The class covers the analysis and modeling of stochastic processes. Topics include measure theoretic probability, martingales, filtration, and stopping theorems, elements of large deviations theory, Brownian motion and reflected Brownian motion, stochastic integration and Ito calculus and functional limit theorems. In addition, the class will go over some applications to finance theory, insurance, queueing and inventory models.

Explores how organizations can use system dynamics to achieve important goals. Student teams work with client managers to tackle the clients' most pressing issues. Students discuss experiences with their clients, and learn modeling and consulting skills they need to be effective. Focus on gaining practical insight from the system dynamics process. Projects are sponsored by diverse organizations from a range of industries and sizes from start-ups to the Fortune 500.

Focuses on modeling, quantification, and analysis of uncertainty by teaching random variables, simple random processes and their probability distributions, Markov processes, limit theorems, elements of statistical inference, and decision making under uncertainty. This course extends the discrete probability learned in the discrete math class. It focuses on actual applications, and places little emphasis on proofs. A problem set based on identifying tumors using MRI (Magnetic Resonance Imaging) is done using Matlab.

Physics, modeling, application, and technology of compound semiconductors (primarily III-Vs) in electronic, optoelectronic, and photonic devices and integrated circuits. Topics: properties, preparation, and processing of compound semiconductors; theory and practice of heterojunctions, quantum structures, and pseudomorphic strained layers; metal-semiconductor field effect transistors (MESFETs); heterojunction field effect transistors (HFETs) and bipolar transistors (HBTs); and optoelectronic devices.

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art numerical methods for the analysis of the nonlinear continuum response of materials. The range of material behavior considered in this course will include: linear and finite deformation elasticity, inelasticity and dynamics. Numerical formulation and algorithms will include: Variational formulation and variational constitutive updates, finite element discretization, error estimation, constrained problems, time integration algorithms and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout.

" This course will guide graduate students through the process of using rapid prototyping and CAD/CAM devices in a studio environment. The class has a theoretical focus on machine use within the process of design. Each student is expected to have completed one graduate level of design computing with a full understanding of solid modeling in CAD. Students are also expected to have completed at least one graduate design studio."

Easy Java Simulations (EJS) is a Java program that enables both programmers and novices to quickly and easily prototype, test, and distribute packages of Java simulations. Version 4.1 adds grouping and affine transformations to 2D drawing Elements.

This course provides a review of physical, chemical, ecological, and economic principles used to examine interactions between humans and the natural environment. Mass balance concepts are applied to ecology, chemical kinetics, hydrology, and transportation; energy balance concepts are applied to building design, ecology, and climate change; and economic and life cycle concepts are applied to resource evaluation and engineering design. Numerical models are used to integrate concepts and to assess environmental impacts of human activities. Problem sets involve development of MATLAB® models for particular engineering applications. Some experience with computer programming is helpful but not essential.

This intensive micro-subject provides the necessary skills in Excel spreadsheet modeling for ESD.71 Engineering Systems Analysis for Design. Its purpose is to bring entering students up to speed on some of the advanced techniques that we routinely use in analysis. It is motivated by our experience that many students only have an introductory knowledge of Excel, and thus waste a lot of time thrashing about unproductively. Many people think they know Excel, but overlook many efficient tools--such as Data Table and Goal Seek. It is also useful for a variety of other subjects.

" This intensive micro-subject provides the necessary skills in Microsoft® Excel spreadsheet modeling for ESD.71 Engineering Systems Analysis for Design. Its purpose is to bring entering students up to speed on some of the advanced techniques that we routinely use in analysis. It is motivated by our experience that many students only have an introductory knowledge of Excel, and thus waste a lot of time thrashing about unproductively. Many people think they know Excel, but overlook many efficient tools, such as Data Table and Goal Seek. It is also useful for a variety of other subjects."

Explores fluid properties, hydrostatics, fluid dynamics, similitude, energy and momentum principles, closed conduit flow, open channel flow, and flow measurement. Includes laboratory exercises in flow measurement, open channel flow, pipe friction, physical modeling, and data collection.

This course will focus on understanding aspects of modern technology displaying exponential growth curves and the impact on global quality of life through a weekly updated class project integrating knowledge and providing practical tools for political and business decision-making concerning new aspects of bioengineering, personalized medicine, genetically modified organisms, and stem cells. Interplays of economic, ethical, ecological, and biophysical modeling will be explored through multi-disciplinary teams of students, and individual brief reports.

During this course, we will be exploring basic questions of architecture through several short design exercises. Working with many different media, students will discover the interrelationship of architecture and its related disciplines, such as structures, sustainability, architectural history and the visual arts. Each problem will focus on one of these disciplines and one exploration and presentation technique.

Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute.

Examines both the structure of cities and ways they can be changed. Includes historical forces that have produced cities, models of urban analysis, contemporary theories of urban design, implementation strategies. Core lectures supplemented by discussion group focusing on student work. Speakers present cases involving current projects illustrating the scope and methods of urban design practice. This course introduces graduate students to ideas about the form of cities and how they are designed and developed. Part 1 explores the forces which act to shape and to change cities. Part 2 surveys models of urban design which have been invented in response to forces acting on cities.

Why are the Rocky Mountains so far inland? How do we preserve the changing Amazon rain forest? When will the Sun fling parts of itself towards Earth? The video magazine "Journeys through Earth and Space" follows three NASA research teams tackling these questions with supercomputers. "Journeys" begins with a short introduction that explains what supercomputers do and how scientists tap their power to recreate the universe mathematically. The three stories then show how the teams are using their software to better understand, and perhaps one day predict, nature. Researcher interviews mix with scientific imagery (observations, visualizations, animations), and stunning nature footage. An accompanying Video Resource Guide provides background material and classroom activities for Grades 9-12 (length: 18:00 minutes).

First of two-term sequence on modeling, analysis and control of dynamic systems. Mechanical translation, uniaxial rotation, electrical circuits and their coupling via levers, gears and electro-mechanical devices. Analytical and computational solution of linear differential equations and state-determined systems. Laplace transforms, transfer functions. Frequency response, Bode plots. Vibrations, modal analysis. Open- and closed-loop control, instability. Time-domain controller design, introduction to frequency-domain control design techniques. Case studies of engineering applications.

One aspect of discrete-time signal processing that has no counterpart in the analog world is developing models of systems to describe how signals arise.

In this assignment you will apply Monte Carlo computer simulations to study the effects of genetic drift and selection pressure on a single locus with two alleles: ?A? and ?a?. You will be running these simulations on a computer using a simple simulation