Core Undergraduate Subjects
16.001 Unified Engineering: Materials and Structures
 ( ) 
Prereq: Calculus II (GIR) and Physics I (GIR); Coreq: 16.002 and 18.03
Units: 5-1-6
 Lecture: M9,T10,R9-11 (35-225) Lab: TBA Recitation: W9 (35-225) +final
Presents fundamental principles and methods of materials and structures for aerospace engineering, and engineering analysis and design concepts applied to aerospace systems. Topics include statics; analysis of trusses; analysis of statically determinate and indeterminate systems; stress-strain behavior of materials; analysis of beam bending, buckling, and torsion; material and structural failure, including plasticity, fracture, fatigue, and their physical causes. Experiential lab and aerospace system projects provide additional aerospace context.
R.A. Radovitzky
No textbook information available
16.002 Unified Engineering: Signals and Systems
()
Prereq: Calculus II (GIR); Coreq: Physics II (GIR), 16.001, and (18.03 or 18.032)
Units: 5-1-6
Lecture: MT10,F9-11 (35-225) Lab: TBA Recitation: W10 (35-225) +final
Presents fundamental principles and methods of signals and systems for aerospace engineering, and engineering analysis and design concepts applied to aerospace systems. Topics include linear and time invariant systems; convolution; Fourier and Laplace transform analysis in continuous and discrete time; modulation, filtering, and sampling; and an introduction to feedback control. Experiential lab and system projects provide additional aerospace context. Labs, projects, and assignments involve the use of software such as MATLAB and/or Python.
J. How
No textbook information available
16.003 Unified Engineering: Fluid Dynamics
( )
Prereq: Calculus II (GIR), Physics II (GIR), and (18.03 or 18.032); Coreq: 16.004
Units: 5-1-6
Presents fundamental principles and methods of fluid dynamics for aerospace engineering, and engineering analysis and design concepts applied to aerospace systems. Topics include aircraft and aerodynamic performance, conservation laws for fluid flows, quasi-one-dimensional compressible flows, shock and expansion waves, streamline curvature, potential flow modeling, an introduction to three-dimensional wings and induced drag. Experiential lab and aerospace system projects provide additional aerospace context.
A. Lozano-Duran
16.004 Unified Engineering: Thermodynamics and Propulsion
()
Prereq: Calculus II (GIR), Physics II (GIR), and (18.03 or 18.032); Coreq: Chemistry (GIR) and 16.003
Units: 5-1-6
Presents fundamental principles and methods of thermodynamics for aerospace engineering, and engineering analysis and design concepts applied to aerospace systems. Topics include thermodynamic state of a system, forms of energy, work, heat, the first law of thermodynamics, heat engines, reversible and irreversible processes, entropy and the second law of thermodynamics, ideal and non-ideal cycle analysis, two-phase systems, and introductions to thermochemistry and heat transfer. Experiential lab and aerospace system projects provide additional aerospace context.
Z.S. Spakovszky
16.06 Principles of Automatic Control
()
Prereq: 16.002
Units: 3-1-8
Introduction to design of feedback control systems. Properties and advantages of feedback systems. Time-domain and frequency-domain performance measures. Stability and degree of stability. Root locus method, Nyquist criterion, frequency-domain design, and some state space methods. Strong emphasis on the synthesis of classical controllers. Application to a variety of aerospace systems. Hands-on experiments using simple robotic systems.
J.P. How, S.R. Hall
16.07 Dynamics
()
Prereq: (16.001 or 16.002) and (16.003 or 16.004)
Units: 4-0-8
Lecture: TR11-12.30 (35-225) Recitation: F3 (35-225) +final
Fundamentals of Newtonian mechanics. Kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.
R. Linares
No textbook information available
16.09 Statistics and Probability
()
Prereq: Calculus II (GIR)
Units: 4-0-8
TBA.
Introduction to statistics and probability with applications to aerospace engineering. Covers essential topics, such as sample space, discrete and continuous random variables, probability distributions, joint and conditional distributions, expectation, transformation of random variables, limit theorems, estimation theory, hypothesis testing, confidence intervals, statistical tests, and regression.
E.H. Modiano
No textbook information available
16.C20[J] Introduction to Computational Science and Engineering
(, ); second half of term
(Same subject as 9.C20[J], 18.C20[J], CSE.C20[J])
Prereq: 6.100A; Coreq: 8.01 and 18.01
Units: 2-0-4
Credit cannot also be received for 6.100B
Begins Oct 28. Lecture: MW3-4.30 (33-419)
Provides an introduction to computational algorithms used throughout engineering and science (natural and social) to simulate time-dependent phenomena; optimize and control systems; and quantify uncertainty in problems involving randomness, including an introduction to probability and statistics. Combination of 6.100A and 16.C20J counts as REST subject.
Fall: D.L. Darmofal, N. Seethapathi
Spring: D.L. Darmofal, N. Seethapathi
No textbook information available
Mechanics and Physics of Fluids
16.100 Aerodynamics
()
Prereq: 16.003 and 16.004
Units: 3-1-8
Lecture: MWF11 (33-419) Lab: F1 (33-319) or F2 (33-319) or F3 (33-418) or F4 (33-418)
Extends fluid mechanic concepts from Unified Engineering to aerodynamic performance of wings and bodies in sub/supersonic regimes. Addresses themes such as subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Material may vary from year to year depending upon focus of design problem.
Q. Wang
No textbook information available
16.101 Topics in Fluids
() 
Prereq: Permission of department
Units arranged
Provides credit for work on undergraduate-level material in fluids outside of regularly scheduled subjects. Intended for transfer credit and study abroad. Credit may be used to satisfy specific degree requirements in the Course 16 and Course 16-ENG programs. Requires prior approval. Consult department.
Z. C. Cordero, Z.S. Spakovszky
16.110 Flight Vehicle Aerodynamics
 ()
Prereq: 16.100 or permission of instructor
Units: 3-1-8
Lecture: TR1.30-3 (33-419)
Aerodynamic flow modeling and representation techniques. Potential farfield approximations. Airfoil and lifting-surface theory. Laminar and turbulent boundary layers and their effects on aerodynamic flows. Nearfield and farfield force analysis. Subsonic, transonic, and supersonic compressible flows. Experimental methods and measurement techniques. Aerodynamic models for flight dynamics.
D.L. Darmofal
No textbook information available
16.120 Compressible Internal Flow
 ()
Prereq: 2.25 or permission of instructor
Units: 3-0-9
Internal compressible flow with applications in propulsion and fluid systems. Control volume analysis of compressible flow devices. Compressible channel flow and extensions, including effects of shock waves, momentum, energy and mass addition, swirl, and flow non-uniformity on Mach numbers, flow regimes, and choking.
E. M. Greitzer
16.122 Aerothermodynamics
()
Prereq: 2.25, 18.085, or permission of instructor
Units: 3-0-9
Analysis of external inviscid and viscous hypersonic flows over thin airfoils, lifting bodies of revolution, wedges, cones, and blunt nose bodies. Analyses formulated using singular perturbation and multiple scale methods. Hypersonic equivalence principle. Hypersonic similarity. Newtonian approximation. Curved, detached shock waves. Crocco theorem. Entropy layers. Shock layers. Blast waves. Hypersonic boundary layers.
W. L. Harris
16.13 Aerodynamics of Viscous Fluids
()
Prereq: 16.100, 16.110, or permission of instructor
Units: 3-0-9
Boundary layers as rational approximations to the solutions of exact equations of fluid motion. Physical parameters influencing laminar and turbulent aerodynamic flows and transition. Effects of compressibility, heat conduction, and frame rotation. Influence of boundary layers on outer potential flow and associated stall and drag mechanisms. Numerical solution techniques and exercises.
M. Drela
16.18 Fundamentals of Turbulence
()
Prereq: 2.25 or permission of instructor
Units: 3-0-9
Lecture: TR2.30-4 (33-418)
Introduces the fundamentals of turbulent flows, i.e., the chaotic motion of gases and liquids, along with the mathematical tools for turbulence research. Topics range from the classic viewpoint of turbulence to the theories developed in the last decade. Combines theory, data science, and numerical simulations, and is designed for a wide audience in the areas of aerospace, mechanical engineering, geophysics, and astrophysics.
A. Lozano-Duran
No textbook information available
Materials and Structures
16.20 Structural Mechanics
()
Prereq: 16.001
Units: 5-0-7
Applies solid mechanics to analysis of high-technology structures. Structural design considerations. Review of three-dimensional elasticity theory; stress, strain, anisotropic materials, and heating effects. Two-dimensional plane stress and plane strain problems. Torsion theory for arbitrary sections. Bending of unsymmetrical section and mixed material beams. Bending, shear, and torsion of thin-wall shell beams. Buckling of columns and stability phenomena. Introduction to structural dynamics. Exercises in the design of general and aerospace structures.
B. L. Wardle
16.201 Topics in Materials and Structures
(,  , )
Not offered regularly; consult department
Prereq: Permission of department
Units arranged
Provides credit for undergraduate-level work in materials and structures outside of regularly scheduled subjects. Intended for transfer credit and study abroad. Credit may be used to satisfy specific degree requirements in the Course 16 program. Requires prior approval. Consult M. A. Stuppard.
Fall: Y. Marzouk
IAP: Y. Marzouk
Spring: Y. Marzouk
16.202 Manufacturing with Advanced Composite Materials
()
Not offered regularly; consult department
Prereq: None
Units: 1-3-2
Introduces the methods used to manufacture parts made of advanced composite materials with work in the Technology Laboratory for Advanced Composites. Students gain hands-on experience by fabricating, machining, instrumenting, and testing graphite/epoxy specimens. Students also design, build, and test a composite structure as part of a design contest. Lectures supplement laboratory sessions with background information on the nature of composites, curing, composite machining, secondary bonding, and the testing of composites.
Staff
16.215[J] Topology Optimization of Structures
(New)
()
(Same subject as 1.583[J], 2.083[J])
Prereq: None
Units: 3-0-9
Lecture: MW1-2.30 (5-233)
Covers free-form topology design of structures using formal optimization methods and mathematical programs, including design of structural systems, mechanisms, and material architectures. Strong emphasis on designing with gradient-based optimizers, finite element methods, and design problems governed by structural mechanics. Incorporates optimization theory and computational mechanics fundamentals, problem formulation, sensitivity analysis; and introduces cutting-edge extensions, including to other and multiple physics.
J. Carstensen
No textbook information available
16.221[J] Structural Dynamics
 ()
(Same subject as 1.581[J], 2.060[J])
(Subject meets with 1.058)
Prereq: 18.03 or permission of instructor
Units: 3-1-8
Examines response of structures to dynamic excitation: free vibration, harmonic loads, pulses and earthquakes. Covers systems of single- and multiple-degree-of-freedom, up to the continuum limit, by exact and approximate methods. Includes applications to buildings, ships, aircraft and offshore structures. Students taking graduate version complete additional assignments.
T. Cohen
16.223[J] Mechanics of Heterogeneous Materials
()
(Same subject as 2.076[J])
Prereq: 2.002, 3.032, 16.20, or permission of instructor
Units: 3-0-9
Mechanical behavior of heterogeneous materials such as thin-film microelectro- mechanical systems (MEMS) materials and advanced filamentary composites, with particular emphasis on laminated structural configurations. Anisotropic and crystallographic elasticity formulations. Structure, properties and mechanics of constituents such as films, substrates, active materials, fibers, and matrices including nano- and micro-scale constituents. Effective properties from constituent properties. Classical laminated plate theory for modeling structural behavior including extrinsic and intrinsic strains and stresses such as environmental effects. Introduction to buckling of plates and nonlinear (deformations) plate theory. Other issues in modeling heterogeneous materials such as fracture/failure of laminated structures.
B. L. Wardle, S-G. Kim
16.225[J] Computational Mechanics of Materials
()
(Same subject as 2.099[J])
Prereq: Permission of instructor
Units: 3-0-9
Formulation of numerical (finite element) methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered includes finite deformation elasticity and inelasticity. Numerical formulation and algorithms include variational formulation and variational constitutive updates; finite element discretization; constrained problems; time discretization and convergence analysis. Strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. The application to real engineering applications and problems in engineering science are stressed throughout. Experience in either C++, C, or Fortran required.
R. Radovitzky
16.230[J] Plates and Shells: Static and Dynamic Analysis
()
(Same subject as 2.081[J])
Prereq: 2.071, 2.080, or permission of instructor
Units: 3-1-8
Stress-strain relations for plate and shell elements. Differential equations of equilibrium. Energy methods and approximate solutions. Bending and buckling of rectangular plates. Post-buckling and ultimate strength of cold formed sections and typical stiffened panels used in aerospace, civil, and mechanical engineering; offshore technology; and ship building. Geometry of curved surfaces. General theory of elastic, axisymmetric shells and their equilibrium equations. Buckling, crushing and bending strength of cylindrical shells with applications. Propagation of 1-D elastic waves in rods, geometrical and material dispersion. Plane, Rayleigh surface, and 3-D waves. 1-D plastic waves. Response of plates and shells to high-intensity loads. Dynamic plasticity and fracture. Application to crashworthiness and impact loading of structures.
W. M. van Rees
16.235 Design with High Temperature Materials
()
Prereq: Permission of instructor
Units: 3-0-9
Introduction to materials design for high-temperature applications. Fundamental principles of thermodynamics and kinetics of the oxidation and corrosion of materials in high-temperature, chemically aggressive environments. Relationship of oxidation theory to design of metals (iron-, cobalt-, nickel-, refractory- and intermetallic alloys), ceramics, composites (metal-, ceramic- and carbon-matrix, coated materials). Relationships between deformation mechanisms (creep, viscoelasticity, thermoelasticity) and microstructure for materials used at elevated temperature. Discussions of high-temperature oxidation, corrosion, and damage problems that occur in energy and aerospace systems.
Z. C. Cordero
Information and Control Engineering
16.30 Feedback Control Systems
()
(Subject meets with 16.31)
Prereq: 16.06 or permission of instructor
Units: 4-1-7
Lecture: MW2.30-4 (32-144) Lab: TBA Recitation: F1 (33-419) or F2 (33-419) +final
Studies state-space representation of dynamic systems, including model realizations, controllability, and observability. Introduces the state-space approach to multi-input-multi-output control system analysis and synthesis, including full state feedback using pole placement, linear quadratic regulator, stochastic state estimation, and the design of dynamic control laws. Also covers performance limitations and robustness. Extensive use of computer-aided control design tools. Applications to various aerospace systems, including navigation, guidance, and control of vehicles. Laboratory exercises utilize a palm-size drone. Students taking graduate version complete additional assignments.
C. Fan
No textbook information available
16.301 Topics in Control, Dynamics, and Automation
()
Prereq: Permission of department
Units arranged
Provides credit for work on undergraduate-level material in control and/or dynamics and/or automation outside of regularly scheduled subjects. Intended for transfer credit and study abroad. Credit may be used to satisfy specific degree requirements in the Course 16 program. Requires prior approval. Consult department.
G. Long
16.31 Feedback Control Systems
()
(Subject meets with 16.30)
Prereq: 16.06 or permission of instructor
Units: 3-1-8
Lecture: MW2.30-4 (32-144) Lab: TBA +final
Graduate-level version of 16.30; see description under 16.30. Includes additional homework questions, laboratory experiments, and a term project beyond 16.30 with a particular focus on the material associated with state-space realizations of MIMO transfer function (matrices); MIMO zeros, controllability, and observability; stochastic processes and estimation; limitations on performance; design and analysis of dynamic output feedback controllers; and robustness of multivariable control systems.
C. Fan
No textbook information available
16.32 Principles of Optimal Control and Estimation
()
Prereq: 16.31
Units: 3-0-9
Fundamentals of optimal control and estimation for discrete and continuous systems. Briefly reviews constrained function minimization and stochastic processes. Topics in optimal control theory include dynamic programming, variational calculus, Pontryagin's maximum principle, and numerical algorithms and software. Topics in estimation include least-squares estimation, and the Kalman filter and its extensions for estimating the states of dynamic systems. May include an individual term project.
S.R. Hall
16.332 Formal Methods for Safe Autonomous Systems
()
Prereq: Permission of instructor
Units: 3-0-9
Covers formal methods for designing and analyzing autonomous systems. Focuses on both classical and state-of-the-art rigorous methods for specifying, modeling, verifying, and synthesizing various behaviors for systems where embedded computing units monitor and control physical processes. Additionally, covers advanced material on combining formal methods with control theory and machine learning theory for modern safety critical autonomous systems powered by AI techniques such as robots, self-driving cars, and drones. Strong emphasis on the use of various mathematical and software tools to provide safety, soundness, and completeness guarantees for system models with different levels of fidelity.
C. Fan
16.338[J] Dynamic Systems and Control
()
(Same subject as 6.7100[J])
Prereq: 6.3000 and 18.06
Units: 4-0-8
Linear, discrete- and continuous-time, multi-input-output systems in control, related areas. Least squares and matrix perturbation problems. State-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, and minimality. Internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, and observer-based compensators. Measures of control performance, robustness issues using singular values of transfer functions. Introductory ideas on nonlinear systems. Recommended prerequisite: 6.3100.
Staff
16.343 Spacecraft and Aircraft Sensors and Instrumentation
()
Prereq: Permission of instructor
Units: 3-0-9
Covers fundamental sensor and instrumentation principles in the context of systems designed for space or atmospheric flight. Systems discussed include basic measurement system for force, temperature, pressure; navigation systems (Global Positioning System, Inertial Reference Systems, radio navigation), air data systems, communication systems; spacecraft attitude determination by stellar, solar, and horizon sensing; remote sensing by incoherent and Doppler radar, radiometry, spectrometry, and interferometry. Also included is a review of basic electromagnetic theory and antenna design and discussion of design considerations for flight. Alternate years.
K. Cahoy
16.346 Astrodynamics
()
Prereq: 18.03
Units: 3-0-9
Fundamentals of astrodynamics; the two-body orbital initial-value and boundary-value problems with applications to space vehicle navigation and guidance for lunar and planetary missions with applications to space vehicle navigation and guidance for lunar and planetary missions including both powered flight and midcourse maneuvers. Topics include celestial mechanics, Kepler's problem, Lambert's problem, orbit determination, multi-body methods, mission planning, and recursive algorithms for space navigation. Selected applications from the Apollo, Space Shuttle, and Mars exploration programs.
G. Lavezzi
16.35 Real-Time Systems and Software
()
Prereq: 1.00 or 6.100B
Units: 3-0-9
Concepts, principles, and methods for specifying and designing real-time computer systems. Topics include concurrency, real-time execution implementation, scheduling, testing, verification, real-time analysis, and software engineering concepts. Additional topics include operating system architecture, process management, and networking.
J.A. Shah
16.355[J] Concepts in the Engineering of Software
()
(Same subject as IDS.341[J])
Prereq: Permission of instructor
Units: 3-0-9
Reading and discussion on issues in the engineering of software systems and software development project design. Includes the present state of software engineering, what has been tried in the past, what worked, what did not, and why. Topics may differ in each offering, but are chosen from the software process and life cycle; requirements and specifications; design principles; testing, formal analysis, and reviews; quality management and assessment; product and process metrics; COTS and reuse; evolution and maintenance; team organization and people management; and software engineering aspects of programming languages. Enrollment may be limited.
N. G. Leveson
16.36 Communication Systems and Networks
()
(Subject meets with 16.363)
Prereq: (6.3000 or 16.002) and (6.3700 or 16.09)
Units: 3-0-9
Introduces the fundamentals of digital communications and networking. Topics include elements of information theory, sampling and quantization, coding, modulation, signal detection and system performance in the presence of noise. Study of data networking includes multiple access, reliable packet transmission, routing and protocols of the internet. Concepts discussed in the context of aerospace communication systems: aircraft communications, satellite communications, and deep space communications. Students taking graduate version complete additional assignments.
E. H. Modiano
16.363 Communication Systems and Networks
()
(Subject meets with 16.36)
Prereq: (6.3000 or 16.004) and (6.3700 or 16.09)
Units: 3-0-9
Introduces the fundamentals of digital communications and networking, focusing on the study of networks, including protocols, performance analysis, and queuing theory. Topics include elements of information theory, sampling and quantization, coding, modulation, signal detection and system performance in the presence of noise. Study of data networking includes multiple access, reliable packet transmission, routing and protocols of the internet. Concepts discussed in the context of aerospace communication systems: aircraft communications, satellite communications, and deep space communications. Students taking graduate version complete additional assignments.
E. H. Modiano
16.37[J] Data-Communication Networks
()
(Same subject as 6.7450[J])
Prereq: 6.3700 or 18.204
Units: 3-0-9
TBA.
Provides an introduction to data networks with an analytic perspective, using wireless networks, satellite networks, optical networks, the internet and data centers as primary applications. Presents basic tools for modeling and performance analysis. Draws upon concepts from stochastic processes, queuing theory, and optimization.
E. Modiano
No textbook information available
16.391 Statistics for Engineers and Scientists
()
Prereq: Calculus II (GIR), 18.06, 6.431, or permission of instructor
Units: 3-0-9
Lecture: MW1-2.30 (56-154)
Rigorous introduction to fundamentals of statistics motivated by engineering applications. Topics include exponential families, order statistics, sufficient statistics, estimation theory, hypothesis testing, measures of performance, notions of optimality, analysis of variance (ANOVA), simple linear regression, and selected topics.
M. Win
No textbook information available
16.393 Statistical Communication and Localization Theory
()
Prereq: None
Units: 3-0-9
Rigorous introduction to statistical communication and localization theory, covering essential topics such as modulation and demodulation of signals, derivation of optimal receivers, characterization of wireless channels, and devising of ranging and localization techniques. Applies decision theory, estimation theory, and modulation theory to the design and analysis of modern communication and localization systems exploring synchronization, diversity, and cooperation. Selected topics will be discussed according to time schedule and class interest.
M. Z. Win
16.395 Principles of Wide Bandwidth Communication
()
Not offered regularly; consult department
Prereq: 6.3010, 16.36, or permission of instructor
Units: 3-0-9
Introduction to the principles of wide bandwidth wireless communication, with a focus on ultra-wide bandwidth (UWB) systems. Topics include the basics of spread-spectrum systems, impulse radio, Rake reception, transmitted reference signaling, spectral analysis, coexistence issues, signal acquisition, channel measurement and modeling, regulatory issues, and ranging, localization and GPS. Consists of lectures and technical presentations by students.
M. Z. Win
Humans and Automation
16.400 Human Systems Engineering
()
(Subject meets with 16.453[J], HST.518[J])
Prereq: 6.3700, 16.09, or permission of instructor
Units: 3-0-9
Lecture: TR9.30-11 (3-370)
Provides a fundamental understanding of human factors that must be taken into account in the design and engineering of complex aviation, space, and medical systems. Focuses primarily on derivation of human engineering design criteria from sensory, motor, and cognitive sources. Includes principles of displays, controls and ergonomics, manual control, the nature of human error, basic experimental design, and human-computer interaction in supervisory control settings. Students taking graduate version complete a research project with a final written report and oral presentation.
A.M. Liu
No textbook information available
16.401 Topics in Communication and Software
(, , )
Not offered regularly; consult department
Prereq: Permission of department
Units arranged
Provides credit for undergraduate-level work in communications and/or software outside of regularly scheduled subjects. Intended for transfer credit and study abroad. Credit may be used to satisfy specific degree requirements in the Course 16 program. Requires prior approval. Consult M. A. Stuppard.
Fall: Y. Marzouk
IAP: Y. Marzouk
Spring: Y. Marzouk
16.405[J] Robotics: Science and Systems
() 
(Same subject as 2.124[J], 6.4200[J])
Prereq: ((1.00 or 6.100A) and (2.003, 6.1010, 6.1210, or 16.06)) or permission of instructor
Units: 2-6-4
Presents concepts, principles, and algorithmic foundations for robots and autonomous vehicles operating in the physical world. Topics include sensing, kinematics and dynamics, state estimation, computer vision, perception, learning, control, motion planning, and embedded system development. Students design and implement advanced algorithms on complex robotic platforms capable of agile autonomous navigation and real-time interaction with the physical word. Students engage in extensive written and oral communication exercises. Enrollment limited.
Staff
16.410[J] Principles of Autonomy and Decision Making
()
(Same subject as 6.4130[J])
(Subject meets with 6.4132[J], 16.413[J])
Prereq: 6.100B or 6.9080
Units: 4-0-8
Lecture: MW9.30-11 (4-163) Recitation: F10 (33-319) or F3 (33-319) +final
Surveys decision making methods used to create highly autonomous systems and decision aids. Applies models, principles and algorithms taken from artificial intelligence and operations research. Focuses on planning as state-space search, including uninformed, informed and stochastic search, activity and motion planning, probabilistic and adversarial planning, Markov models and decision processes, and Bayesian filtering. Also emphasizes planning with real-world constraints using constraint programming. Includes methods for satisfiability and optimization of logical, temporal and finite domain constraints, graphical models, and linear and integer programs, as well as methods for search, inference, and conflict-learning. Students taking graduate version complete additional assignments.
B.C. Williams
Textbooks (Fall 2024)
16.412[J] Cognitive Robotics
()
(Same subject as 6.8110[J])
Prereq: (6.4100 or 16.413) and (6.1200, 6.3700, or 16.09)
Units: 3-0-9
Highlights algorithms and paradigms for creating human-robot systems that act intelligently and robustly, by reasoning from models of themselves, their counterparts and their world. Examples include space and undersea explorers, cooperative vehicles, manufacturing robot teams and everyday embedded devices. Themes include architectures for goal-directed systems; decision-theoretic programming and robust execution; state-space programming, activity and path planning; risk-bounded programming and risk-bounded planners; self-monitoring and self-diagnosing systems, and human-robot collaboration. Student teams explore recent advances in cognitive robots through delivery of advanced lectures and final projects, in support of a class-wide grand challenge. Enrollment may be limited.
B. C. Williams
16.413[J] Principles of Autonomy and Decision Making
()
(Same subject as 6.4132[J])
(Subject meets with 6.4130[J], 16.410[J])
Prereq: 6.100B, 6.9080, or permission of instructor
Units: 3-0-9
Lecture: MW9.30-11 (4-163) +final
Surveys decision making methods used to create highly autonomous systems and decision aids. Applies models, principles and algorithms taken from artificial intelligence and operations research. Focuses on planning as state-space search, including uninformed, informed and stochastic search, activity and motion planning, probabilistic and adversarial planning, Markov models and decision processes, and Bayesian filtering. Also emphasizes planning with real-world constraints using constraint programming. Includes methods for satisfiability and optimization of logical, temporal and finite domain constraints, graphical models, and linear and integer programs, as well as methods for search, inference, and conflict-learning. Students taking graduate version complete additional assignments.
B.C. Williams
Textbooks (Fall 2024)
16.420 Planning Under Uncertainty
()
(Subject meets with 6.4110)
Prereq: 16.413
Units: 3-0-9
Lecture: MW9.30-11 (4-370) +final
Concepts, principles, and methods for planning with imperfect knowledge. Topics include state estimation, planning in information space, partially observable Markov decision processes, reinforcement learning and planning with uncertain models. Students will develop an understanding of how different planning algorithms and solutions techniques are useful in different problem domains. Previous coursework in artificial intelligence and state estimation strongly recommended.
N. Roy, L. P. Kaelbling, T. Lozano-Perez
16.422 Human Supervisory Control of Automated Systems
()
Prereq: Permission of instructor
Units: 3-1-8
Principles of supervisory control and telerobotics. Different levels of automation are discussed, as well as the allocation of roles and authority between humans and machines. Human-vehicle interface design in highly automated systems. Decision aiding. Trade-offs between human control and human monitoring. Automated alerting systems and human intervention in automatic operation. Enhanced human interface technologies such as virtual presence. Performance, optimization, and social implications of the human-automation system. Examples from aerospace, ground, and undersea vehicles, robotics, and industrial systems.
J.A. Shah, B.D. Armstrong
16.423[J] Aerospace Biomedical and Life Support Engineering
()
(Same subject as HST.515[J], IDS.337[J])
Prereq: 16.06, 16.400, or permission of instructor
Units: 3-0-9
Fundamentals of human performance, physiology, and life support impacting engineering design and aerospace systems. Topics include effects of gravity on the muscle, skeletal, cardiovascular, and neurovestibular systems; human/pilot modeling and human/machine design; flight experiment design; and life support engineering for extravehicular activity (EVA). Case studies of current research are presented. Assignments include a design project, quantitative homework sets, and quizzes emphasizing engineering and systems aspects.
L. Petersen
16.445[J] Entrepreneurship in Aerospace and Mobility Systems
()
(Same subject as STS.468[J])
Prereq: Permission of instructor
Units: 3-0-9
Examines concepts and procedures for new venture creation in aerospace and mobility systems, and other arenas where safety, regulation, and infrastructure are significant components. Includes space systems, aviation, autonomous vehicles, urban aerial mobility, transit, and similar arenas. Includes preparation for entrepreneurship, founders' dilemmas, venture finance, financial modeling and unit economics, fundraising and pitching, recruiting, problem definition, organizational creation, value proposition, go-to-market, and product development. Includes team-based final projects on problem definition, technical innovation, and pitch preparation.
D. A. Mindell
16.453[J] Human Systems Engineering
()
(Same subject as HST.518[J])
(Subject meets with 16.400)
Prereq: 6.3700, 16.09, or permission of instructor
Units: 3-0-9
Lecture: TR9.30-11 (3-370)
Provides a fundamental understanding of human factors that must be taken into account in the design and engineering of complex aviation, space, and medical systems. Focuses primarily on derivation of human engineering design criteria from sensory, motor, and cognitive sources. Includes principles of displays, controls and ergonomics, manual control, the nature of human error, basic experimental design, and human-computer interaction in supervisory control settings. Students taking graduate version complete a research project with a final written report and oral presentation.
A.M. Liu
No textbook information available
16.456[J] Biomedical Signal and Image Processing
()
(Same subject as 6.8800[J], HST.582[J])
(Subject meets with 6.8801[J], HST.482[J])
Prereq: (6.3700 and (2.004, 6.3000, 16.002, or 18.085)) or permission of instructor
Units: 3-1-8
Fundamentals of digital signal processing with emphasis on problems in biomedical research and clinical medicine. Basic principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. Lab projects, performed in MATLAB, provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs. Students taking graduate version complete additional assignments.
Staff
16.459 Bioengineering Journal Article Seminar
(, )
Prereq: None
Units: 1-0-1
Lecture: R1 (33-422)
Each term, the class selects a new set of professional journal articles on bioengineering topics of current research interest. Some papers are chosen because of particular content, others are selected because they illustrate important points of methodology. Each week, one student leads the discussion, evaluating the strengths, weaknesses, and importance of each paper. Subject may be repeated for credit a maximum of four terms. Letter grade given in the last term applies to all accumulated units of 16.459.
Fall: C. Oman
Spring: A. M. Liu, M. Lin
No textbook information available
16.470 Statistical Methods in Experimental Design
()
Prereq: 6.3700, 16.09, or permission of instructor
Units: 3-0-9
Statistically based experimental design inclusive of forming hypotheses, planning and conducting experiments, analyzing data, and interpreting and communicating results. Topics include descriptive statistics, statistical inference, hypothesis testing, parametric and nonparametric statistical analyses, factorial ANOVA, randomized block designs, MANOVA, linear regression, repeated measures models, and application of statistical software packages.
Staff
16.475 Human-Computer Interface Design Colloquium
()
Not offered regularly; consult department
Prereq: None
Units: 2-0-2
Provides guidance on design and evaluation of human-computer interfaces for students with active research projects. Roundtable discussion on developing user requirements, human-centered design principles, and testing and evaluating methodologies. Students present their work and evaluate each other's projects. Readings complement specific focus areas. Team participation encouraged. Open to advanced undergraduates.
Staff
16.485 Visual Navigation for Autonomous Vehicles
()
Prereq: 16.32 or permission of instructor
Units: 3-2-7
Lecture: MWF1 (35-225) Lab: W3-5 (33-116)
Covers the mathematical foundations and state-of-the-art implementations of algorithms for vision-based navigation of autonomous vehicles (e.g., mobile robots, self-driving cars, drones). Topics include geometric control, 3D vision, visual-inertial navigation, place recognition, and simultaneous localization and mapping. Provides students with a rigorous but pragmatic overview of differential geometry and optimization on manifolds and knowledge of the fundamentals of 2-view and multi-view geometric vision for real-time motion estimation, calibration, localization, and mapping. The theoretical foundations are complemented with hands-on labs based on state-of-the-art mini race car and drone platforms. Culminates in a critical review of recent advances in the field and a team project aimed at advancing the state-of-the-art.
L. Carlone
No textbook information available
Propulsion and Energy Conversion
16.50 Aerospace Propulsion
()
Prereq: 16.003 and (2.005 or 16.004)
Units: 3-0-9
Presents aerospace propulsive devices as systems, with functional requirements and engineering and environmental limitations. Requirements and limitations that constrain design choices. Both air-breathing and rocket engines covered, at a level which enables rational integration of the propulsive system into an overall vehicle design. Mission analysis, fundamental performance relations, and exemplary design solutions presented.
C. Guerra Garcia, P. Prashanth, J. Sabnis
16.501 Topics in Propulsion
(, )
Not offered regularly; consult department
Prereq: Permission of department
Units arranged
Provides credit for work on undergraduate-level material in propulsion outside of regularly scheduled subjects. Intended for transfer credit and study abroad. Credit may be used to satisfy specific degree requirements in the Course 16 and Course 16-ENG programs. Requires prior approval. Consult department.
Staff
16.511 Aircraft Engines and Gas Turbines
()
Prereq: 16.50 or permission of instructor
Units: 3-0-9
Lecture: TR1-2.30 (33-319) +final
Performance and characteristics of aircraft jet engines and industrial gas turbines, as determined by thermodynamic and fluid mechanic behavior of engine components: inlets, compressors, combustors, turbines, and nozzles. Discusses various engine types, including advanced turbofan configurations, limitations imposed by material properties and stresses. Emphasizes future design trends including reduction of noise, pollutant formation, fuel consumption, and weight.
Z.S. Spakovzky
Textbooks (Fall 2024)
16.512 Rocket Propulsion
()
Prereq: 16.50 or permission of instructor
Units: 3-0-9
Chemical rocket propulsion systems for launch, orbital, and interplanetary flight. Modeling of solid, liquid-bipropellant, and hybrid rocket engines. Thermochemistry, prediction of specific impulse. Nozzle flows including real gas and kinetic effects. Structural constraints. Propellant feed systems, turbopumps. Combustion processes in solid, liquid, and hybrid rockets. Cooling; heat sink, ablative, and regenerative.
P.C. Lozano, J. Sabnis
16.522 Space Propulsion
()
Prereq: 8.02 or permission of instructor
Units: 3-3-6
Reviews rocket propulsion fundamentals. Discusses advanced concepts in space propulsion with emphasis on high-specific impulse electric engines. Topics include advanced mission analysis; the physics and engineering of electrothermal, electrostatic, and electromagnetic schemes for accelerating propellant; and orbital mechanics for the analysis of continuous thrust trajectories. Laboratory term project emphasizes the design, construction, and testing of an electric propulsion thruster.
P.C. Lozano
16.530 Advanced Propulsion Concepts
()
Not offered regularly; consult department
Prereq: 16.50, 16.511, 16.512, or 16.522
Units: 3-0-9
Considers the challenge of achieving net-zero climate impacts, as well as the opportunities presented by the resurgence of investment in new or renewed ideas. Explores advanced propulsion concepts that are not in use or well-developed, but that have established operation principles and could either contribute to environmental performance or are applicable to new aerospace services. Topics vary but may include: electric and turbo-electric aircraft propulsion; batteries, cryogenic fuels, and biofuels; combustion and emissions control concepts; propulsion for UAVs and urban air mobility; propulsion for supersonic and hypersonic vehicles; reusable space access vehicle propulsion; and propulsion in very low earth orbit. Includes a project to evaluate an advanced propulsion concept.
S. Barrett, J. J. Sabnis, Z. Spakovszky
16.540 Internal Flows in Turbomachines
()
Prereq: 2.25 or permission of instructor
Units: 3-0-9
Internal fluid motions in turbomachines, propulsion systems, ducts and channels, and other fluid machinery. Useful basic ideas, fundamentals of rotational flows, loss sources and loss accounting in fluid devices, unsteady internal flow and flow instability, flow in rotating passages, swirling flow, generation of streamwise vorticity and three-dimensional flow, non-uniform flow in fluid components.
Staff
16.55[J] Ionized Gases
()
(Same subject as 22.64[J])
Prereq: 8.02 or permission of instructor
Units: 3-0-9
Lecture: TR9.30-11 (33-319)
Properties and behavior of low-temperature plasmas for energy conversion, plasma propulsion, and gas lasers. Equilibrium of ionized gases: energy states, statistical mechanics, and relationship to thermodynamics. Kinetic theory: motion of charged particles, distribution function, collisions, characteristic lengths and times, cross sections, and transport properties. Gas surface interactions: thermionic emission, sheaths, and probe theory. Radiation in plasmas and diagnostics.
C. Guerra Garcia
No textbook information available
Other Undergraduate Subjects
16.00 Introduction to Aerospace and Design
()
Not offered regularly; consult department
Prereq: None
Units: 2-2-2
Highlights fundamental concepts and practices of aerospace engineering through lectures on aeronautics, astronautics, and the principles of project design and execution. Provides training in the use of Course 16 workshop tools and 3-D printers, and in computational tools, such as CAD. Students engage in teambuilding during an immersive, semester-long project in which teams design, build, and fly radio-controlled lighter-than-air (LTA) vehicles. Emphasizes connections between theory and practice and introduces students to fundamental systems engineering practices, such as oral and written design reviews, performance estimation, and post-flight performance analysis.
J. A. Hoffman, R. J. Hansman
16.UR Undergraduate Research
(, , ,  )
Prereq: None
Units arranged [P/D/F]
TBA.
Undergraduate research opportunities in aeronautics and astronautics.
Consult M. A. Stuppard
No required or recommended textbooks (Summer 2024); Textbooks arranged individually (Fall 2024)
16.C25[J] Real World Computation with Julia
()
(Same subject as 1.C25[J], 6.C25[J], 12.C25[J], 18.C25[J], 22.C25[J])
Prereq: 6.100A, 18.03, and 18.06
Units: 3-0-9
Lecture: MW1-2.30 (4-149)
Focuses on algorithms and techniques for writing and using modern technical software in a job, lab, or research group environment that may consist of interdisciplinary teams, where performance may be critical, and where the software needs to be flexible and adaptable. Topics include automatic differentiation, matrix calculus, scientific machine learning, parallel and GPU computing, and performance optimization with introductory applications to climate science, economics, agent-based modeling, and other areas. Labs and projects focus on performant, readable, composable algorithms, and software. Programming will be in Julia. Expects students to have some familiarity with Python, Matlab, or R. No Julia experience necessary.
A. Edelman, R. Ferrari, B. Forget, C. Leiseron,Y. Marzouk, J. Williams
No textbook information available
16.EPE UPOP Engineering Practice Experience
(, )
Engineering School-Wide Elective Subject.
(Offered under: 1.EPE, 2.EPE, 3.EPE, 6.EPE, 8.EPE, 10.EPE, 15.EPE, 16.EPE, 20.EPE, 22.EPE)
Prereq: None
Units: 0-0-1 [P/D/F]
Lab: M11 (3-333) or M1 (3-442) or W11 (3-333) or W1 (3-133) or F11 (3-333) or F1 (37-212)
Provides students with skills to prepare for and excel in the world of industry. Emphasizes practical application of career theory and professional development concepts. Introduces students to relevant and timely resources for career development, provides students with tools to embark on a successful internship search, and offers networking opportunities with employers and MIT alumni. Students work in groups, led by industry mentors, to improve their resumes and cover letters, interviewing skills, networking abilities, project management, and ability to give and receive feedback. Objective is for students to be able to adapt and contribute effectively to their future employment organizations. A total of two units of credit is awarded for completion of the fall and subsequent spring term offerings. Application required; consult UPOP website for more information.
Fall: D. Fordell, C. Greaney
Spring: D. Fordell, C. Greaney
No textbook information available
16.EPW UPOP Engineering Practice Workshop
(, , )
Engineering School-Wide Elective Subject.
(Offered under: 1.EPW, 2.EPW, 3.EPW, 6.EPW, 10.EPW, 16.EPW, 20.EPW, 22.EPW)
Prereq: 2.EPE
Units: 1-0-0 [P/D/F]
TBA.
Provides sophomores across all majors with opportunities to develop and practice communication, teamwork, and problem-solving skills to become successful professionals in the workplace, particularly in preparation for their summer industry internship. This immersive, multi-day Team Training Workshop (TTW) is comprised of experiential learning modules focused on expanding skills in areas that employers report being most valuable in the workplace. Modules are led by MIT faculty with the help of MIT alumni and other senior industry professionals. Skills applied through creative simulations, team problem-solving challenges, oral presentations, and networking sessions with prospective employers. Enrollment limited to those in the UPOP program.
Fall: C. Greaney
IAP: C. Greaney
Spring: C. Greaney
No textbook information available
16.S684 Special Subject in Aeronautics and Astronautics
(, ) ; partial term
Prereq: None
Units arranged [P/D/F]
Opportunity for study or lab work related to aeronautics and astronautics not covered in regularly scheduled subjects. Subject to approval of faculty in charge. Prior approval required.
Staff
16.S685 Special Subject in Aeronautics and Astronautics
() ; partial term
Prereq: Permission of instructor
Units arranged [P/D/F]
Basic undergraduate topics not offered in regularly scheduled subjects. Subject to approval of faculty in charge. Prior approval required.
M. Paluszek
16.S686 Special Subject in Aeronautics and Astronautics
(, )
Not offered regularly; consult department
Prereq: Permission of instructor
Units arranged
Opportunity for study or lab work related to aeronautics and astronautics not covered in regularly scheduled subjects. Subject to approval of faculty in charge. Prior approval required.
Fall: A. Edelman, R. Ferrari, Y. M. Marzouk, J. Williams
Spring: Y. M. Marzouk
16.S688 Special Subject in Aeronautics and Astronautics
(, )
Not offered regularly; consult department
Prereq: None
Units arranged
Opportunity for study or lab work related to aeronautics and astronautics but not covered in regularly scheduled subjects. Prior approval required.
Consult M. A. Stuppard
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