4 hrs. lecture Prerequisites- 24-322 & 24-221 or equivalents


24-629 Direct Solar and Thermal Energy Conversion
Fall: 12 units               

This course introduces graduates and senior undergraduates the principles and technologies for directly converting heat and solar light into electricity using solid-state devices. The first part of the course reviews the fundamentals of quantum mechanics, solid state physics and semiconductor device physics for understanding solid-state energy conversion. The second part discusses the underlying principles of thermoelectric energy conversion, thermionic energy conversion, and photovoltaics. Various solar thermal technologies will be reviewed, followed by an introduction to the principles of solar thermophotovoltaics and solar thermoelectrics. Spectral control techniques which are critical for solar thermal systems will also be discussed. By applying the basic energy conversion theory and principles covered in lectures, students will finish a set of 4 homework assignments. This course also requires one project in which students will work individually to review one present solar or thermal energy conversion technology.

24-631 Special Topics in Thermal Design

12 Credit Units

This course guides students through the design process of a practical thermal system. The course plan assumes a mastery of the fundamentals of thermodynamics, fluid mechanics and heat transfer at the undergraduate level. Lectures aim at design aspects and analysis techniques commonly used in the development of thermal systems. Lecture topics include heat sinks, heat pipes, compact heat exchangers, sensors and instrumentation, thermoelectric devices, and special topics closely related to the theme of the design activity for the semester. Design activity is conducted in teams and includes several cycles of oral presentations, class discussions, and a final written report. System design and analysis of performance are heavily based on computer-added design tools and simulation means. Student performance in this course is evaluated based on individual homework assignments on the various topics presented in class and on a team design project. Prerequisite- 24-322 (Heat Transfer) or equivalent


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. Prerequisite- Undergraduate Thermodynamics course


24-650 Applied Finite Element Analysis
Intermittent: 12 units 

This is an introductory course on the finite element method with emphasis on application of the method to a wide variety of problems. The theory of finite element analysis is presented and students learn various applications of the method through assignments utilizing standard finite element software packages commonly used in industry. Various types of analyses are considered, which may include, for example, static, pseudo-static, dynamic, modal, buckling, contact, heat transfer, thermal stress and thermal shock. Students also learn to use a variety of element types in the models created, such as truss, beam, spring, solid, plate, and shell elements.


24-651 Material Selection for Mechanical Engineers
Spring: 12 units

This course provides a methodology for selecting materials for a given application. It aims to provide an overview of the different classes of materials (metal, ceramic, glass, polymer, elastomer or hybrid) and their properties including modulus, strength, ductility, toughness, thermal conductivity, and resistance to corrosion in various environments. Students will also learn how materials are processed and shaped (e.g., injection molding, casting, forging, extrusion, etc.), and will explore the origins of the properties, which vary by orders of magnitude. Topics include: Materials selection by stiffness, strength, fracture toughness and fatigue. Shape factors and materials processing. Binary phase and time temperature transformation diagrams, microstructure. Polymer types and structures. Alloying and strengthening of metals, types of steels. Corrosion, oxidation, tribology and thermal properties.


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. Prerequisite: Instructor permission.


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


24-672 Special Topics in DIY Design and Fabrication
Fall: 12 units   

The traditional principles of mass production are being challenged by concepts of highly customized and personalized goods. A growing number of do-it-yourself (DIY) inventors, designers, makers, and entrepreneurs is accelerating this trend. This class offers students hands-on experience in DIY product design and fabrication processes. Over the course of the semester, students work individually or in small groups to design customized and personalized products of their own and build them using various DIY fabrication methods, including 3D laser scanning, 3D printing, laser cutting, molding, vacuum forming, etc. In addition to design and fabrication skills, the course teaches students skills for communicating their ideas effectively through industrial design sketches and presenting their products with aesthetically refined graphics.


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 robot. Prerequisites: Statics and Stress Analysis or equivalents.


24-674 Design of Biomechatronic Systems for Humans
Intermittent: 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. Lecture 4 hrs.


24-680 Quantitative Entrepreneurship: Analysis for New Technology Commercialization
Intermittent: 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, model integration and interpretation, and professional communication skills. Students will apply theory and methods to a team project for a new product or emerging technology, developing a business plan to defend technical and economic competitiveness. This course assumes fluency with basic calculus, linear algebra, and probability theory.


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


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

Design for Manufacturing 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 that will be studied include: assembly, robustness and quality, platform design, maintenance and safety, economics and costing, lean manufacturing and globalization. In addition, 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. Prerequisites: Senior standing in mechanical engineering, or permission of instructor 4 hrs lec.


24-685 Special Topics: Additive Manufacturing Current Practices and State of the Art

Spring: 3 units

Introduction to additive manufacturing (AM) fundamentals and applications using Solidworks 3-D CAD software and a variety of polymer and metal AM machines. Includes a brief history of AM processing, a review of and technical fundamentals of current AM processes, a study of the current AM market, and future directions of the technology. Lab Sessions will support an open-ended design project and study and presentation of papers on the state of the art. Equivalent of 24-202 Intro to CAD is required.


24-687 Special Topics: Graduate Design Project

Spring: 12 units          

This course is an opportunity for graduate students to experience a capstone design experience. This is a project-based course with the objective of learning product conceptualization and realization; it follows a design-build-test approach. Students will learn about the design process, specific design techniques, analysis and synthesis applied to design, project management, teamwork and other relevant design-related skills. The course takes advantage of masters level expertise to tackle complex design projects requiring increased depth in design understanding and progressing at a faster pace. Requirement: graduate standing.


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. Units: 12 Format: 2 hrs. Lec. and 2 hrs. computer lab


24-689 Special Topics: Global and Regional Sustainable Design

Intermittent: 12 units             

Engineers face unique challenges in a globalized and rapidly changing world, where decisions should be made so that our environment is preserved, social justice is promoted, and the needs of all people are provided through the global economy. Through the design activity, engineers creatively produce technical solutions to global challenges, such as depletion of resources, environmental pollution, rapid population growth and damage to ecosystems. In this project-based course students will learn about life cycle analysis, design sustainability, design for extreme affordability, socio-economic and cultural diversity considerations while working on a community-based project to design a mechanical technical product solution.


24-691 Special Topics: Mechanical Engineering Project Management

Intermittent: 12 units

Organizations are increasingly adopting formal project management techniques to successfully initiate, plan, execute, monitor, control, and close out projects.  In this course, students will learn many project management tools which are commonly applied in industry. 

Students will incorporate these tools into a documented plan for a project on which they are currently working or have previously completed. The project plan will address the ten knowledge areas of project management, including the management of project integration, scope, time, cost, quality, human resources, communications, risk, procurement, and stakeholders.  Students will also assume the role of a project manager, functional/line manager, or engineer in a ten-week simulation of managing three simultaneous projects.  Real world constraints, challenges, and incentives will be applied. Additional special topics in project management will be discussed based on student interest, which may include lean, iterative, incremental, and industry-specific approaches, as well as project management certification.


24-701 Mathematical Techniques in Engineering
Intermittent: 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 Legendre 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
Fall: 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
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. 12 units Prerequisites(s) 26-211, or 36-220 or equivalent. Cross listed 12-704


24-711 Fluid Dynamics
Intermittent: 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.


24-718 Computational Fluid Dynamics
Intermittent: 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 hr. 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. 12 units 4 hrs. lecture


24-721 Advanced Thermodynamics
Intermittent: 12 units

Advanced Thermodynamics Intermittent: 12 units Course Website: 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
Fall: 12 units   

This course focuses on the thermodynamic modeling of energy systems with emphasis on energy/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. Students are expected to have completed an undergraduate course in thermodynamics comparable to 24-221. (12 units) 4 hrs lec. Pre-requisite: 24-221 or 06-221 or 27-215, or equivalent


24-727 Special Topics: 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 focuses upon application of exact and approximate analytical methods to problems on conduction heat transfer, steady state and transient analysis using separation of variables, Laplace transforms, variation of parameters, integral equations, and similarity techniques, as well as numerical solution methods including iteration, relaxation and finite differences. Radiative heat transfer including gaseous radiation is also explored. 4 hrs. lec Corequisite: 24-701 or permission of instructor.


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.


24-740 Combustion and Air Pollution Control
Intermittent: 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. Cross listed 19-740, 19-440, 24-425


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.


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


24-755 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. 12 Units Prerequisite(s): Graduate standing or consent of instructor. Crosslisted 12-755


24-767 Mechanics of Fracture and Fatigue
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. 12 Units Prerequisite(s): Graduate standing or consent of instructor


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. Prerequisite: An undergraduate course in classical control engineering or consent of the instructor.


24-776 Nonlinear Controls

Spring: 12 units          

This course provides an introduction to the analysis and design of nonlinear systems and nonlinear control systems; stability analysis using Lyapunov, input-output and asymptotic methods; and design of stabilizing controllers using a variety of methods selected from linearization, vibrational control, sliding modes, feedback linearization and geometric control. 4 hrs. lec. Prerequisite: 24-771.

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) programming in C++, (2) visualization using OpenGL, (3) basic data structures, and (4) basic algorithms. The course covers computational techniques required for solving common engineering problems and background algorithms and data structures used in modern Computer-Aided Design, Computer-Aided Manufacturing, and Computer-Aided Engineering tools. The course also offers intensive hands-on computational assignments for practice of common applications. 4 hrs lec.  Prerequisites:  None

24-781 Computational Engineering Project
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. MCDSM students only. 12/24 hrs lab
12/24 hrs lab  Prerequisite:  24-781


24-783 Special Topics: Advanced Engineering Computation

Spring: 12 units          

This course covers the advanced programming and computational skills necessary for solving engineering problems. These include (1) efficient data structures and algorithms for modeling and processing real-world data sets such as trees, hash tables, searching, priority queues, etc. (2) techniques for simulation and visualization such as numerically solving ODEs and PDEs, viewing control, programmable shader, etc., (4) tools for version controlling, scripting, and code building including sub-version, git, and cmake. Students will experience practical training in the above knowledge and programming skills through bi-weekly assignments and a final team project. Prerequisites- 24-780 Engineering Computation or equivalent C++ and OpenGL programming experience. Prerequisite: 24-780


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. 4 hrs.lecture Prerequisites: None


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


24-791/792  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 PhD Internship in Teaching Counterpoint
Fall and Spring: Variable units

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 Graduate Reading and Research
Summer: Variable units


24-797 Thesis Research
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.


24799 - Practicum in Mechanical Engineering

Fall and Summer: Variable units         

The Department of Mechanical Engineering at Carnegie Mellon considers experiential learning opportunities important educational options for its graduate students. One such option is an internship, normally completed during the summer. If a student receives an internship, the Mechanical Engineering Department will add the internship course to the student's schedule, and the student will be assessed tuition for 3 units. Upon completion of the internship, students must submit a 2-3 page report with supervisor signature detailing the work experience and including how the internship was related to Mechanical Engineering. After the report has been reviewed and approved, a letter grade will be assigned and these 3 units will count towards degree requirements. International students interested in registering for the practicum must also be authorized for Curricular Practical Training (CPT). Further information is available on the Office of International Educations website: