The lesson begins with a demonstration introducing students to the force between two current carrying loops, comparing the attraction and repulsion between the loops to that between two magnets. After formal lecture on Ampere's law, students begin to use the concepts to calculate the magnetic field around a loop. This is applied to determine the magnetic field of a toroid, imagining a toroid as a looped solenoid.

Students design, build and test model roller coasters using foam tubing. The design process integrates energy concepts as they test and evaluate designs that address the task as an engineer would. The goal is for students to understand the basics of engineering design associated with kinetic and potential energy to build an optimal roller coaster. The marble starts with potential energy that is converted to kinetic energy as it moves along the track. The diameter of the loops that the marble traverses without falling out depends on the kinetic energy obtained by the marble.

An introductory course in analog circuit synthesis for microelectronic designers. Topics include: Review of analog design basics; linear and non-linear analog building blocks: harmonic oscillators, (static and dynamic) translinear circuits, wideband amplifiers, filters; physical layout for robust analog circuits; design of voltage sources ranging from simple voltage dividers to high-performance bandgaps, and current source implementations from a single resistor to high-quality references based on negative-feedback structures.

Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Continues 18.100, in the direction of manifolds and global analysis. Differentiable maps, inverse and implicit function theorems, n-dimensional Riemann integral, change of variables in multiple integrals, manifolds, differential forms, n-dimensional version of Stokes' theorem. 18.901 helpful but not required.

A comprehensive introduction to control system synthesis in which the digital computer plays a major role, reinforced with hands-on laboratory experience. Covers elements of real-time computer architecture; input-output interfaces and data converters; analysis and synthesis of sampled-data control systems using classical and modern (state-space) methods; analysis of trade-offs in control algorithms for computation speed and quantization effects. Laboratory projects emphasize practical digital servo interfacing and implementation problems with timing, noise, nonlinear devices.

This course develops the fundamentals of feedback control using linear transfer function system models. Topics covered include analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and use of z-plane design. Students will complete an extended design case study. Students taking the graduate version (2.140) will attend the recitation sessions and complete additional assignments.

This class analyzes complex biological processes from the molecular, cellular, extracellular, and organ levels of hierarchy. Emphasis is placed on the basic biochemical and biophysical principles that govern these processes. Examples of processes to be studied include chemotaxis, the fixation of nitrogen into organic biological molecules, growth factor and hormone mediated signaling cascades, and signaling cascades leading to cell death in response to DNA damage. In each case, the availability of a resource, or the presence of a stimulus, results in some biochemical pathways being turned on while others are turned off. The course examines the dynamic aspects of these processes and details how biochemical mechanistic themes impinge on molecular/cellular/tissue/organ-level functions. Chemical and quantitative views of the interplay of multiple pathways as biological networks are emphasized. Student work will culminate in the preparation of a unique grant application in an area of biological networks.

The goal of this course is to investigate with students backgrounds on some of the pivotal events that have shaped our understanding and approach to architecture. Emphasis of discussion will be primarily on buildings and works of individual architects. Canonical architects, buildings and movements that have exerted significant influences on the development of architecture will be studied in detail. We will visit some of these buildings for a first-hand look and to evaluate for ourselves their significance or lack thereof. As a final project, each student will analyze a building through drawings, text, bibliography and a physical model in a format ready for documentation and exhibition.

An analysis of historical structures is presented in this class, presented in themed sections based around construction materials. Structures from all periods of history are analyzed. The goal of the class is to provide an understanding of the preservation of historic structures for all students.

This short activity helps students analyze a political cartoon about U.S. imperialism in the Philippines. To complete the activity, the teacher will need either a map or a globe to show students the relative distance between the United States and Philippines.

Analytical chemistry is more than a collection of analytical methods and an understanding of equilibrium chemistry; it is an approach to solving chemical problems. Although equilibrium chemistry and analytical methods are important, their coverage should not come at the expense of other equally important topics. The introductory course in analytical chemistry is the ideal place in the undergraduate chemistry curriculum for exploring topics such as experimental design, sampling, calibration strategies, standardization, optimization, statistics, and the validation of experimental results. Analytical methods come and go, but best practices for designing and validating analytical methods are universal. Because chemistry is an experimental science it is essential that all chemistry students understand the importance of making good measurements.

As currently taught in the United States, introductory courses in analytical chemistryemphasize quantitative (and sometimes qualitative) methods of analysis along with a heavydose of equilibrium chemistry. Analytical chemistry, however, is much more than a collection ofanalytical methods and an understanding of equilibrium chemistry; it is an approach to solvingchemical problems. Although equilibrium chemistry and analytical methods are important, theircoverage should not come at the expense of other equally important topics.

The introductory course in analytical chemistry is the ideal place in the undergraduate chemistry curriculum forexploring topics such as experimental design, sampling, calibration strategies, standardization,optimization, statistics, and the validation of experimental results. Analytical methods comeand go, but best practices for designing and validating analytical methods are universal. Becausechemistry is an experimental science it is essential that all chemistry students understand theimportance of making good measurements.

My goal in preparing this textbook is to find a more appropriate balance between theoryand practice, between “classical” and “modern” analytical methods, between analyzing samplesand collecting samples and preparing them for analysis, and between analytical methods anddata analysis. There is more material here than anyone can cover in one semester; it is myhope that the diversity of topics will meet the needs of different instructors, while, perhaps,suggesting some new topics to cover.

This subject is designed to inform students on the analytical foundations of inviscid subsonic aerodynamics. A primary goal of this subject is to equip students with the scientific rigor, applied mathematical complexity, and physical understanding that form the foundation of classical subsonic aerodynamics. Perturbation methods that both simplify mathematical complexity and expand physical understanding of critical phenomenon in fluid flow provides a framework for the subject. The subject offers lectures in classical subsonic aerodynamics at the graduate level on inviscid, subsonic, steady flow over slender aerodynamic bodies. Topics will be selected from: fundamentals of fluid mechanics [review]; singular-perturbation methods; similitude; subsonic flows with axial symmetry; linearized subsonic flow; slender body theory; similarity rules for subsonic flows; two-dimensional flow past a wave-shaped wall; thin wing theory; Kaplan’s higher approximations.

This is a laboratory course supplemented by lectures that focus on selected analytical facilities that are commonly used to determine the mineralogy, elemental abundance and isotopic ratios of Sr and Pb in rocks, soils, sediments and water.

This course presents real-world examples in which quantitative methods provide a significant competitive edge that has led to a first order impact on some of today's most important companies. We outline the competitive landscape and present the key quantitative methods that created the edge (data-mining, dynamic optimization, simulation), and discuss their impact.

This course covers the key quantitative methods of finance: financial econometrics and statistical inference for financial applications; dynamic optimization; Monte Carlo simulation; stochastic (ItĺŞ) calculus. These techniques, along with their computer implementation, are covered in depth. Application areas include portfolio management, risk management, derivatives, and proprietary trading.

This course teaches students how to understand the rationality behind how organizations and their programs behave, and to be comfortable and analytical with a live organization. It thereby builds analytic skills for evaluating programs and projects, organizations, and environments. It draws on the literature of the sociology of organizations, political science, public administration, and historical experience-and is based on both developing-country and developed-country experience.

In this task, the students are not asked to find an answer, but are asked to analyze word problems and explain their thinking. In the process, they are faced with varying ways of thinking about multiplication.

This course focuses on alternative ways in which the issues of growth, restructuring, innovation, knowledge, learning, and accounting and measurements can be examined, covering both industrialized and emerging countries. We give special emphasis to recent transformations in regional economies throughout the world and to the implications these changes have for the theories and research methods used in spatial economic analyses. Readings will relate mainly to the United States, but we cover pertinent material on foreign countries in lectures.