This class examines the relationship between a number of mind-altering substances and cultural processes. We look at the relationship between drugs and such phenomena as poverty, religion, technology, inter-generational conflict, colonialism, and global capitalism. We read about the physiological and psychological effects of these substances – ranging from alcohol to LSD, cocaine and ecstasy – and ask why different societies prohibit and sanction different drugs. We examine the use of mind-altering substances in a number of “traditional” societies, and follow the development of a global trade in such substances as sugar, coffee, tea, nicotine, cocaine, and marijuana concurrent with the evolution of global capitalism. We look at the use of LSD as a mind-control substance by the CIA and as a mind-altering substance in the 1960’s counter-culture, and we look at the rise of Prozac® and Viagra® as popular, if controversial, pharmaceutical products in recent years. Finally, we evaluate America’s current drug laws.

This class is a multidisciplinary introduction to pharmacology, neurotransmitters, drug mechanisms, and brain diseases from addiction to schizophrenia.
From Abilify® to Zyrtec®, the world is full of fascinating drugs. If you are poisoned by sarin nerve gas, you may be able to save your life by huffing some BZ nerve gas. This class will explain that chemical curiosity, along with a host of other interesting tidbits of pharmacology. The structure of the class interleaves basic concepts with specific examples and entertaining tangents, so it is not loaded with boring abstract theory. In the first class you will learn what a neurotransmitter is, and you will immediately apply that knowledge when we discuss the mechanism of caffeine. The class is highly multidisciplinary, including topics such as patent law, medical ethics, history, and the physics of crack pipes.

The first two weeks of this course are an overview of performing improvisation with introductory and advanced exercises in the techniques of improvisation. The final four weeks focus on applying these concepts in business situations to practice and mastering these improvisation tools in leadership learning.

The unifying theme of this course is best captured by the title of our main reference book: “Recursive Methods in Economic Dynamics”. We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. We then study the properties of the resulting dynamic systems. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We shall stress applications and examples of all these techniques throughout the course.

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.

The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. We will also discuss approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions.
We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.

This course covers the fundamentals of Newtonian mechanics, including kinematics, motion relative to accelerated reference frames, work and energy, impulse and momentum, 2D and 3D rigid body dynamics. The course pays special attention to applications in aerospace engineering including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. By the end of the semester, students should be able to construct idealized (particle and rigid body) dynamical models and predict model response to applied forces using Newtonian mechanics.

This course reviews momentum and energy principles, and then covers the following topics: Hamilton’s principle and Lagrange’s equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems.
This course was originally developed by Professor T. Akylas.

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange’s equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange’s equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLAB® to solve dynamics and vibrations problems.
This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.

Upon successful completion of this course, students will be able to:

Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains
Make quantitative estimates of model parameters from experimental measurements
Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods
Obtain the frequency-domain response of linear systems to sinusoidal inputs
Compensate the transient response of dynamic systems using feedback techniques
Design, implement and test an active control system to achieve a desired performance measure

Mastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.

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-energy (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.
This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.013J. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject merged with 2.003.

This seminar will focus on dynamical change in biogeochemical cycles accompanying early animal evolution – beginning with the time of the earliest known microscopic animal fossils (~600 million years ago) and culminating (~100 million years later) with the rapid diversification of marine animals known as the “Cambrian explosion.” Recent work indicates that this period of intense biological evolution was both a cause and an effect of changes in global biogeochemical cycles. We will seek to identify and quantify such coevolutionary changes. Lectures and discussions will attempt to unite the perspectives of quantitative theory, organic geochemistry, and evolutionary biology.

In this class we will critically review both classical works and recent literature on complexity in ecology. The emphasis will be on developing quantitative theories in the context of experimental and observational data. We will meet twice weekly for roundtable discussions.

In this class we will critically review both classical works and recent literature on ecological theory. Emphasis will be on providing a theoretical and phenomenological foundation for the study of computational models. We will meet twice weekly for roundtable discussions.

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.

1.464 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.

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.