Mechanical and Aerospace Engineering

Academic Year 2023 – 2024

General Information

41 Olden Street, Engineering Quadrangle, Princeton, NJ 08544

Program Offerings:

  • Ph.D.
  • M.S.E.
  • M.Eng.

Department for program:

Director of Graduate Studies:

Graduate Program Administrator:


The mission of the Department of Mechanical and Aerospace Engineering is to educate leaders in engineering and applied sciences through a rigorous graduate program that defines the frontiers of knowledge in our field and prepares them for careers in academia, industry, and government. Our program emphasizes achieving fundamental understanding in a broad range of topics, a deep understanding in a particular area, and excellent communications skills. The majority of outstanding technical problems in today’s engineering and applied sciences require a multi-disciplinary approach. Our department has a strong tradition in defining and pursuing new research areas at the intersection of engineering, physics, chemistry, biological sciences, and applied mathematics.

We offer exciting opportunities for graduate study in areas as diverse as applied physics; biomechanics, and biomaterials; control, robotics, and dynamical systems; fluid mechanics; materials science; and propulsion and energy sciences. In addition, Princeton University is at the forefront of interdisciplinary research. Students are encouraged to sample the opportunities provided by other departments and programs within the School of Engineering and Applied Science and allied departments and programs across campus.

There are normally about 100 students in residence selected from a diverse pool of applicants worldwide. The size of the student population ensures close collaboration between each student and a faculty adviser that continues from arrival to the completion of the degree program.

The department offers three separate degree programs: Master of Engineering (M.Eng.), Master of Science in Engineering (M.S.E), and Doctor of Philosophy (Ph.D.). Applicants interested in the Ph.D. program may apply directly to that program; a master’s degree is not required.


Application deadline
Ph.D. and M.S.E. - December 1, 11:59 p.m. Eastern Standard Time; M.Eng. - December 15, 11:59 p.m. (This deadline is for applications for enrollment beginning in fall 2024)
Program length
Ph.D. 5 years, M.S.E. 2 years, M.Eng. 1 year
General Test - not accepted

Additional departmental requirements

Ph.D. applicants are required to select two areas of research interest when applying.

The M.Eng. program in Mechanical and Aerospace Engineering for academic year 2024-25 is intended only for Princeton seniors in the Class of 2024. We discourage applications from others, who will not be admitted.



Program Offerings

Program Offering: Ph.D.

Program description

As a candidate for the doctoral program, the student, in consultation with a faculty adviser and the student's Ph.D. committee, develops an integrated program of study in preparation for a comprehensive general examination. After passing the general examination, the student prepares a dissertation displaying technical mastery of the field and contributions to the advancement of knowledge, followed by a public presentation of the material to the technical community. Candidates in this program are required to complete a minimum of 10 courses throughout their enrollment. Eight of these courses must be completed before the general examination, with at least six courses in the first year of enrollment. Candidates are also required to be an assistant in instruction (teaching assistant) for a minimum of three half-time appointments (or the equivalent) after passing the general examination. The Ph.D. program typically lasts five years and includes full financial support. In addition, all admitted Ph.D. students are automatically considered for the prestigious Wu and Upton Fellowships.

With the permission of the Departmental Graduate Committee and the Graduate School, students in good standing in the Ph.D. program may transfer to the M.S.E. program to satisfy newly realized goals, provided they have not already been awarded the incidental M.A.


Students are expected to take 10 courses over the period of enrollment. Before standing for the general examination, students are expected to complete eight courses for a grade, two of which may be MAE 503 Directed Research. At least one of the courses must be in mathematics. Students must maintain a GPA of 3.0 or higher. Courses from other departments may be taken, and members of these departments may be invited to participate in the general examination.

Additional pre-generals requirements

Research with an Adviser
Students are expected to conduct research under the supervision of a faculty adviser before standing for the general examination. Students are expected to match with advisers by the end of the second term of enrollment.

During the first year of enrollment, student must participate in the department’s seminar courses, which includes weekly seminars by internal and external speakers as well as a discussion, which may include an assigned reading. Students are also encouraged to meet with at least one seminar speaker during the academic year.

Pre-Generals Committee Meeting
Approximately two months prior to the general exam, the student must meet with the student's Ph.D. committee to discuss the topics the student will be expected to be familiar with for the general exam.  Prior to this meeting, the student must prepare a two-page extended abstract that summarizes the research conducted so far and plans for the research going forward. The main objectives of this meeting are to inform the committee about the research area the candidate is working in and the candidate’s progress to date; to give the candidate feedback about the extended abstract and the content of the seminar to be given for the research component of the general exam; and for the committee to agree on a set of topics the student will be expected to be familiar with for the subject component of the general exam. These topics could involve specific courses, books, and/or research papers.

General exam

The Ph.D. in Mechanical and Aerospace Engineering is a certification that the graduating student is well versed in the fundamentals of the student's chosen field; is capable of performing creative, independent research; and has the ability to communicate ideas to a broad audience effectively. The general examination procedure exercises the department's responsibility for determining a student's potential to satisfactorily complete a Ph.D. and simultaneously encourages the student to review and consolidate the material from various courses and research activities. The general examination process consists of two components: the research component, consisting of a 30-minute presentation with an open question period, followed by the subject component, a 90-minute oral examination covering the broader subject area related to the student's research. The general exam is normally taken in January of the second year.

Qualifying for the M.A.

The Master of Arts (M.A.) degree is normally an incidental degree on the way to full Ph.D. candidacy and is earned after a student successfully passes the general examination.

Please note, students admitted to the Ph.D. program who do not wish to complete the program may be considered for an M.S.E. degree with approval from the department and the Graduate School. Ph.D. students who have already been awarded the incidental M.A. are not eligible to earn an M.S.E. 


It is a requirement for students to teach a minimum of three (3) half-time assistant in instruction assignments in order to qualify for their Ph.D.

Post-Generals requirements

After successfully completing the general exam, the balance of the program is spent on dissertation research, teaching obligations, and additional courses. Candidates meet with their Ph.D. committee each year to review their research progress.

Dissertation and FPO

The culmination of the Ph.D. program is the writing of a dissertation on a research topic explored by the student and a presentation of this work in a final public oral examination. The dissertation must contain significant and original contributions to the advancement of a field of knowledge. Upon acceptance of the dissertation by the departmental faculty, candidates are admitted to the final public oral examination.

The Ph.D. is awarded after the candidate’s doctoral dissertation has been accepted and the final public oral examination sustained.

Program Offering: M.S.E.

Program description

Candidates for the M.S.E. program complete eight courses for a grade. Students are also expected to write an acceptable thesis. The thesis is central to the program and is considered an integral aspect of graduate education in the field. It is the culmination of prior training and research and is expected to address a realistic and important problem. The thesis must be presented in good literary form and be written in good English. The technical quality is also expected to be high and differs from that expected for the Ph.D. only in the quantity of material presented. The M.S.E. program typically covers two years. The number of master’s students admitted each year is limited.

Candidates for this program generally provide their own financial support.


To qualify for the M.S.E., each student must complete all Graduate School requirements and complete a minimum of eight courses selected in consultation with the faculty adviser. Students must achieve a GPA of 2.0 or higher.


A thesis is required of all M.S.E. candidates and is the culmination of the student’s program of research conducted under the supervision of a faculty adviser. The M.S.E. thesis must be judged to contain material of publishable quality, presented in correct scholarly form, and written using good English.

Program Offering: M.Eng.

Program description

The Master of Engineering (M.Eng.) program is particularly suited to those interested in obtaining a more fundamental understanding of their field or broadening their experiences to include disciplines outside of their particular technical focus areas. The M.Eng. degree is a coursework-based degree with no research or thesis requirement. Candidates for the M.Eng. degree will normally satisfy degree requirements within one (10-month) academic year.


Candidates for the M.Eng. degree must successfully complete eight (8) graduate courses. Six of these courses must be technical, with no more than two being independent projects. A minimum of four of the technical courses must be taken in the Department. For candidates who earned an undergraduate degree at the University, none of the eight courses may be courses that were also taken as part of that undergraduate degree program. To qualify for the M.Eng. degree, the eight courses must be passed with at least a 3.0 or “B” average, and no more than one “C” grade will be permitted to count towards the eight courses.

The M.Eng. degree program is intended to be individualized and as unconstrained as possible, and a coherent program of study is developed in consultation with a faculty advisor. Opportunities for study exist within the various research areas of the Department, including Applied Physics; Biomechanics and Biomaterials; Controls, Robotics, and Dynamical Systems; Fluid Mechanics; Materials Science; and Propulsion and Energy Sciences.


  • Chair

    • Naomi E. Leonard
  • Associate Chair

    • Michael E. Mueller
  • Director of Graduate Studies

    • Alexander Glaser (acting) (spring)
    • Andrej Kosmrlj (fall)
  • Director of Undergraduate Studies

    • Michael G. Littman
  • Professor

    • Craig B. Arnold
    • Emily Ann Carter
    • Edgar Y. Choueiri
    • Mikko P. Haataja
    • Marcus N. Hultmark
    • Yiguang Ju
    • Chung K. Law
    • Naomi E. Leonard
    • Michael G. Littman
    • Luigi Martinelli
    • Michael E. Mueller
    • Radhika Nagpal
    • Clarence W. Rowley
    • Howard A. Stone
  • Associate Professor

    • Luc Deike
    • Alexander Glaser
    • Egemen Kolemen
    • Andrej Kosmrlj
    • Julia Mikhailova
    • Daniel M. Nosenchuck
  • Assistant Professor

    • Christine Allen-Blanchette
    • Ryne Beeson
    • Daniel J. Cohen
    • Kelsey B. Hatzell
    • Jesse D. Jenkins
    • Anirudha Majumdar
    • Aditya Sood
    • Aimy Wissa
  • Associated Faculty

    • Amir Ali Ahmadi, Oper Res and Financial Eng
    • Elie R. Bou-Zeid, Civil and Environmental Eng
    • Nathaniel J. Fisch, Astrophysical Sciences
    • Bruce E. Koel, Chemical and Biological Eng
    • David J. McComas, Vice President, PPL
    • David N. Spergel, Astrophysical Sciences
    • Salvatore Torquato, Chemistry
    • Robert J. Vanderbei, Oper Res and Financial Eng
    • Claire E. White, Civil and Environmental Eng
  • Lecturer

    • Glenn A. Northey
    • Janine K. Nunes

For a full list of faculty members and fellows please visit the department or program website.

Permanent Courses

Courses listed below are graduate-level courses that have been approved by the program’s faculty as well as the Curriculum Subcommittee of the Faculty Committee on the Graduate School as permanent course offerings. Permanent courses may be offered by the department or program on an ongoing basis, depending on curricular needs, scheduling requirements, and student interest. Not listed below are undergraduate courses and one-time-only graduate courses, which may be found for a specific term through the Registrar’s website. Also not listed are graduate-level independent reading and research courses, which may be approved by the Graduate School for individual students.

APC 523 - Numerical Algorithms for Scientific Computing (also AST 523/CSE 523/MAE 507)

A broad introduction to scientific computation using examples drawn from astrophysics. From computer science, practical topics including processor architecture, parallel systems, structured programming, and scientific visualization will be presented in tutorial style. Basic principles of numerical analysis, including sources of error, stability, and convergence of algorithms. The theory and implementation of techniques for linear and nonlinear systems of equations, ordinary and partial differential equations will be demonstrated with problems in stellar structure and evolution, stellar and galactic dynamics, and cosmology.

APC 524 - Software Engineering for Scientific Computing (also AST 506/CSE 524/MAE 506)

The goal of this course is to teach basic tools and principles of writing good code, in the context of scientific computing. Specific topics include an overview of relevant compiled and interpreted languages, build tools and source managers, design patterns, design of interfaces, debugging and testing, profiling and improving performance, portability, and an introduction to parallel computing in both shared memory and distributed memory environments. The focus is on writing code that is easy to maintain and share with others. Students will develop these skills through a series of programming assignments and a group project.

AST 551 - General Plasma Physics I (also MAE 525)

This is an introductory course to plasma physics, with sample applications in fusion, space and astrophysics, semiconductor etching, microwave generation: characterization of the plasma state, Debye shielding, plasma and cyclotron frequencies, collision rates and mean-free paths, atomic processes, adiabatic invariance, orbit theory, magnetic confinement of single-charged particles, two-fluid description, magnetohydrodynamic waves and instabilities, heat flow, diffusion, kinetic description, and Landau damping. The course may be taken by undergraduates with permission of the instructor.

CBE 517 - Soft Matter Mechanics: Fundamentals & Applications (also MAE 517)

We cover fundamental aspects of the mechanics of soft matter and see how they provide useful insights about novel engineering designs and materials (3D printing, soft robotics, metamaterials). Particular attention is given to interfacial effects, which dominate the physics of small objects. Topics include, drops, bubbles, wetting, coatings, instabilities. We also cover the mechanics of thin elastic objects whose deformability characterizes many biological systems. Students learn how to build quantitative physical models, combining experimental observations, scaling analysis and formal approaches.

CEE 530 - Continuum Mechanics and Thermodynamics (also MAE 560/MSE 530)

The course covers the fundamentals of the mechanics and thermodynamics of continua. It reviews concepts of tensor analysis on manifolds and tensor calculus. It then proceeds by developing the fundamental concepts of the kinematics of a deforming continuum. The notion of stress is then introduced and measures of stresses are discussed. Conservation of mass, balance of momentum and moment of momentum, conservation of energy in thermodynamic are discussed. Constitutive theories and the restriction of the second law are presented. The Euler-Lagrange equations are re-connected with balance laws.

CEE 545 - Origami Engineering (also MAE 556/MSE 535)

This class acquaints the student with the state-of-art concepts and algorithms to design and analyze origami systems (assemblies, structures, tessellations, etc). Students learn how to understand, create and transform geometries by folding and unfolding concepts, and thus apply origami concepts to solve engineering and societal problems. In addition, using origami as a tool, we outreach to some fundamental concepts in differential geometry.

ECE 521 - Linear System Theory (also MAE 547)

This course covers the fundamentals of linear system theory. Various topics important for further study in dynamic systems, control and communication and signal processing are presented.

ECE 523 - Nonlinear System Theory (also MAE 548)

A study of the mathematical techniques found useful in the analysis and design of nonlinear systems. Topics include stability and qualitative behavior of differential equations, functional analysis and input/output behavior of systems, and "modern'' nonlinear system theory, which uses both geometric and algebraic techniques. Prerequisite: 521.

ECE 532 - Safety-Critical Robotic Systems (also COS 572/MAE 572)

The course covers the mathematical foundations of dynamical system safety analysis and modern algorithmic approaches for robotic decision making in safety-critical contexts. The focus is on safe robot learning, multiagent systems, and interaction with humans, paying special attention to uncertainty and the reality gap between mathematical models and the physical world.

ENE 506 - Synchrotron and Neutron Techniques for Energy Materials (also CBE 566/CEE 506/MAE 536/MSE 586)

Topics include an introduction to radiation generation at synchrotron and neutron facilities, elastic scattering techniques, inelastic scattering techniques, imaging and spectroscopy. Specific techniques include X-ray and neutron diffraction, small-angle scattering, inelastic neutron scattering, reflectometry, tomography, microscopy, fluorescence and infrared imaging, and photoemission spectroscopy. Emphasis is placed on application of the techniques for uncovering the material structure-property relationship, including energy storage devices, sustainable concrete, CO2 storage, magnetic materials, mesostructured materials and nanoparticles.

ENE 522 - Introduction to the Electricity Sector-Engineering, Economics, and Regulation (also MAE 533)

This course provides an introduction to the electricity sector drawing on engineering, economics, and regulatory policy perspectives. It introduces the engineering principles behind various power generation technologies and transmission and distribution networks; the economics of electricity markets; and the regulation of electricity generation, transmission, distribution, and retail sales. Open challenges related to the growth of distributed energy resources, the transition to low-carbon electricity sources, and the role of the electricity sector in mitigating global climate change are also discussed.

ENE 570 - Advanced Optimization Methods for Energy Systems Engineering (also CBE 570/MAE 570)

The course covers (1) basic theory, (2) modeling techniques, (3) basic algorithms and solution methods, and (4) software tools for optimization. We also discuss how optimization methods can be used to design, analyze, and operate energy systems.

MAE 501 - Mathematical Methods of Engineering Analysis I (also APC 501/CBE 509)

Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, Sturm-Liouville theory, Green's functions for the solution of ordinary differential equations and Poisson's equation, and the calculus of variations.

MAE 502 - Mathematical Methods of Engineering Analysis II (also APC 506)

A complementary presentation of theory, analytical methods, and numerical methods. The objective is to impart a set of capabilities commonly used in the research areas represented in the Department. Standard computational packages will be made available in the courses, and assignments will be designed to use them. An extension of MAE 501.

MAE 503 - Directed Research

Under the direction of a faculty member, the student carries out a one-semester research project chosen jointly by the student and the faculty. Directed is normally taken during the first year of study. The project culminates in a written paper, in the style of a journal article, and presentation to at least one faculty member from the department who was involved in the research project. Students need to enroll at the beginning of the semester and must obtain permission from the instructor and the department.

MAE 510 - Advanced Topics in Engineering Mathematics II

Selected topics in mathematical methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include analytical methods for differential equations, numerical solution of hyperbolic equations, and statistical methods.

MAE 511 - Experimental Methods I

A laboratory course that focuses on basic electronics techniques, digital electronics, and data acquisition and analysis. Topics include introduction to digital and analog electronics, digital-to-analog and analog-to-digital conversion, microcomputer sampling, and data analysis. There are four laboratory hours and two lecture hours per week. There is one project.

MAE 513 - Independent Project I

Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.

MAE 514 - Master of Engineering Independent Project II

Continuation of MAE 513. Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.

MAE 515 - Extramural Summer Project

A summer research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor that will provide practical experience relevant to the student's thesis topic.

MAE 516 - Bioinspired Design

This bioinspired design course offers interdisciplinary, advanced design and critical thinking experience. Students work in teams to integrate biological knowledge into the engineering design process. The course uses case studies to show how biological solutions can be transferred into engineering design. The case studies include themes such as locomotion, materials, and sensing. By the end of the course, students are able to use analogical design concepts to engineer a prototype based on biological function.

MAE 518 - Virtual and Augmented Reality for Scientists, Engineers, and Architects (also ARC 516/ENE 528)

VR/AR can enable engineers, scientists, and architects to plan and conduct their work in fundamentally new ways, visualize and communicate their findings more effectively, and work in environments that are otherwise difficult, impossible, or too costly to experience in person. This course explores the basic concepts of effective VR/AR experiences and builds the skills needed to develop and support innovative science, engineering, or architecture projects. In the second half of the semester, working in small teams, students develop and implement VR/AR projects of their choice.

MAE 519 - Practical Experimental Methods

This hands-on course is designed to introduce students to a diverse array of experimental techniques to empower interdisciplinary research. Specific modules include: practical electronics (microprocessors, op-amps and transistors, debugging); fluid mechanics (high-speed imaging and flow analysis); cellular biomechanics (cell culture, live microscopy, bio-microfabrication); and advanced imaging and materials characterization (electron microscopy, AFM). Students should leave the course comfortable in performing a diverse array of experiments and forming collaborations outside their core area.

MAE 520 - Advanced Topics in Experimental Methods II

Selected topics in experimental methods, with an emphasis on advances relevant to research activities represented in the department. Possible topics include dynamic data analysis; instrumentation and systems analysis, scanning probe techniques, and nanoscale materials property measurements.

MAE 521 - Optics and Lasers (also MSE 561)

An introduction to principles of lasers. Topics include a review of propagation theory, interaction of light and matter, Fourier optics, a survey and description of operational characteristics of lasers, light scattering, and nonlinear optics. Some introductory quantum mechanics will be covered to give students an appreciation of the basic tools for the interaction of light with matter and nonlinear optical phenomena.

MAE 522 - Applications of Quantum Mechanics to Spectroscopy and Lasers (also AST 564)

An intermediate-level course in applications of quantum mechanics to modern spectroscopy. The course begins with an introduction to quantum mechanics as a "tool" for atomic and molecular spectroscopy, followed by a study of atomic and molecular spectra, radiative, and collisional transitions, with the final chapters dedicated to plasma and flame spectroscopic and laser diagnostics. Prerequisite: one semester of quantum mechanics.

MAE 527 - Physics of Gases

Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; chemical and physical equilibria; adiabatic temperatures of complex reacting systems; quantum mechanical analysis of atomic and molecular structure and atomic-scale collision phenomena; transport properties; reaction kinetics, including chemical, vibrational, and ionization phenomena; and propagation, emission, and absorption of radiation.

MAE 528 - Physics of Plasma Propulsion (also AST 566)

Focus of this course is on fundamental processes in plasma thrusters for spacecraft propulsion with emphasis on recent research findings. Start with a review of the fundamentals of mass, momentum & energy transport in collisional plasmas, wall effects, & collective (wave) effects, & derive a generalized Ohm's law useful for discussing various plasma thruster concepts. Move to detailed discussions of the acceleration & dissipation mechanisms in Hall thrusters, magnetoplasmadynamic thrusters, pulsed plasma thrusters, & inductive plasma thrusters, & derive expressions for the propulsive efficiencies of each of these concepts.

MAE 529 - Advanced Topics in Applied Physics I

Selected topics in applied physics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced plasma propulsion, linear and nonlinear wave phenomena, and x-ray lasers in biological investigations.

MAE 531 - Combustion (also ENE 531)

Fundamentals of combustion: thermodynamics; chemical kinetics; explosive and general oxidative characteristics of fuels; premixed and diffusion flames; laminar and turbulent flame phenomena; ignition and flame stabilization; detonation, environmental combustion considerations; and coal combustion.

MAE 532 - Combustion Theory

Theoretical aspects of combustion: the conservation equations of chemically-reacting flows; activation energy asymptotics; chemical and dynamic structures of laminar premixed and nonpremixed flames; aerodynamics and stabilization of flames; pattern formation and geometry of flame surfaces; ignition, extinction, and flammability phenomena; turbulent combustion; boundary layer combustion; droplet, particle, and spray combustion; and detonation and flame stabilization in supersonic flows.

MAE 535 - Turbulent Reacting Flows

Detailed treatment of the physics and modeling of turbulent combustion. Turbulent premixed, nonpremixed, and partially premixed combustion are all discussed. Emphasis in the course is placed on understanding relevant physical and chemical phenomena that lead to various modeling approaches (derived from both experiment and computation), the implicit and explicit assumptions in these modeling approaches, and the relative strengths and weaknesses of these modeling approaches.

MAE 538 - Electrochemical Engineering for Decarbonizing Energy Systems (also ENE 538)

This class provides a survey of electrochemical technologies for decarbonizing transportation, separations and emerging chemical applications. It introduces the electrochemistry fundamentals and how they are applied to systems related to batteries, fuel cells, electrochemical fuel production and supercapacitors. The class covers thermodynamics, kinetics, and transport related topics as they pertain to electrochemical systems. The context of the class overlaps with fundamental principles taught in chemical engineering, material science, mechanical engineering, and electrical engineering. A working knowledge of general chemistry is required.

MAE 539 - Advanced Topics in Combustion I (also CBE 551)

Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion and power plants.

MAE 540 - Advanced Topics in Combustion II

Selected topics in theoretical and experimental combustion, with an emphasis on advances relevant to research activities represented in the department. Possible topics include turbulent combustion, theoretical calculations of rate constants, plasma fuels and natural resources, and nuclear propulsion and power plants.

MAE 541 - Applied Dynamical Systems (also APC 571)

Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; and Melnikov's method, the Smale horseshoe, symbolic dynamics, and strange attractors. Offered in alternate years.

MAE 542 - Advanced Dynamics

Principles and methods for formulating and analyzing mathematical models of physical systems; Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid and elastic body dynamics; canonical transformations, Hamilton-Jacob-Jacobi; Theory; and integrable and nonintegrable systems. Additional topics are explored at the discretion of the instructor.

MAE 543 - Advanced Orbital Mechanics

An advanced course in orbital motion of earth satellites, interplanetary probes, and celestial mechanics. Topics include orbit specification, orbit determination, Lambert's problem, Hill's equations, intercept and rendezvous, air-drag and radiation pressure, lagrange points, numerical methods, general perturbations and variation of parameters, earth-shape effects on orbits, Hamiltonian treatment of orbits, Lagrange's planetary equations, orbit resonances, and higher-order perturbation effects.

MAE 544 - Nonlinear Control

Nonlinear control of dynamical systems, with an emphasis on the geometric approach. The course gives an introduction to differential geometry, nonlinear controllability and constructive controllability, nonlinear observability, state-space transformations and stability, followed by study of a selection of nonlinear control design methods, including techniques motivated by geometric mechanics.

MAE 545 - Special Topics in Mechanical & Aerospace Engineering

Topics vary according to the interests of the class but are drawn from emerging numerical discretization methods (finite elements, finite volume, spectral, boundary element and vortex methods), boundary condition treatment, complex geometry modeling and grid generation, solution algorithms (direct solvers, conjugate gradient, multigrid, Fourier and wavelet transforms), and parallel software and computer architectures.

MAE 546 - Optimal Control

An introduction to stochastic optimal control theory and application. It reviews mathematical foundations and explores parametric optimization, conditions for optimality, constraints and singular control, numerical optimization, and neighboring-optimal solutions. Least-squares estimates, propagation of state estimates and uncertainty, and optimal filters and predictors; optimal control in the presence of uncertainty; certainty equivalence and the linear-quadratic-Gaussian regulator problem; frequency-domain solutions for linear multivariable systems; and robustness of closed-loop control are all studied.

MAE 549 - Introduction to Robotics

Robotics is a rapidly-growing field with applications including unmanned aerial vehicles, autonomous cars, and robotic manipulators. This course provides an introduction to the basic theoretical and algorithmic principles behind robotic systems. The course also allows students to get hands-on experience through project-based assignments. Topics include inverse kinematics, motion planning, localization, mapping, vision, and reinforcement learning.

MAE 550 - Lessons from Biology for Engineering Tiny Devices (also MSE 560)

In this course we present a survey of problems at the interface of biology, physics and engineering to discuss how nature invented many tiny sensors, machines and structures that are important for functions of cells and organisms. Using this knowledge, we comment how to engineer and self-assemble tiny devices with DNA origami, how to design thin structures that can transform into specific shapes in response to external stimulus, how to make structures with tunable surface properties (drag, adhesion, hydrophobicity/hydrophilicity), how to make flexible electronics, how to make metamaterials with unusual properties, etc.

MAE 551 - Fluid Mechanics

An introduction to fluid mechanics. The course explores the development of basic conservation laws in integral and differential form; one-dimensional compressible flows, shocks and expansion waves; effects of energy addition and friction; unsteady and two-dimensional flows and method of characteristics. Reviews classical incompressible flow concepts, including vorticity, circulation, and potential flows. Introduces viscous and diffusive phenomena.

MAE 552 - Viscous Flows and Boundary Layers (also CBE 557)

The mechanics of viscous flows. The course explores the kinematics and dynamics of viscous flows; solution of the Navier Stokes equations; the behavior of vorticity; the boundary layer approximation; laminar boundary layer with and without pressure gradient; separation; integral relations and approximate methods; compressible laminar boundary layers; instability and transition; and turbulent boundary layers and self-preserving turbulent shear flows.

MAE 553 - Turbulent Flow

Physical and statistical descriptions of turbulence, and a critical review of phenomenological theories for turbulent flows. The course examines scales of motion; correlations and spectra; homogeneous turbulent flows; inhomogeneous shear flows; turbulent flows in pipes and channels; turbulent boundary layers; calculation methods for turbulent flows (Reynolds stress equations, LES, DNS); and current directions in turbulence research. This course is offered in alternate years.

MAE 555 - Non-Equilibrium Gas Dynamics and Chemistry

Noncontinuum description of fluid flow and Liouville and Boltzmann equations. The course examines molecular collisions; detailed balancing; Chapman-Enskog expansion for near-equilibrium flows; transport phenomena; flows with transnational, vibrational and chemical non-equilibrium; shock structure; and shear and mixing layers with chemical reactions.

MAE 557 - Simulation and Modeling of Fluid Flows (also CSE 557)

Numerical methods are applied to solve the equations that govern fluid motion. Fluid flow problems involve convection, diffusion, and source terms. The governing equations are non-linear and coupled. Finite-difference and finite volume methods are considered, together with concepts of accuracy, consistency, stability, convergence, conservation, and shock capturing. A range of current methods is reviewed with emphasis on multidimensional steady and unsteady compressible flows. Homework topics include writing codes to solve the conservation equation for a scalar, boundary layer flow, shock tube flow, application to curvilinear coordinates.

MAE 558 - Simulation and Modeling of Turbulent Fluid Flows

The foundation of CFD as applied to turbulent flows. Concepts of numerical accuracy and bandwidth are introduced. Aliasing and Nyquist criteria are discussed. Solutions in differential form and wave space are studied. The numerical representation of turbulent transport, production, and dissipation are discussed. Techniques for the simulation and modeling of turbulent flows are described, including direct numerical simulation (DNS), large-eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS). Homework topics include writing codes to solve isotropic turbulence using DNS, LES, and RANS methodologies.

MAE 559 - Advanced Topics in Fluid Mechanics I

Selected topics in fluid mechanics, with an emphasis on advances relevant to research activities represented in the department. Possible topics include advanced computational fluid dynamics, turbulence in fluids and plasmas, hydrodynamic stability and turbulence.

MAE 562 - Fracture Mechanics (also MSE 540)

Fracture involves processes at multiple time and length scales. This course covers the basic topics including energy balance, crack tip fields, toughness, dissipative processes, and subcritical cracking. Fracture processes are then examined as they occur in some modern technologies, such as advanced ceramics, coatings, composites, and integrated circuits. The course also explores fracture at high temperatures and crack nucleation processes.

MAE 563 - Instabilities in Fluids: Linear and Non-Linear Analysis of Waves and Patterns in the Environment (also AOS 563)

This course describes natural patterns arising from instabilities in nature, and discusses their importance in the environment. We analyze phenomena at various scales, as diverse as wave breaking at the ocean surface, internal mixing in the atmosphere and the ocean, volcanic plumes, convection cells in the atmosphere, the break-up of fluid ligaments or bubble bursting at an interface. The course details mathematical tools (linear and non-linear stability analysis, symmetry arguments, solitons to non-linear equations such as shocks and solitions), as well as present laboratory and numerical demonstration of the instabilities.

MAE 564 - Structural Materials (also MSE 564)

Stress/strain behavior of materials; dislocation theory and strengthening mechanisms; yield strength; materials selection. Fundamentals of plasticity, Tresca and Von Mieses yield criteria. Case study on forging: upper and lower bounds. Basic elements of fracture. Fracture mechanics. Mechanisms of fracture. The fracture toughness. Case studies and design. Fatigue mechanisms and life prediction methodologies.

MAE 566 - Biomechanics and Biomaterials: From Cells to Organisms (also CBE 561)

Bioengineering is proof that exciting developments happen at the interfaces between fields. This course introduces students to approaches spanning biomechanics and biophysics, biomaterials and tissue engineering, and biomedical device design. These approaches are explored in the context of single cells, tissues, and whole organisms. Sample topics include: mechanobiology, surface chemistry and the cell:material interface, the biomechanics of locomotion, and "lab on a chip"technologies. Special emphasis is placed on introducing practical biomedical examples from the bench to the operating room.

MAE 567 - Crowd Control: Understanding and Manipulating Collective Behaviors and Swarm Dynamics (also CBE 568)

Collective behaviors are all around us, from bird flocking, to mosh pit dynamics, to how the cells in our bodies work together. In this course, we explore not only how to understand and quantify these behaviors, but also how we can start to engineer them to reduce traffic, heal faster, develop new materials, and introduce new robotics approaches. The course spans three modules: hands-on training in analyzing real-world swarming systems; fundamental concepts underlying collective behaviors; and key case studies in manipulating these systems.

MAE 569 - Advanced Topics in Materials and Mechanical Systems I

Selected topics in materials and mechanical systems, with an emphasis on advances relevant to research activities represented in the department. Possible topics include high temperature protective coatings, multifunctional materials, MEMS, advanced computational methods in materials engineering.

MAE 573 - Applied Optimization for Energy Systems Engineering (also ENE 539)

In this course students learn practical applications of optimization methods in energy systems engineering. Students also gain familiarity with techniques via survey of canonical problems in power systems operations and planning. The course teaches practical model development, including formulation and implementation of linear and mixed integer programs in an algebraic programming language. The second half surveys advanced topics, including: managing dimensionality in large-scale problems, technology evaluation, policy evaluation, decision making under uncertainty, and multi-objective optimization.

MAE 574 - Unmaking the Bomb:The Science &Technology of Nuclear Nonproliferation, Disarmament, and Verification

Nuclear weapons have re-emerged as one of the main global security challenges of our time. Reducing the dangers posed by these weapons will require new verification technologies, and this course covers the relevant science and technology. Part I examines the fundamental principles of nuclear fission, nuclear radiation, and radiation detection. Hands-on prototyping team projects in Part II explore possible new inspection systems. These projects can involve autonomous robots, machine learning techniques, IoT devices, and new detector types. In a virtual-reality exercise at the end of the semester, we examine the viability of these systems.

MAE 580 - Advanced Topics in Energy and Environment II

Selected topics in energy and the environment, with an emphasis on advances relevant to research activities represented in the department. Possible topics include combustion control and emissions, economic development and energy resources, and energy efficiency.

MAE 595 - Extramural Research Project

A research project designed in conjunction with the student's advisor and an industrial, NGO, or government sponsor that provides practical experience relevant to the student's thesis topic. The full- time research project is conducted at the host institution. A final paper is required. Enrollment is limited to post-Generals students and requires the support of both the student's advisor and the Director of Graduate Studies. The course does not count toward the post-Generals course requirement.

MAE 597 - Graduate Seminar in Mechanical and Aerospace Engineering

A seminar of graduate students and staff presenting the results of their research and recent advances in flight, space, and surface transportation; fluid mechanics; energy conversion; propulsion; combustion; environmental studies; applied physics; and materials sciences. There is one seminar per week and participation at presentations by distinguished outside speakers. Participation is required by first year graduate students.

MAE 598 - Graduate Seminar in Mechanical & Aerospace Engineering

A seminar of graduate students and staff presenting the results of their research and recent advances in flight, space, and surface transportation; fluid mechanics; energy conversion; propulsion; combustion; environmental studies; applied physics; and materials sciences. There is one seminar per week and participation at presentations by distinguished outside speakers. Partipcation by first year graduate students is required.

MSE 501 - Introduction to Materials (also CBE 514/CEE 561/MAE 561)

Emphasizes the connection between microstructural features of materials (e.g., grain size, boundary regions between grains, defects) and their properties, and how processing conditions control structure. Topics include thermodynamics and phase equilibria, microstructure, diffusion, kinetics of phase transitions, nucleation and crystal growth, phase separation, spinodal decomposition, glass formation, and the glass transition.

MSE 517 - Structural and Material Optimization (also CEE 517/MAE 571)

This class addresses the practical aspects, theory, implementation and utilization of optimization in conjunction with analysis tools. It aims to acquaint the student with the state-of-the-art optimization techniques and their application to engineering problems. Besides traditional methods, it introduces the modern and powerful topology optimization method together with its application to material and structural systems. In this context, it also introduces rapid prototyping and 3D/4D printing techniques at different scales.