Fall: Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Method of characteristics. Review of Lebesgue integration. Distributions. Fourier transform. Homogeneous distributions. Asymptotic methods. Spring: Sobolev spaces. Fredholm alternative. Variable coefficient elliptic, parabolic and hyperbolic linear partial differential equations. Variational methods. Viscosity solutions of fully nonlinear partial differential equations. The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.

" 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."

The "Digital Lab Techniques Manual" is a series of videos designed to help you prepare for your chemistry laboratory class. Each video provides a detailed demonstration of a common laboratory technique, as well as helpful tips and information. These videos are meant to supplement, and not replace, your lab manual and assigned reading. In fact, you will most benefit from watching the videos if you have already read the appropriate background information. To be a great experimentalist, you must understand both theory and technique! If you have questions about what you see, make sure to ask your TA or your instructor. WARNING NOTICE: The experiments described in these materials are potentially hazardous and require a high level of safety training, special facilities and equipment, and supervision by appropriate individuals. You bear the sole responsibility, liability, and risk for the implementation of such safety procedures and measures. MIT shall have no responsibility, liability, or risk for the content or implementation of any of the material presented.

This is an advanced subject in computer modeling and CAD CAM fabrication, with a focus on building large-scale prototypes and digital mock-ups within a classroom setting. Prototypes and mock-ups are developed with the aid of outside designers, consultants, and fabricators. Field trips and in-depth relationships with building fabricators demonstrate new methods for building design. The class analyzes complex shapes, shape relationships, and curved surfaces fabrication at a macro scale leading to new architectural languages, based on methods of construction.

This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace. Advances in integrated circuit technology have had a major impact on the technical areas to which digital signal processing techniques and hardware are being applied. A thorough understanding of digital signal processing fundamentals and techniques is essential for anyone whose work is concerned with signal processing applications. Digital Signal Processing begins with a discussion of the analysis and representation of discrete-time signal systems, including discrete-time convolution, difference equations, the z-transform, and the discrete-time Fourier transform. Emphasis is placed on the similarities and distinctions between discrete-time. The course proceeds to cover digital network and nonrecursive (finite impulse response) digital filters. Digital Signal Processing concludes with digital filter design and a discussion of the fast Fourier transform algorithm for computation of the discrete Fourier transform.

This class introduces studies in the algorithmic manipulation of type as word, symbol, and form. Problems covered will include semantic filtering, inherently unstable letterforms, and spoken letters. The history and traditions of typography, and their entry into the digital age, will be studied. Weekly problem sets using Java will explore new ways of looking at and manipulating type.

" This course introduces principles and technologies for converting heat into electricity via solid-state devices. The first part of the course discusses thermoelectric energy conversion and thermoelectric materials, thermionic energy conversion, and photovoltaics. The second part of the course discusses solar thermal technologies. Various solar heat collection systems will be reviewed, followed by an introduction to the principles of solar thermophotovoltaics and solar thermoelectrics. Spectral control techniques, which are critical for solar thermal systems, will be discussed."

In recent years, the redistribution of risk has created conditions for natural and technological disasters to become more widespread, more difficult to manage, and more discriminatory in their effects. Policy and planning decision-makers frequently focus on the impact that human settlement patterns, land use decisions, and risky technologies can have on vulnerable populations. However, to ensure safety and promote equity, they also must be familiar with the social and political dynamics that are present at each stage of the disaster management cycle. Therefore, this course will provide students with: 1) An understanding of the breadth of factors that give rise to disaster vulnerability; and 2) A foundation for assessing and managing the social and political processes associated with disaster policy and planning.

Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.

Representation, analysis, and design of discrete time signals and systems. Review of Z-transforms, discrete-time Fourier transforms, and difference equations. Discrete-time processing of continuous-time signals. Decimation, interpolation, and sampling rate conversion. Flowgraph structures for DT systems. Time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform, FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms, Cepstral analysis, various applications.

This course examines the growing importance of medicine in culture, economics and politics. It uses an historical approach to examine the changing patterns of disease, the causes of morbidity and mortality, the evolution of medical theory and practice, the development of hospitals and the medical profession, the rise of the biomedical research industry, and the ethics of health care in America.

This course intends to provide a rigorous introduction to the most important research results in the area of distributed algorithms, and prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed.

This is a course about how research knowledge and other types of knowledge come to be actionable and influential in the world‰ŰÓor not. The course explores ways to make research knowledge more accessible, credible, and useful in the realm of public policy and practice‰ŰÓa project in which the course faculty collectively bring decades of professional experience, in both academic and non-academic roles. The course addresses the politics of the policymaking process, the power of framing and agenda-setting, fads and paradigms in the design professions and society in general, how knowledge diffuses along knowledge and influence networks, and how varied types of knowledge (rational, craft, other) and deliberation shape decision-making and action. The course engages a number of guests to present case studies of research in use (and abuse) in varied fields, highlighting rich areas for potential research contribution, along with major conflicts in public values, political interests, ethical obligations, and more. The resulting dilemmas confront scholars, policymakers, practitioners, and others as they look to research‰ŰÓsometimes‰ŰÓfor useful guidance, influence, or both.

This Doctoral Seminar in Engineering Systems examines the core theory and contextual applications of the emerging field of Engineering Systems. There is a focus on doctoral-level analysis of scholarship on key concepts such as complexity, uncertainty, fragility, and robustness, as well as a critical look at the historical roots of the field and related areas such as systems engineering, systems dynamics, agent modeling, and systems simulations. Contextual applications of the course range from aerospace to technology implementation to regulatory systems to large-scale systems change. Special attention is given to the interdependence of social and technical dimensions of engineering systems.

Introduces the process of social research, emphasizing the conceptualization of research choices to ensure validity, relevance, and discovery. Includes research design and techniques of data collection as well as issues in the understanding, analysis, and interpretation of data. This course is designed to lay the foundations of good empirical research in the social sciences. It does not deal with specific techniques per se, but rather with the assumptions and the logic underlying social research. Students become acquainted with a variety of approaches to research design, and are helped to develop their own research projects and to evaluate the products of empirical research.

A large proportion of contemporary research on organizations, strategy, innovation and management relies on quantitative research methods. Subject examines the research process as the goal is to help students understand the relationship between theory, data and statistical methods. It is designed to provide an introduction to some of the most commonly used quantitative techniques, including logit/probit models, count models, event history models, and pooled cross-section techniques.

" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems."

Focuses on the role of the business improvement district (BID) as a popular and contemporary tool for urban revitalization. Explores BID origins, theoretical underpinnings, enabling legislation, and organizational issues. Emphasizes BID service provision including advocacy, marketing, sanitation, streetscape improvement, security and transportation, while examining BID performance using such indicators as crime rates, vacancy rates, and retail sales. Considers BID organizations throughout North America as well as comparable schemes in Australia, Holland, Japan, New Zealand, South Africa, and the United Kingdom. This course focuses on the origins, functions, and implications of downtown management organizations (DMOs), such as business improvement districts, in a variety of national contexts including the United States, Canada, South Africa, and the United Kingdom. It critically examines how a range of urban theories provide a rationale for the establishment and design of DMOs; the evolution and transnational transfer of DMO policy; and the spatial and political externalities associated with the local proliferation of DMOs. Particular emphasis is given to the role of DMOs in securing public space.