Online courses directory (19947)

The main objective of 1.054/1.541 is to provide students with a rational basis of the design of reinforced concrete members and structures through advanced understanding of material and structural behavior. This course is offered to undergraduate (1.054) and graduate students (1.541). Topics covered include: Strength and Deformation of Concrete under Various States of Stress; Failure Criteria; Concrete Plasticity; Fracture Mechanics Concepts; Fundamental Behavior of Reinforced Concrete Structural Systems and their Members; Basis for Design and Code Constraints; High-performance Concrete Materials and their use in Innovative Design Solutions; Slabs: Yield Line Theory; Behavior Models and Nonlinear Analysis; and Complex Systems: Bridge Structures, Concrete Shells, and Containments.

Professor Oral Buyukozturk thanks Tzu-Yang Yu, a graduate student at MIT, for his valuable assistance in preparing course documents.

This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.

This course continues from Analysis I (18.100B), in the direction of manifolds and global analysis. The first half of the course covers multivariable calculus. The rest of the course covers the theory of differential forms in n-dimensional vector spaces and manifolds.

This is a undergraduate course. It will cover normed spaces, completeness, functionals, Hahn-Banach theorem, duality, operators; Lebesgue measure, measurable functions, integrability, completeness of L-p spaces; Hilbert space; compact, Hilbert-Schmidt and trace class operators; as well as spectral theorem.

This course continues the content covered in 18.100 Analysis I. Roughly half of the subject is devoted to the theory of the Lebesgue integral with applications to probability, and the other half to Fourier series and Fourier integrals.

This class serves as an introduction to mass transport in environmental flows, with emphasis given to river and lake systems. The class will cover the derivation and solutions to the differential form of mass conservation equations. Class topics to be covered will include: molecular and turbulent diffusion, boundary layers, dissolution, bed-water exchange, air-water exchange and particle transport.

Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

This course discusses the Linearized theory of wave phenomena in applied mechanics. Examples are chosen from elasticity, acoustics, geophysics, hydrodynamics and other subjects. The topics include: basic concepts, one dimensional examples, characteristics, dispersion and group velocity, scattering, transmission and reflection, two dimensional reflection and refraction across an interface, mode conversion in elastic waves, diffraction and parabolic approximation, radiation from a line source, surface Rayleigh waves and Love waves in elastic media, waves on the sea surface and internal waves in a stratified fluid, waves in moving media, ship wave pattern, atmospheric lee waves behind an obstacle, and waves through a laminated media.

This intensive micro-subject provides the necessary skills in Microsoft® Excel spreadsheet modeling for ESD.71 Engineering Systems Analysis for Design. Its purpose is to bring entering students up to speed on some of the advanced techniques that we routinely use in analysis. It is motivated by our experience that many students only have an introductory knowledge of Excel, and thus waste a lot of time thrashing about unproductively. Many people think they know Excel, but overlook many efficient tools, such as Data Table and Goal Seek. It is also useful for a variety of other subjects.

This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.

This is an advanced undergraduate course dealing with calculus in one complex variable with geometric emphasis. Since the course Analysis I (18.100B) is a prerequisite, topological notions like compactness, connectedness, and related properties of continuous functions are taken for granted.

This course offers biweekly problem sets with solutions, two term tests and a final exam, all with solutions.

This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed.

This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

This course covers concepts of computation used in analysis of engineering systems. It includes the following topics: data structures, relational database representations of engineering data, algorithms for the solution and optimization of engineering system designs (greedy, dynamic programming, branch and bound, graph algorithms, nonlinear optimization), and introduction to complexity analysis. Object-oriented, efficient implementations of algorithms are emphasized.

Approaching transportation as a complex, large-scale, integrated, open system (CLIOS), this course strives to be an interdisciplinary systems subject in the "open" sense. It introduces qualitative modeling ideas and various techniques and philosophies of modeling complex transportation enterprises. It also introduces conceptual frameworks for qualitative analysis, such as frameworks for regional strategic planning, institutional change analysis, and new technology development and deployment. And it covers transportation as a large-scale, integrated system that interacts directly with the social, political, and economic aspects of contemporary society. Fundamental elements and issues shaping traveler and freight transportation systems are covered, along with underlying principles governing transportation planning, investment, operations, and maintenance.

Design, operation, and management of traffic flows over complex transportation networks are the foci of this course. It covers two major topics: traffic flow modeling and traffic flow operations. Sub-topics include deterministic and probabilistic models, elements of queuing theory, and traffic assignment. Concepts are illustrated through various applications and case studies. This is a half-term subject offered during the second half of the semester.

This course examines the policy, politics, planning, and engineering of transportation systems in urban areas, with a special focus on the Boston area. It covers the role of the federal, state, and local government and the MPO, public transit in the era of the automobile, analysis of current trends and pattern breaks; analytical tools for transportation planning, traffic engineering, and policy analysis; the contribution of transportation to air pollution, social costs, and climate change; land use and transportation interactions, and more. Transportation sustainability is a central theme throughout the course, as well as consideration of if and how it is possible to resolve the tension between the three E's (environment, economy, and equity). The goal of this course is to elicit discussion, stimulate independent thinking, and encourage students to understand and challenge the "conventional wisdom" of transportation planning.

Transmedia narratives exist across multiple storytelling platforms, using the advantages of each to enhance the experience of the audience. No matter which medium nor how many, the heart of any successful transmedia project is a good story. In this class we will spend time on the basics of solid storytelling in speculative fiction before we move on to how to translate those elements into various media. We will then explore how different presentations in different media can complement and enhance our storytelling. While we will read scholarly articles and discuss ideas about transmedia, this is primarily a class in making speculative fiction transmedia projects. We will analyze the strengths and weaknesses of various mediums and consider how they complement each other, and how by using several different media we can give the audience a more complete, rewarding, and immersive experience.

This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.