This course covers the design, construction, and testing of field robotic systems, …
This course covers the design, construction, and testing of field robotic systems, through team projects with each student responsible for a specific subsystem. Projects focus on electronics, instrumentation, and machine elements. Design for operation in uncertain conditions is a focus point, with ocean waves and marine structures as a central theme. Topics include basic statistics, linear systems, Fourier transforms, random processes, spectra, ethics in engineering practice, and extreme events with applications in design.
This course takes a ‘back to the beginning’ view that aims to …
This course takes a ‘back to the beginning’ view that aims to better understand the end result. What might be the developmental processes that lead to the organization of ‘booming, buzzing confusions’ into coherent visual objects? This course examines key experimental results and computational proposals pertinent to the discovery of objects in complex visual inputs. The structure of the course is designed to get students to learn and to focus on the genre of study as a whole; to get a feel for how science is done in this field.
The main goal of this course is to give the students a …
The main goal of this course is to give the students a solid foundation in the theory of elliptic and parabolic linear partial differential equations. It is the second semester of a two-semester, graduate-level sequence on Differential Analysis.
This is the first semester of a two-semester sequence on Differential Analysis. …
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.
In this course, we study elliptic Partial Differential Equations (PDEs) with variable …
In this course, we study elliptic Partial Differential Equations (PDEs) with variable coefficients building up to the minimal surface equation. Then we study Fourier and harmonic analysis, emphasizing applications of Fourier analysis. We will see some applications in combinatorics / number theory, like the Gauss circle problem, but mostly focus on applications in PDE, like the Calderon-Zygmund inequality for the Laplacian, and the Strichartz inequality for the Schrodinger equation. In the last part of the course, we study solutions to the linear and the non-linear Schrodinger equation. All through the course, we work on the craft of proving estimates.
Differential Equations are the language in which the laws of nature are …
Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE’s) deal with functions of one variable, which can often be thought of as time.
The laws of nature are expressed as differential equations. Scientists and engineers …
The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Course Format This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:
Lecture Videos by Professor Arthur Mattuck. Course Notes on every topic. Practice Problems with Solutions. Problem Solving Videos taught by experienced MIT Recitation Instructors. Problem Sets to do on your own with Solutions to check your answers against when you’re done. A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts. A full set of Exams with Solutions, including practice exams to help you prepare.
Content Development Haynes Miller Jeremy Orloff Dr. John Lewis Arthur Mattuck
This course is an introduction to differential geometry. The course itself is …
This course is an introduction to differential geometry. The course itself is mathematically rigorous, but still emphasizes concrete aspects of geometry, centered on the notion of curvature.
This is an advanced subject in computer modeling and CAD CAM fabrication, …
This is an advanced subject in computer modeling and CAD CAM fabrication, with a focus on building large-scale prototypes and digital mock-ups within a classroom setting. Prototypes and mock-ups are developed with the aid of outside designers, consultants, and fabricators. Field trips and in-depth relationships with building fabricators demonstrate new methods for building design. The class analyzes complex shapes, shape relationships, and curved surfaces fabrication at a macro scale leading to new architectural languages, based on methods of construction.
Discrete stochastic processes are essentially probabilistic systems that evolve in time via …
Discrete stochastic processes are essentially probabilistic systems that evolve in time via random changes occurring at discrete fixed or random intervals. This course aims to help students acquire both the mathematical principles and the intuition necessary to create, analyze, and understand insightful models for a broad range of these processes. The range of areas for which discrete stochastic-process models are useful is constantly expanding, and includes many applications in engineering, physics, biology, operations research and finance.
This class addresses the representation, analysis, and design of discrete time signals …
This class addresses the representation, analysis, and design of discrete time signals and systems. The major concepts covered include: 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 and various applications. Acknowledgements I would like to express my thanks to Thomas Baran, Myung Jin Choi, and Xiaomeng Shi for compiling the lecture notes on this site from my individual lectures and handouts and their class notes during the semesters that they were students in the course. These lecture notes, the text book and included problem sets and solutions will hopefully be helpful as you learn and explore the topic of Discrete-Time Signal Processing.
A large proportion of contemporary research on organizations, strategy and management relies …
A large proportion of contemporary research on organizations, strategy and management relies on quantitative research methods. This course is designed to provide an introduction to some of the most commonly used quantitative techniques, including logit/probit models, count models, event history models, and pooled cross-section techniques.
Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations …
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.
The aim of this course is to highlight some technical aspects of …
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 unifying theme of this course is best captured by the title …
The unifying theme of this course is best captured by the title of our main reference book: “Recursive Methods in Economic Dynamics”. We start by covering deterministic and stochastic dynamic optimization using dynamic programming analysis. We then study the properties of the resulting dynamic systems. Finally, we will go over a recursive method for repeated games that has proven useful in contract theory and macroeconomics. We shall stress applications and examples of all these techniques throughout the course.
This course focuses on dynamic optimization methods, both in discrete and in …
This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.
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.
The course addresses dynamic systems, i.e., systems that evolve with time. Typically …
The course addresses dynamic systems, i.e., systems that evolve with time. Typically these systems have inputs and outputs; it is of interest to understand how the input affects the output (or, vice-versa, what inputs should be given to generate a desired output). In particular, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain linearity and time-invariance conditions. We will analyze the response of these systems to inputs and initial conditions. It is of particular interest to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. We will learn how to design (control) systems that ensure desirable properties (e.g., stability, performance) of the interconnection with a given dynamic system.
Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. …
Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. 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; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.
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 MATLAB® to solve dynamics and vibrations problems. This version of the class stresses kinematics and builds around a strict but powerful approach to kinematic formulation which is different from the approach presented in Spring 2007. Our notation was adapted from that of Professor Kane of Stanford University.
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