Boundary layers as rational approximations to the solutions of exact equations of fluid motion. Physical parameters influencing laminar and turbulent aerodynamic flows and transition. Effects of compressibility, heat conduction, and frame rotation. Influence of boundary layers on outer potential flow and associated stall and drag mechanisms. Numerical solution techniques and exercises. The major focus of 16.13 is on boundary layers, and boundary layer theory subject to various flow assumptions, such as compressibility, turbulence, dimensionality, and heat transfer. Parameters influencing aerodynamic flows and transition and influence of boundary layers on outer potential flow are presented, along with associated stall and drag mechanisms. Numerical solution techniques and exercises are included.

Classical dynamics beyond Unified Engineering. Application of vector kinematics to analyze the translation and rotation of rigid bodies. Formulation and solution of the equations of motion using both Newtonian and Lagrangian methods. Analytical and numerical solutions to rigid body dynamics problems. Applications to aircraft flight dynamics and spacecraft attitude dynamics.

Explains bounded input, bounded output stability.

This course aims to connect the principles, concepts, and laws/postulates of classical and statistical thermodynamics to applications that require quantitative knowledge of thermodynamic properties from a macroscopic to a molecular level. It covers their basic postulates of classical thermodynamics and their application to transient open and closed systems, criteria of stability and equilibria, as well as constitutive property models of pure materials and mixtures emphasizing molecular-level effects using the formalism of statistical mechanics. Phase and chemical equilibria of multicomponent systems are covered. Applications are emphasized through extensive problem work relating to practical cases.

Examines political institutions from a rational choice perspective. The now burgeoning rational choice literature on legislatures, bureaucracies, courts, and elections constitutes the chief focus. Some focus on institutions from a comparative and/or international perspective. Graduate students are expected to pursue the subject in greater depth through reading and individual research. Advanced undergrads may take subject with faculty approval. This is an applied theory course covering topics in the political economy of democratic countries. This course examines political institutions from a rational choice perspective. The now burgeoning rational choice literature on legislatures, bureaucracies, courts, and elections constitutes the chief focus. Some focus will be placed on institutions from a comparative and/or international perspective.

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 measure

Mastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.

Treatment of electromechanical transducers, rotating and linear electric machines. Lumped-parameter electromechanics of interaction. Development of device characteristics: energy conversion density, efficiency; and of system interaction characteristics: regulation, stability, controllability, and response. Use of electric machines in drive systems. Problems taken from current research. Alternate years. 6.685 explores concepts in electromechanics, using electric machinery as examples. It teaches an understanding of principles and analysis of electromechanical systems. By the end of the course, students are capable of doing electromechanical design of the major classes of rotating and linear electric machines, and have an understanding of the principles of the energy conversion parts of Mechatronics. In addition to design, students learn how to estimate the dynamic parameters of electric machines and understand what the implications of those parameters are on the performance of systems incorporating those machines.

Explica las estabilidad de entrada acotada, salida acotada.

Introduction to design of feedback systems. Properties and advantages of feedback systems. Time-domain and frequency-domain performance measures. Stability and degree of stability. Nyquist criterion. Frequency-domain design. Root locus method. Compensation techniques. Application to a wide variety of physical systems. Some previous laboratory experience with electronic systems is assumed (6.002 or 6.071 or 16.040).

The purpose of this activity is to demonstrate some of the different parts of an airplane through the construction of a paper airplane. Students will build several different kinds of paper airplanes in order to figure out what makes an airplane fly and what can be changed to influence the flying characteristics of an airplane.

You will design a fourth-order notch filter and investigate the effects of filter-coefficient quantization. You will compare the response of the filter having unquantized coefficients with that of a filter having coefficients quantized as a single, fourth-order stage and with that of a filter having coefficients quantized as a cascade of two, second-order stages.

" This seminar is designed to be an experimental and hands-on approach to applied chemistry (as seen in cooking). Cooking may be the oldest and most widespread application of chemistry and recipes may be the oldest practical result of chemical research. We shall do some cooking experiments to illustrate some chemical principles, including extraction, denaturation, and phase changes."

You will design a fourth-order notch filter and investigate the effects of filter-coefficient quantization. You will compare the response of the filter having unquantized coefficients with that of a filter having coefficients quantized as a single, fourth-order stage and with that of a filter having coefficients quantized as a cascade of two, second-order stages.

" This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods."

This module includes three interactive examples for studying system stability using phase plane analysis in LabVIEW. The equations used in the examples are from the textbook "Applied Nonlinear Control" by Jean-Jacques E. Slotine and Weiping Li.

This course is being offered in conjunction with the colloquium The Politics of Reconstructing Iraq, which is sponsored by MIT's Center for International Studies and Department of Urban Studies and Planning. Fundamentally, the course focuses on contemporary post-conflict countries (or in-conflict countries) and the role of planning and reconstruction in building nations, mitigating conflicts, reshaping the social, spatial, geopolitical, and political life, and determining the country's future.

Introduction to fundamental concepts in "continuous" applied mathematics. Extensive use of demonstrational software. Discussion of computational and modelling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.

Introduction to design of feedback control systems. Properties and advantages of feedback systems. Time-domain and frequency-domain performance measures. Stability and degree of stability. Root locus method, Nyquist criterion, frequency-domain design, and state space methods. Application to a variety of aircraft and spacecraft systems.

This is an advanced topics course in model theory whose main theme is simple theories. We treat simple theories in the framework of compact abstract theories, which is more general than that of first order theories. We cover the basic properties of independence (i.e., non-dividing) in simple theories, the characterisation of simple theories by the existence of a notion of independence, and hyperimaginary canonical bases.