Representation, analysis, and design of discrete time signals and systems. Review of …
Representation, analysis, and design of discrete time signals and systems. Review of Z-transforms, discrete-time Fourier transforms, and difference equations. Discrete-time processing of continuous-time signals. Decimation, interpolation, and sampling rate conversion. Flowgraph structures for DT systems. Time-and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform, FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms, Cepstral analysis, various applications.
Design and analysis of concurrent algorithms, emphasizing those suitable for use in …
Design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks. Process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation. Course Description 6.852J / 18.437J intends to: (1) provide a rigorous introduction to the most important research results in the area of distributed algorithms, and (2) prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed.
This course intends to provide a rigorous introduction to the most important …
This course intends to provide a rigorous introduction to the most important research results in the area of distributed algorithms, and prepare interested students to carry out independent research in distributed algorithms. Topics covered include: design and analysis of concurrent algorithms, emphasizing those suitable for use in distributed networks, process synchronization, allocation of computational resources, distributed consensus, distributed graph algorithms, election of a leader in a network, distributed termination, deadlock detection, concurrency control, communication, and clock synchronization. Special consideration is given to issues of efficiency and fault tolerance. Formal models and proof methods for distributed computation are also discussed.
" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their …
" Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems."
Seminar on a selected topic from Renaissance architecture. Requires original research and …
Seminar on a selected topic from Renaissance architecture. Requires original research and presentation of a report. The aim of this course is to highlight some technical aspects of the classical tradition in architecture that have so far received only sporadic attention. It is well known that quantification has always been an essential component of classical design: proportional systems in particular have been keenly investigated. But the actual technical tools whereby quantitative precision was conceived, represented, transmitted, and implemented in pre-modern architecture remain mostly unexplored. By showing that a dialectical relationship between architectural theory and data-processing technologies was as crucial in the past as it is today, this course hopes to promote a more historically aware understanding of the current computer-induced transformations in architectural design.
The course covers the basic models and solution techniques for problems of …
The course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages. This includes systems with finite or infinite state spaces, as well as perfectly or imperfectly observed systems. We will also discuss approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.
Momentum principles and energy principles. Lagrange's equations, Hamilton's principle. Applications to mechanical …
Momentum principles and energy principles. Lagrange's equations, Hamilton's principle. Applications to mechanical systems including gyroscopic effects. Study of steady motions and nature of small deviations therefrom. Natural modes and natural frequencies for continuous and lumped parameter systems. Forced vibrations. Dynamic stability theory. Causes of instability. This course reviews momentum and energy principles, and then covers the following topics: Hamilton's principle and Lagrange's equations; three-dimensional kinematics and dynamics of rigid bodies; steady motions and small deviations therefrom, gyroscopic effects, and causes of instability; free and forced vibrations of lumped-parameter and continuous systems; nonlinear oscillations and the phase plane; nonholonomic systems; and an introduction to wave propagation in continuous systems. This course was originally developed by Professor T. Akylas.
This class is an introduction to the dynamics and vibrations of lumped-parameter …
This class is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics include kinematics; force-momentum formulation for systems of particles and rigid bodies in planar motion; work-energy concepts; virtual displacements and virtual work; Lagrange's equations for systems of particles and rigid bodies in planar motion; linearization of equations of motion; linear stability analysis of mechanical systems; free and forced vibration of linear multi-degree of freedom models of mechanical systems; and matrix eigenvalue problems. The class includes an introduction to numerical methods and using MATLABĺ¨ to solve dynamics and vibrations problems.
Upon successful completion of this course, students will be able to: * …
Upon successful completion of this course, students will be able to: * Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains * Make quantitative estimates of model parameters from experimental measurements * Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods * Obtain the frequency-domain response of linear systems to sinusoidal inputs * Compensate the transient response of dynamic systems using feedback techniques * Design, implement and test an active control system to achieve a desired performance measureMastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional …
Introduction to dynamics and vibration of lumped-parameter models of mechanical systems. Three-dimensional particle kinematics. Force-momentum formulation for systems of particles and for rigid bodies (direct method). Newton-Euler equations. Work-enery (variational) formulation for systems particles and for rigid bodies (indirect method). Virtual displacements and work. Lagrange's equations for systems of particles and for rigid bodies. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear damped lumped parameter multi-degree of freedom models of mechanical systems. Application to the design of ocean and civil engineering structures such as tension leg platforms.
An introduction to theoretical studies of systems of many interacting components, the …
An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.
An introduction to theoretical studies of systems of many interacting components, the …
An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.
An introduction to theoretical studies of systems of many interacting components, the …
An introduction to theoretical studies of systems of many interacting components, the individual dynamics of which may be simple, but the collective dynamics of which are often nonlinear and analytically intractable. Topics vary from year to year. Format includes both pedagogical lectures and round-table reviews of current literature. Subjects of interest include: problems in natural science (e.g., geology, ecology, and biology) where quantitative theory is still in development; problems in physics, such as turbulence, that demonstrate powerful concepts such as scaling and universality; and modern computational methods for the simulation and study of such problems. Discussions in context of contemporary experimental or observational data.
Introduction to nonlinear deterministic dynamical systems. Nonlinear ordinary differential equations. Planar autonomous systems. Fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma. Stability of equilibria by Lyapunov's first and second methods. Feedback linearization. Application to nonlinear circuits and control systems. Alternate years. Description from course website: This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.
This course begins with a study of the role of dynamics in …
This course begins with a study of the role of dynamics in the general physics of the atmosphere, the consideration of the differences between modeling and approximation, and the observed large-scale phenomenology of the atmosphere. Only then are the basic equations derived in rigorous manner. The equations are then applied to important problems and methodologies in meteorology and climate, with discussions of the history of the topics where appropriate. Problems include the Hadley circulation and its role in the general circulation, atmospheric waves including gravity and Rossby waves and their interaction with the mean flow, with specific applications to the stratospheric quasi-biennial oscillation, tides, the super-rotation of Venus' atmosphere, the generation of atmospheric turbulence, and stationary waves among other problems. The quasi-geostrophic approximation is derived, and the resulting equations are used to examine the hydrodynamic stability of the circulation with applications ranging from convective adjustment to climate.
The Early Universe provides an introduction to modern cosmology. The first part …
The Early Universe provides an introduction to modern cosmology. The first part of the course deals with the classical cosmology, and later part with modern particle physics and its recent impact on cosmology.
Ecologies of Construction examines the resource requirements for the making and maintenance …
Ecologies of Construction examines the resource requirements for the making and maintenance of the contemporary built environment. This course introduces the field of industrial ecology as a primary source of concepts and methods in the mapping of material and energy expenditures dedicated to construction activities.
" We will cover fundamentals of ecology, considering Earth as an integrated …
" We will cover fundamentals of ecology, considering Earth as an integrated dynamic system. Topics include coevolution of the biosphere, geosphere, atmosphere and oceans; photosynthesis and respiration; the hydrologic, carbon and nitrogen cycles. We will examine the flow of energy and materials through ecosystems; regulation of the distribution and abundance of organisms; structure and function of ecosystems, including evolution and natural selection; metabolic diversity; productivity; trophic dynamics; models of population growth, competition, mutualism and predation. This course is designated as Communication-Intensive; instruction and practice in oral and written communication provided. Biology is a recommended prerequisite."
Econometrics is the study of estimation and inference for economic models using …
Econometrics is the study of estimation and inference for economic models using economic data. Econometric theory concerns the study and development of tools and methods for applied econometric applications. Applied econometrics concerns the application of these tools to economic data.
Choice of material has implications throughout the life-cycle of a product, influencing …
Choice of material has implications throughout the life-cycle of a product, influencing many aspects of economic and environmental performance. This course will provide a survey of methods for evaluating those implications. Lectures will cover topics in material choice concepts, fundamentals of engineering economics, manufacturing economics modeling methods, and life-cycle environmental evaluation.
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