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.

In this class, students use data and systems knowledge to build models of complex socio-technical systems for improved system design and decision-making. Students will enhance their model-building skills, through review and extension of functions of random variables, Poisson processes, and Markov processes; move from applied probability to statistics via Chi-squared t and f tests, derived as functions of random variables; and review classical statistics, hypothesis tests, regression, correlation and causation, simple data mining techniques, and Bayesian vs. classical statistics. A class project is required.

This undergraduate course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics.

Selective survey of Latin American history from the wars of independence at the start of the nineteenth century to the present. Issues studied include: independence and its aftermath, slavery and its abolition, Latin America in the global economy, relations between Latin America and the US, dictatorships and democracies in the twentieth century, and revolution in Mexico, Cuba, and Central America.

This lesson teaches students how to make decisions in the face of uncertainty by using decision trees. It is aimed for high school kids with a minimal background in probability; the students only need to know how to calculate the probability of two uncorrelated events both occurring (ie flipping 2 heads in a row). Over the course of this lesson, students will learn about the role of uncertainty in decision making, how to make and use a decision tree, how to use limiting cases to develop an intuition, and how this applies to everyday life. The video portion is about fifteen minutes, and the whole lesson, including activities, should be completed in about forty-five minutes. Some of the activities call for students to work in pairs, but a larger group is also okay, especially for the discussion centered activities. The required materials for this lesson are envelopes, small prizes, and some things similar in size and shape to the prize.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

This course is a continuation of 18.014. It covers the same material as 18.02 (Multivariable Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.

This lesson will explore the connections between magnetism in natural materials and electromagnetism. The ultimate goal will be for students to form an understanding that the source of magnetism in natural materials is moving charges. It is helpful, but not required, for the students to have some work with electricity, and other distance forces (such as gravity or the electric force). The lesson will probably take two 50-minute periods to complete. Although the video footage is brief, the activities are in depth, inquiry-based, and can take time for the students to explore. The materials are not specifically prescribed, but can include things such as bar magnets, compasses, iron filings, wire, batteries, steel bolts, coils, straws, and hot glue. The activities include drawing the magnetic fields of bar magnets and electromagnets. The activities also include making a magnet from a drinking straw and iron filings.

In this video lesson, the concept of momentum applied to hard-body collisions is explained using a number of simple demonstrations, all of which can be repeated in the classroom. Understanding Newton's Laws is fundamental to all of physics, and this lesson introduces the vital concepts of momentum and energy, and their conservation. Only some preliminary ideas of algebra are used here, and all the concepts presented can be found in any high-school level physics book. In terms of materials required, getting hold of large steel balls may not be easy, but large ball bearings can be procured easily. On the basis of what students have learned in the video, teachers can easily generate a large number of questions that relate to one's daily experiences, or which pose new challenges: for example, in a collision between a heavy and light vehicle, why do those inside the lighter one suffer less injury?

In this class we will come to understand the vast changes in Spanish life that have taken place since Franco's death in 1975. We will focus on the new freedom from censorship, the re-emergence of movements for regional autonomy, the new cinema, reforms in education and changes in daily life: Sex roles, work, and family that have occurred in the last decade. In so doing, we will examine myths that are often considered commonplaces when describing Spain and its people.

This class introduces elementary programming concepts including variable types, data structures, and flow control. After an introduction to linear algebra and probability, it covers numerical methods relevant to mechanical engineering, including approximation (interpolation, least squares and statistical regression), integration, solution of linear and nonlinear equations, ordinary differential equations, and deterministic and probabilistic approaches. Examples are drawn from mechanical engineering disciplines, in particular from robotics, dynamics, and structural analysis. Assignments require MATLAB programming.

Introduction to numerical methods: interpolation, differentiation, integration, systems of linear equations. Solution of differential equations by numerical integration, partial differential equations of inviscid hydrodynamics: finite difference methods, panel methods. Fast Fourier Transforms. Numerical representation of sea waves. Computation of the motions of ships in waves. Integral boundary layer equations and numerical solutions.

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

In this video lesson, students will learn about linear programming (LP) and will solve an LP problem using the graphical method. Its focus is on the famous "Stigler's diet" problem posed by the 1982 Nobel Laureate in economics, George Stigler. Based on his problem, students will formulate their own diet problem and solve it using the graphical method. The prerequisites to this lesson are basic algebra and geometry. The materials needed for the in-class activities include graphing paper and pencil. This lesson can be completed in one class of approximately one hour. If the teacher would like to cover the simplex algorithm by George Dantzig as an alternative solution method, an additional whole class period is suggested.

Fundamentals of characterizing and recognizing patterns and features of interest in numerical data. Basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. Decision theory, statistical classification, maximum likelihood and Bayesian estimation, non-parametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research.

This learning video explores the mysterious physics behind boomerangs and other rapidly spinning objects. Students will get to make and throw their own boomerangs between video segments! A key idea presented is how torque causes the precession of angular momentum. One class period is required to complete this learning video, and the optimal prerequisites are a familiarity with forces, Newton's laws, vectors and time derivatives. Each student would need the following materials for boomerang construction: cardboard (roughly the size of a postcard), ruler, pencil/pen, scissors, protractor, and a stapler.

This video lesson explores Newton's Third Law of Motion through examination of several real world examples of this law in action, including that of a donkey cart - a site common in the streets of Pakistan. Students will understand that forces act on objects even if the objects appear to be static and that certain conditions - gravity in particular - affect how two objects interact. The time needed to complete this lesson is approximately 50-60 minutes, and students should be familiar with basic mechanics such as Newton's laws, levers, etc. The materials required are a couple of spring balances, a meter rule, tape, pencil, two desks, and some lab weights (few grams each). The types of in-class activities for between the video breaks include active discussions and participation by students in activities related to the Third Law.

The objective of this lesson is to illustrate how a common everyday experience (such as playing pool) can often provide a learning moment. In the example chosen, we use the game of pool to help explain some key concepts of physics. One of these concepts is the conservation of linear momentum since conservation laws play an extremely important role in many aspects of physics. The idea that a certain property of a system is maintained before and after something happens is quite central to many principles in physics and in the pool example, we concentrate on the conservation of linear momentum. The latter half of the video looks at angular momentum and friction, examining why certain objects roll, as opposed to slide. We do this by looking at how striking a ball with a cue stick at different locations produces different effects.

SP.255 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.