Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-enery (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.

An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.

An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.

An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.

Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. Application to nonlinear circuits and control systems. Alternate years. Description from course website: This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

This course begins with a study of the role of dynamics in the general physics of the atmosphere, the consideration of the differences between modeling and approximation, and the observed large-scale phenomenology of the atmosphere. Only then are the basic equations derived in rigorous manner. The equations are then applied to important problems and methodologies in meteorology and climate, with discussions of the history of the topics where appropriate. Problems include the Hadley circulation and its role in the general circulation, atmospheric waves including gravity and Rossby waves and their interaction with the mean flow, with specific applications to the stratospheric quasi-biennial oscillation, tides, the super-rotation of Venus' atmosphere, the generation of atmospheric turbulence, and stationary waves among other problems. The quasi-geostrophic approximation is derived, and the resulting equations are used to examine the hydrodynamic stability of the circulation with applications ranging from convective adjustment to climate.

Examines the long term effects of information technology on business strategy in the real estate and construction industry. Considerations include: supply chain, allocation of risk, impact on contract obligations and security, trends toward consolidation, and the convergence of information transparency and personal effectiveness. Resources are drawn from the world of dot.com entrepreneurship and "old economy" responses. Taught by case study method and grading is based on class participation and papers.

This course examines European music from the early Middle Ages until the end of the Renaissance. It includes a chronological survey and intensive study of three topics: chant and its development, music in Italy 1340-1420, and music in Elizabethan England. Instruction focuses on methods and pitfalls in studying music of the distant past. Students' papers, problem sets, and presentations explore lives, genres, and works in depth. Works are studied in facsimile of original notation, and from original manuscripts at MIT, where possible.

If you are an entrepreneur, one of your priorities, in addition to building your company, is ensuring you have enough money at the right times. Early Stage Capital will consider a broad range of questions that entrepreneurs deal with on this front, including the following: What should your strategy and your priorities be in raising early stage capital? What are the market norms and standards in structuring VC deals? What are the critical negotiating strategies and tactics? How will your company be valued? How can you obtain the optimal valuation for your new venture? What are the critical elements in the relationship between venture capitalists and entrepreneurs? How is the "venture model" evolving? Is it broken? What is the impact of Super Angels and micro VCs? These are key questions that face all entrepreneurs in 2010, particularly first-time entrepreneurs. This course aims to prepare you for these decisions, as either a potential entrepreneur or venture capitalist. Using live interactions with leading figures in the venture finance community, most of the class sessions will analyze fundamental strategies of the venture-capital investment process and the critical importance of the relationship between entrepreneur and investor. As well, we will have a tactical focus on demystifying the legalities and jargon of the term sheet and the "A round" financing process. Significantly for 2010, we will also frequently consider the rapid and arguably fundamental change in VC today as the "lean startup" model threatens much of the traditional role and value of the venture investor. Disclaimer: The websites for this course and the materials they offer are provided for educational use only. They are not a substitute for the advice of an attorney and no attorney-client relationship is created by using them. All materials are provided "as-is", without any express or implied warranties.

The Early Universe provides an introduction to modern cosmology. The first part of the course deals with the classical cosmology, and later part with modern particle physics and its recent impact on cosmology.

Examines traditional forms of East Asian culture (including literature, art, performance, food, and religion) as well as contemporary forms of popular culture (film, pop music, karaoke, and manga). Covers China, Japan, Korea, Taiwan, and Hong Kong, with an emphasis on China. Attention given to women's culture. The influence and presence of Asian cultural expressions in the US are also considered. Use made of resources in the Boston area, including the MFA, the Children's Museum, and the Sackler collection at Harvard. Taught in English.

Ecologies of Construction examines the resource requirements for the making and maintenance of the contemporary built environment. This course introduces the field of industrial ecology as a primary source of concepts and methods in the mapping of material and energy expenditures dedicated to construction activities.

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 MATLABĺ¨ models for particular engineering applications. Some experience with computer programming is helpful but not essential.

We will cover fundamentals of ecology, considering Earth as an integrated dynamic system. Topics include coevolution of the biosphere, geosphere, atmosphere and oceans; photosynthesis and respiration; the hydrologic, carbon and nitrogen cycles. We will examine the flow of energy and materials through ecosystems; regulation of the distribution and abundance of organisms; structure and function of ecosystems, including evolution and natural selection; metabolic diversity; productivity; trophic dynamics; models of population growth, competition, mutualism and predation. This course is designated as Communication-Intensive; instruction and practice in oral and written communication provided. Biology is a recommended prerequisite.

Introduction to econometric models and techniques, emphasizing regression. Advanced topics include instrumental variables, panel data methods, measurement error, and limited dependent variable models. Includes problem sets. May not count toward HASS requirement.

15.010 is the Sloan School's core subject in microeconomics, with sections for non-Sloan students labeled 15.011. Our objective is to give you a working knowledge of the analytical tools that bear most directly on the economic decisions firms must regularly make. We will emphasize market structure and industrial performance, including the strategic interaction of firms. We will examine the behavior of individual markets--and the producers and consumers that sell and buy in those markets--in some detail, focusing on cost analysis, the determinants of market demand, pricing strategy, market power, and the implications of government regulatory policies. We will also examine the implications of economics on other business practices, such as incentive plans, auctions, and transfer pricing.

An introduction to current macroeconomic concerns with particular emphasis on medium-run economic fluctuations, economic crises, and the role of asset markets. Topics include the explanation of high chronic unemployment in some nations, the source of modern liquidity crises, the origin and end of speculative bubbles, and the factors that lead to substantial periods of economic stagnation.

Analyzes the theoretical and historical reasons why governments in latecomer countries have intervened with a wide array of policies to foster industrial development at various turning points: the initiation of industrial activity; the diversification of the industrial base; the restructuring of major industrial institutions; and the entry into high-technology sectors.

The economic growth of developing countries requires the acquisition of technological capabilities. In countries at the world technological frontier, such capabilities refer to cutting edge skills to innovate entirely new products. In developing countries, the requisite technological capabilities are broader, and include production engineering, project execution and incremental innovation to make borrowed technology work. Theories of technology acquisition are examined. The empirical evidence is taken from two sets of developing countries; the most advanced (Taiwan, Korea, India, China and Brazil) and the least advanced (Africa and Middle Eastern countries).

Choice of material has implications throughout the life-cycle of a product, influencing many aspects of economic and environmental performance. This course will provide a survey of methods for evaluating those implications. Lectures will cover topics in material choice concepts, fundamentals of engineering economics, manufacturing economics modeling methods, and life-cycle environmental evaluation.