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.

Device and circuit level optimization of digital building blocks. MOS and bipolar device models and second order effects. Circuit design styles and arithmetic structures. Estimation and minimization of energy consumption. Interconnect models and parasitics; driver design; timing issues (clock skew, self-timed circuits, etc.). Memory architectures, circuits (sense amplifiers) and devices. Testing of integrated circuits. Extensive use of circuit layout and SPICE in design projects and software labs.

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 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."

" 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."

Anatomy and Physiology is a dynamic textbook for the two-semester human anatomy and physiology course for life science and allied health majors. The book is organized by body system and covers standard scope and sequence requirements. Its lucid text, strategically constructed art, career features, and links to external learning tools address the critical teaching and learning challenges in the course. The web-based version of Anatomy and Physiology also features links to surgical videos, histology, and interactive diagrams.

Anatomy and Physiology is a dynamic textbook for the two-semester human anatomy and physiology course for life science and allied health majors. The book is organized by body system and covers standard scope and sequence requirements. Its lucid text, strategically constructed art, career features, and links to external learning tools address the critical teaching and learning challenges in the course. The web-based version of Anatomy and Physiology also features links to surgical videos, histology, and interactive diagrams.

Includes the study of the gross and microscopic structure of the systems of the human body with special emphasis on the relationship between structure and function. Integrates anatomy and physiology of cells, tissues, organs, the systems of the human body, and mechanisms responsible for homeostasis.

Includes sections on the Endocrine System, the Cardiovascular System, the Lymphatic and Immune System, the Respiratory System, the Digestive System, Nutrition, the Urinary System, the Reproductive System, and Development and Inheritance.

This Open Course is an adaptation of OpenStax Anatomy and Physiology and was created under a Round Nine ALG Textbook Transformation Grant.

Topics covered include:

Chemical Organization
Cellular Organization
Tissue Organization
Integumentary System
Skeletal System
Muscular System
Nervous System
Endocrine System
Cardiovascular System
Lymphatic System
Respiratory System
Digestive System
Reproductive System

This course focuses on the archaeology of the Greek and Roman city. It investigates the relationship between urban architecture and the political, social, and economic role of cities in the Greek and Roman world. Analyzes a range of archaeological and literary evidence relevant to the use of space in Greek and Roman cities (e.g. Athens, Paestum, Rome, Pompeii) and a range of theoretical frameworks for the study of ancient urbanism.