This course gives a broad introduction to numerical algorithms used in scientific computing. It covers classical methods to solve Ordinary and Partial Differential Equations such as spectral, finite difference and finite volume methods. A brief introduction to finite element methods is given. Explicit and implicit time integration using various high-order methods are discussed. We review basic methods to solve linear and non-linear systems of equations. Issues related to the implementation of efficient algorithms on modern high-performance computing systems are discussed. Hyperbolic systems of conservations laws are covered in detail.

Power from the nucleus offers a low-carbon source of electricity. Fission power is well developed, but carries risks associated with safety, waste, and nuclear weapons proliferation. Fusion energy research, which presents less such risk, is making important scientific progress and progress towards commercialization. We will study the scientific underpinnings of both of these energy sources, strengthening your physical insight and exercising your mathematical and computational skills. We will also ask ourselves the thorny ethical questions scientists should confront as they contribute to the development of new technologies.

An introduction to numerical and Monte Carlo methods useful for engineering and scientific applications. Topics covered include solution of non-linear equations, interpolation and extrapolation, integration of functions, solution of ordinary and partial differential equations, random number generation, and stochastic sampling (Monte Carlo) methods. The emphasis is on the practical use of these methods. Assignments are expected to be completed using computing tools such as MATLAB, Excel, or Python.

Develops notions of internal forces and displacements, and instructs students how to design and analyze structures. Presents the fundamental principles of structural analysis, determination of internal forces, and deflections under the static load conditions, and introduces the bending theory of plane beams and the basic energy theorems. The theory of the first order will be developed for continuous girders, frames, arches, suspension bridges, and trusses, including both statically determinate and indeterminate structures. Basic principles for construction of influence lines and determination of extreme influences will be presented.

This course presents the Matrix Structural Analysis (MSA) and Finite Element Methods (FEM) in a cohesive framework. The first half of the semester is devoted to MSA topics: derivation of truss, beam, and frame elements; assembly and partitioning of the global stiffness matrix; and equivalent nodal loads. The second half covers the following FEM topics: strong and weak forms of boundary value problems including steady-state heat conduction, and linear elasticity, Galerkin approximations, constant strain triangles, and isoparametric quads. Other topics such as dynamic analysis will also be discussed. MATLAB is used for computer assignments.

Robotic systems are quickly becoming more capable and adaptable, entering new domains from transportation to healthcare. To reliably carry out complex tasks in changing environments and around people, these systems rely on increasingly sophisticated artificial intelligence. This course covers the core concepts and techniques underpinning modern robot autonomy, including planning under uncertainty, imitation and reinforcement learning, multiagent interaction, and safety. The lab component introduces the Robot Operating System (ROS) framework and applies the learned theory to hands-on autonomous driving assignments on 1/16-scale robot trucks.

This class will teach you about optical and photonic sensing technologies and their applications to environmental monitoring. The course will contain elements of atmospheric science and Earth observation, fundamentals of optics, photonics and laser physics, as well as a survey of modern optical and spectroscopic sensing applications. In this course students will be asked to prepare two oral presentations and there will be three laboratory assignments focused on fundamentals of optical sensing

This course examines the field of carbon capture, conversion, and storage. The course is interdisciplinary and surveys fundamental aspects of combustion, kinetics, material science, thermodynamics and electrochemistry. The class will survey the working principles of existing and emerging technologies that aim to make a critical impact on decarbonizing energy systems. Topics related to carbon capture and negative emission technologies will be discussed.

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.

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.

The class will discuss the physics of ocean surface waves and its impacts on human life. We will cover the principle of ocean waves propagation across the oceans, with analogies to optics and acoustics. Using historical observations and modern modeling tools, we will discuss wave forecasting with practical examples including planning of D-Day during the second world war, or local surf forecasting. The influence of ocean waves on human life will be discussed, from their role on beach morphology, mitigation of storm surge, or tsunamis. Finally, we will discuss the ubiquitous representation of waves in arts/movies.

Formulation and solution of equations governing the dynamic behavior of engineering systems. Fundamental principles of Newtonian mechanics. Two and three dimensional kinematics and kinetics of particles and rigid bodies. Motion relative to moving reference frames. Impulse-momentum and work-energy relations. Free and forced vibrations of mechanical systems. Introduction to dynamic analysis of mechanical devices and systems.

Introduction to the physical and analytical description of phenomena associated with the flow of fluids. Topics include the principles of conservation of mass, momentum and energy; lift and drag; open channel flow; dynamic similitude; laminar and turbulent flow and an introduction to compressible subsonic and supersonic internal and external flows.

Students will conduct a series of prepared experiments throughout the semester that will culminate in an independent project of the students' design involving fluid mechanics, thermodynamics and data acquisition tools. Concepts learned will be applied in subsequent labs involving flows in ducts and wind/water tunnels with flow visualization and lift and drag measurements.

Introductory lecture and laboratory course to focus on engineering methods and skills. The course explores contemporary methods for engineering analysis and design. The course introduces foundations of Computer Aided Design (CAD) and Engineering Analysis (CAE). By participating in weekly laboratories, students will gain practical experience and will demonstrate their mastery by completing a final independent project. The final project is the re-creation and technical analysis of a historic scientific instrument or experiment. This elective course is PDF only.

This course introduces the fundamental physical mechanisms behind sustainable energy technologies and the basic concepts to evaluate and compare their efficiency, environmental impact, and costs. Among others, we will examine the potential of wind energy, photovoltaics, geothermal energy, biofuels, and nuclear energy. We will also examine the concepts of intermittency and dispatchability of energy sources and discuss the relevance of the electric grid, energy storage, energy efficiency, and green buildings. Taken together, this will help us assess energy scenarios and possible pathways to a net-zero carbon energy future.

A treatment of the theory and applications of ordinary differential equations with an introduction to partial differential equations. The objective is to provide the student with an ability to solve problems in this field.

This course covers a range of fundamental mathematical techniques and methods that can be employed to solve problems in contemporary engineering and the applied sciences. Topics include algebraic equations, numerical integration, analytical and numerical solution of ordinary and partial differential equations, harmonic functions and conformal maps, and time-series data. The course synthesizes descriptive observations, mathematical theories, numerical methods, and engineering consequences.

This course introduces the technical foundation and basic processes of Mechanical Design, which are appropriate for the design of both mechanical systems, and components. The emphasis is on designing for the complete product life-cycle. Topics in parametric design and design optimization using Finite Element Analysis (FEA), Computer Aided Design (CAD), and Manufacturing (CAM) are introduced in the classroom and online and then reinforced by team and individual assignments.

The course presents contemporary methods of mechanical and structural analysis used in Aerospace. Topics covered include: introduction to aerospace structures components and loads, equations of linear elasticity, virtual work, and energy formulations, and analytical and numerical methods for analyzing aerospace structures, including idealization and finite Element Analysis. If time allows, the course will cover advanced topics such as aeroelasticity and vibrations. The course will culminate in a final project where students will use analytical, numerical, and experimental methods to analyze and evaluate a representative aerospace structure.

This course discusses methods for the design of aircraft. Topics in aerodynamics, and structural design are emphasized in the context of a design project. Students will be required to complete a design project to fulfill the requirements of this class.

Independent work is a one term project. Student selects subject and advisor - defines problem to be studied and proposes work plan. A list of possible subjects of particular interest to faculty and staff members is provided. Written report due at end of semester to faculty, staff, fellow students and guests. 339 Fall Term project; 340 Spring Term project.

One semester independent work project similar to MAE 339-340. Principle difference is that the project must incorporate aspects and principles of design for a system, product, vehicle, device, apparatus, or other design element. Written report at end of semester to faculty, staff, fellow students and guests. 339D Fall Term project; 340D Spring Term project.

Life finds a way, to quote Jurassic Park, and understanding how life does things can help us not only better understand it, but also better build, heal, and design our own living systems. This course focuses on the intersection of mechanics, materials science, and biology and focuses on two themes. (1) We use special engineering principles from different disciplines to understand how mechanics and material properties enable cells to make everything from beating hearts to velociraptors. (2) We apply this knowledge to learn how to design new biomedical devices and biomaterials while considering regulatory and bioethics guidelines.

Introduction to microcomputers for measurement and control. This is a hardware course in the area of electro mechanical systems. Students build microcomputer controllers and apply them to the automation of various aspects of a model railroad. Students work in pairs on a term project. Projects involve mechanical design of mechanisms and structures, design of electronic circuits for sensing and control, and design of an 8-bit microcomputer that is integrated into a serial data network.

This course will cover fundamentals of heat transfer and applications to practical problems in energy conversion and conservation, electronics, and biological systems. Emphasis will be on developing a physical and analytical understanding of conductive, convective, and radiative heat transfer. Numerical methods will be introduced to simulate a variety of steady and unsteady heat transfer applications and will form the basis of the final project.

The study of principles, flight envelopes, and engine designs of rocket and ram/scramjet propulsion systems. Topics include jet propulsion theory, space mission maneuver, combustion control, and system components of chemical and non-chemical rockets (nuclear and electrical propulsion), gas turbine, ramjet, and scramjet engines. Characteristics, optimal flight envelopes, and technical challenges of combined propulsion systems will be analyzed.

Overview of energy utilization in and environmental impacts of propulsion systems for ground and air transportation. Roughly half of the course will be devoted to reciprocating engines for ground transportation, and the other half of the course will be devoted to gas turbine engines for air transportation. The course will focus on device efficiency/performance and emissions with future outlooks for improvements in these areas including alternative fuels and alternative device concepts. Relevant thermodynamics, chemistry, fluid mechanics, and combustion fundamentals will be reviewed or introduced and will permeate the course material.

This course provides an introduction to the application of deep learning to physical problems. Topics include convolutional neural networks, and graph neural networks.

Senior independent work is the culminating experience for the mechanical and aerospace engineering programs. Students select a subject and adviser, define the problem to be studied and propose a work plan. Projects include elements of engineering design, defined as devising a system, component, or process to meet desired needs. A list of possible subjects of particular interest to faculty and staff members is provided. Students must submit a written final report and present their results to faculty, staff, fellow students, and guests at the end of the semester.

Senior thesis is a year-long independent study for individual students. It is the culminating experience for the mechanical and aerospace programs. Work begins in fall, but enrollment is in spring when a double grade is recorded. Projects include engineering design, defined as devising a system, component, or process to meet desired needs. Students develop their own topic or select a faculty proposed topic. Students create a work plan and select an adviser. A written progress report is expected at the end of the fall term. Students submit a written final report and make an oral presentation at the end of the spring term.

Senior project is a year-long independent study intended for students choosing to work in teams of two or more. It is the culminating experience in the mechanical and aerospace programs. Work begins in fall, but enrollment is in spring when a double grade is recorded. Projects include engineering design, defined as devising a system, component, or process to meet desired needs. Groups develop their own topic or select a faculty proposed topic. Groups create a work plan and select an adviser. A written progress report is due at the end of the fall term. Groups submit a written final report and make an oral presentation at the end of spring.

Topics in complex analysis and functional analysis, with emphasis on applications in physics and engineering. Topics include power series, singularities, contour integration, Cauchy's theorems, and Fourier series; an introduction to measure theory and the Lebesgue integral; Hilbert spaces, linear operators, and adjoints; the spectral theorem, and its application to Sturm-Liouville problems.

Under the direction of a faculty member, the student carries out a one-semester research project chosen jointly by the student and the faculty member. Without prior approval of the Director Graduate Studies, directed research can only be taken during the first year of study. At the beginning of the semester, students must submit the topic of the project and the faculty advisor to the Graduate Office. The project culminates in a final presentation in the style of a conference talk at the end of the semester.

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.

Ultrafast lasers are widely used as probes for chemistry, material science, biology, flow dynamics, and environmental science, as well as for generating ultra-intense light, relativistic particle beams, and attosecond light bursts. This course explores the technology and applications of ultrafast lasers, which produce pulses shorter than 1 picosecond. Ultrashort pulse generation techniques - including mode-locked oscillators, chirped pulse amplification, and optical parametric amplification - and pulse measurement methods such as frequency-resolved optical gating and high-order autocorrelations are discussed.

Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; physical equilibria; quantum mechanical analysis of atomic and molecular structure including rotational and vibrational transitions; atomic-scale collision phenomena and excitation and ionization; emission, absorption, and propagation of radiation. Analyses of major greenhouse gases from point of view of molecular absorption and emission properties; discussion of effect of greenhouse gases concentration and disribution on climate equilibria.

Chemical thermodynamics and kinetics, oxidation of hydrogen, hydrocarbons and alternate fuels, pollutant chemistry and control, transport phenomena, laminar premixed and nonpremixed flames, turbulent flames, ignition, extinction, and flammability phenomena, flame stabilization and blowoff, detonation and blast waves, droplet, spray and coal particle combustion, principles of engine operation.

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.

An introduction to the mechanics of viscous flows. The kinematics and dynamics of viscous flows. Exact solutions to the Navier-Stokes equations. Lubrication theory. The behavior of vorticity. The boundary layer approximation. Laminar boundary layers with and without pressure gradients. Introduction to stability. Introduction to turbulence. Several case studies will be introduced to expose students to fluid mechanics themes in biology, polymer processing, complex fluids and reacting flows.

The course deals with the fundamentals of turbulent flows and it is addressed to second year graduate students. Physical and statistical descriptions of turbulence are treated and phenomenological theories of turbulent flows are critically reviewed. The course examines scales of motion; correlations and spectra; homogeneous, isotropic turbulent flows; free shear flows (jets, mixing layers and wakes); wall bounded flows (pipe and channel flows, boundary layers); modeling and simulations of turbulent flows (turbulent viscosity models, Reynolds stress modeling, LES, DNS, RANS-LES); and current directions in turbulence research.

This course examines chemical reaction kinetics and energy transfer processes in high-temperature gases. Course topics include molecular collision theory; Boltzmann equation; transition state theory (derived from both thermodynamics and statistical mechanics); unimolecular dissociation and recombination reactions and their pressure dependence (i.e., Lindemann theory, RRK(M) theory, Master Equation); reaction and explosion mechanisms relevant to propulsion systems; experimental methods and diagnostics used to study gas-phase chemical kinetics; an intro to kinetic modeling tools and solvers; photochemistry; and vibrational relaxation processes.

'Life finds a way.' to quote Jurassic Park, and understanding how Life does things can help us not only better understand it, but also better build, heal, and design our own living systems. This course focuses on the intersection of mechanics, materials science, and biology and focuses on two themes. (1) We use special engineering principles from different disciplines to understand how mechanics and material properties enable cells to make everything from beating hearts to velociraptors. (2) We apply this knowledge to learn how to design new biomedical devices and biomaterials while considering regulatory and bioethics guidelines.

This course covers the theory and numerical algorithms of nonlinear filtering and smoothing, starting with the discrete-time linear Gaussian case and advancing through the general continuous-time nonlinear non-Gaussian case. Variants of Kalman and ensemble methods will be covered with derivations and sketches of important proofs. A review of the necessary elements from probability and stochastic processes is included. Following the theory, numerical algorithms are regularly demonstrated on a suite of problems that include aerospace and geoscience applications.

This course provides an introduction to the geometric deep learning. Topics include convolutional neural networks, and graph neural networks.

A lecture 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. Participation at presentations will be attended by distinguished outside speakers. There is one lecture and one precept discussion per week.