Studies the principles of deterministic optimal control. Variational calculus and Pontryagin's maximum principle. Applications of the theory, including optimal feedback control, time-optimal control, and others. Dynamic programming and numerical search algorithms introduced briefly.

Evolution of Physical Oceanography was created to mark the career of Henry M. Stommel, the leading physical oceanographer of the 20th Century and a longtime MIT faculty member. The authors of the different chapters were asked to describe the evolution of their subject over the history of physical oceanography, and to provide a survey of the state-of-the-art of their subject as of 1980. Many of the chapters in this textbook are still up-to-date descriptions of active scientific fields, and all of them are important historical records. This textbook is made available courtesy of The MIT Press.

The objective of this course is to introduce large-scale atomistic modeling techniques and highlight its importance for solving problems in modern engineering sciences. We demonstrate how atomistic modeling can be used to understand how materials fail under extreme loading, involving unfolding of proteins and propagation of cracks.

Molecular-level engineering and analysis of chemical processes. Use of chemical bonding, reactivity, and other key concepts in the design and tailoring of organic systems. Application and development of structure-property relationships. Descriptions of the chemical forces and structural factors that govern supramolecular and interfacial phenomena for molecular and polymeric systems. This course is an advanced subject in fluid and continuum mechanics. The course content includes kinematics, macroscopic balances for linear and angular momentum, stress tensors, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows.

" This course presents the mechanical, optical, and transport properties of polymers with respect to the underlying physics and physical chemistry of polymers in melt, solution, and solid state. Topics include conformation and molecular dimensions of polymer chains in solutions, melts, blends, and block copolymers; an examination of the structure of glassy, crystalline, and rubbery elastic states of polymers; thermodynamics of polymer solutions, blends, crystallization; liquid crystallinity, microphase separation, and self-assembled organic-inorganic nanocomposites. Case studies include relationships between structure and function in technologically important polymeric systems."

" Here we will learn about the mechanical behavior of structures and materials, from the continuum description of properties to the atomistic and molecular mechanisms that confer those properties to all materials. We will cover elastic and plastic deformation, creep, fracture and fatigue of materials including crystalline and amorphous metals, semiconductors, ceramics, and (bio)polymers, and will focus on the design and processing of materials from the atomic to the macroscale to achieve desired mechanical behavior. We will cover special topics in mechanical behavior for material systems of your choice, with reference to current research and publications."

Our world runs on energy - without it, things come to a screeching halt, as the recent hurricanes have shown. Ever stop to wonder what our energy future is? What are our options for energy, and what are the associated economic and climatic implications? In \Energy and the Environment\" we explore these questions, which together represent one of the great challenges of our time - providing energy for high quality of life and economic growth while avoiding dangerous climate change. This course takes an optimistic view of our prospects, and we'll see how shifting to renewable energy can lead to a viable future.

This is a lecture, discussion, and project based seminar about the physics of rock climbing. Participants are first exposed to the unsolved problems in the climbing community that could be answered by research and then asked to solve a small part of one of these problems. The seminar provides an introduction to engineering problems, an opportunity to practice communication skills, and a brief stab at doing some research. This seminar explicitly does not include climbing instruction nor is climbing/mountaineering experience a prerequisite.

This Freshman Advising Seminar surveys the many applications of magnets and magnetism. To the Chinese and Greeks of ancient times, the attractive and repulsive forces between magnets must have seemed magical indeed. Through the ages, miraculous curative powers have been attributed to magnets, and magnets have been used by illusionists to produce "magical" effects. Magnets guided ships in the Age of Exploration and generated the electrical industry in the 19th century. Today they store information and entertainment on disks and tapes, and produce sound in speakers, images on TV screens, rotation in motors, and levitation in high-speed trains. Students visit various MIT projects related to magnets (including superconducting electromagnets) and read about and discuss the history, legends, pseudoscience, science, and technology of types of magnets, including applications in medicine. Several short written reports and at least one oral presentation will be required of each participant.

This graduate-level course covers fluid systems dominated by the influence of interfacial tension. The roles of curvature pressure and Marangoni stress are elucidated in a variety of fluid systems. Particular attention is given to drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics.

This course is intended to understand the engineering design of nuclear power plants using the basic principles of reactor physics, thermodynamics, fluid flow and heat transfer. This course includes the following: Reactor designs, Thermal analysis of nuclear fuel, Reactor coolant flow and heat transfer, Power conversion cycles, Nuclear safety and Reactor dynamic behavior.

This course is intended to introduce the student to the concepts and methods of transport theory needed in neutron science applications. This course is a foundational study of the effects of multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department. Stochastic and deterministic simulation techniques will be introduced to the students.

The central point of this course is to provide a physical basis that links the structure of materials with their properties, focusing primarily on metals. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals.

Normally taken by physics majors in their sophomore year. Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; particle collisions. Relativity and electricity; Coulomb's law; magnetic fields. Brief introduction to Newtonian cosmology. Introduction to some concepts of General Relativity; principle of equivalence. The Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, Shapiro delay. This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year. Topics include Einstein's postulates, the Lorentz transformation, relativistic effects and paradoxes, and applications involving electromagnetism and particle physics. This course also provides a brief introduction to some concepts of general relativity, including the principle of equivalence, the Schwartzschild metric and black holes, and the FRW metric and cosmology.

Introduction to the main concepts of string theory to undergraduates. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity (8.033) and basic quantum mechanics (8.05). Subject develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism (8.02) and statistical mechanics (8.044). This includes the study of D-branes and string thermodynamics. This course introduces string theory to undergraduate and is based upon Prof. Zwiebach's textbook entitled A First Course in String Theory. Since string theory is quantum mechanics of a relativistic string, the foundations of the subject can be explained to students exposed to both special relativity and basic quantum mechanics. This course develops the aspects of string theory and makes it accessible to students familiar with basic electromagnetism and statistical mechanics.

Basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional e.m.f. and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. This is a graduate level subject which uses appropriate mathematics but whose emphasis is on physical phenomena and principles.

Introduction to quantitative methods and modeling techniques to address key questions in modern biology. Overview of quantitative modeling techniques in evolutionary biology, molecular biology and genetics, cell biology and developmental biology. Description of key experiments that validate models. Specific topics include: Evolutionary biology: theoretical models for evolution, evolution in test tube, evolution experiments with viruses and bacteria, complexity and evolution; Molecular biology and genetics: protein design, bioinformatics and genomics, constructing and modeling of genetic networks, control theory and genetic networks; Cell biology: forces and motion, cell motility, signal transduction pathways, chemotaxis and pheromone response; Development biology: pattern formation, self-organization, and models of Drosophila development.

The basic principles of Einstein's general theory of relativity. Differential geometry. Experimental tests of general relativity. Black holes. Cosmology.

The main objective of this cross disciplinary course is to understand the historical development and the current status of ideas and models, to present and question the constraints from the different research fields, and to investigate if and how the different views on mantle flow can be reconciled with the currently available data.

Mechanics studies how forces affect bodies in motion--how, for example, a bullet is fired from a gun, or a top is set in motion by the flick of a wrist. This course will introduce the student to the core concepts of mechanics as applied to design, testing, and manufacture of safe and reliable products. Upon successful completion of this course, the student will be able to: Identify and use units, notations, and vectors used in mechanics; Identify and explain the concepts of forces, couples, and moments; Use the concept of forces and moments to compute resultants and equivalent systems in mechanics; Analyze mechanics of rigid bodies, such as trusses, frames, and machines; Identify and explain the concepts of friction and internal forces; Compute material properties of solid bodies, such as moments of inertia and mass moments of inertia; Compute strain and stress and understand the relationship of stress and strain for both elastic and plastic bodies; Compute stresses and strain in bodies subjected to tension and torsion; Compute stresses and strain in pressure vessels and composites; Identify and explain the concept of stress tensor and the constitutive relationship between strain and stress; Compute stresses and strain in simple and composite beams due to bending; Explain how stress is computed experimentally or using finite element formulations; Identify and explain material failure scenarios, such as fracture, fatigue, creep, and buckling. (Mechanical Engineering 102)