Relevant material from MIT's introductory courses to support students as they study and educators as they teach the AP Physics curriculum.

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.

Design of shoreline protection along rivers, canals and the sea; load on bed and shoreline by currents, wind waves and ship motion; stability of elements under current and wave conditions; stability of shore protection elements; design methods, construction methods. Flow: recapitulation of basics from fluid mechanics (flow, turbulence), stability of individual grains (sand, but also rock) in different type of flow conditions (weirs, jets), scour and erosion. Porous Media: basic equation, pressures and velocities on the stability on the boundary layer; groundwater flow with impermeable and semi-impermeable structures; granular filters and geotextiles. Waves: recapitulation of the basics of waves, focus on wave forces on the land-water boundary, specific aspects of ship induced waves, stability of elements under wave action (loose rock, placed blocks, impermeable layers) Design: overview of the various types of protections, construction and maintenance; design requirements, deterministic and probabilistic design; case studies, examples Materials and environment: overview of materials to be used, interaction with the aquatic environment, role of the land-water boundary as part of the ecosystem; environmentally sound shoreline design.

First published in 1981 by MIT Press, Continuum Electromechanics, courtesy of MIT Press and used with permission, provides a solid foundation in electromagnetics, particularly conversion of energy between electrical and mechanical forms. Topics include: electrodynamic laws, electromagnetic forces, electromechanical kinematics, charge migration, convection, relaxation, magnetic diffusion and induction interactions, laws and approximations of fluid mechanics, static equilibrium, electromechanical flows, thermal and molecular diffusion, and streaming interactions. The applications covered include transducers, rotating machines, Van de Graaff machines, image processing, induction machines, levitation of liquid metals, shaping of interfaces in plastics and glass processing, orientation of ferrofluid seals, cryogenic fluids, liquid crystal displays, thunderstorm electrification, fusion machines, magnetic pumping of liquid metals, magnetohydrodynamic power generation, inductive and dielectric heating, electrophoretic particle motion, electrokinetic and electrocapillary interactions in biological systems, and electron beams. "

This subject provides an introduction to fluid mechanics. Students are introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of fluids and learn how to solve a variety of problems of interest to civil and environmental engineers. While there is a chance to put skills from Calculus and Differential Equations to use in this subject, the emphasis is on physical understanding of why a fluid behaves the way it does. The aim is to make the students think as a fluid. In addition to relating a working knowledge of fluid mechanics, the subject prepares students for higher-level subjects in fluid dynamics.

This course introduces finite element methods for the analysis of solid, structural, fluid, field, and heat transfer problems. Steady-state, transient, and dynamic conditions are considered. Finite element methods and solution procedures for linear and nonlinear analyses are presented using largely physical arguments. The homework and a term project (for graduate students) involve use of the general purpose finite element analysis program ADINA. Applications include finite element analyses, modeling of problems, and interpretation of numerical results.

This course introduces fluid mechanics, the study of how and why fluids (both gaseous and liquid) behave the way they do. Upon successful completion of this course, the student will be able to: Formulate basic equation for fluid engineering problems; Use the Poiseuille equation, Reynolds number correlations, and Moody chart for description of laminar and turbulent pipe flow; Use tables, figures, and energy equations to predict pressure drop in pipes, across fittings and through pumps and turbines; Use tables and figures to determine the friction energy loss; Perform dimensional analysis and identify important parameters; Calculate pressure distributions, forces on surfaces, and buoyancy; Analyze flow situations and use appropriate methods to obtain quantitative information for engineering applications. (Mechanical Engineering 201)

This course covers the development of the fundamental equations of fluid mechanics and their simplifications for several areas of marine hydrodynamics and the application of these principles to the solution of engineering problems. Topics include the principles of conservation of mass, momentum and energy, lift and drag forces, laminar and turbulent flows, dimensional analysis, added mass, and linear surface waves, including wave velocities, propagation phenomena, and descriptions of real sea waves. Wave forces on structures are treated in the context of design and basic seakeeping analysis of ships and offshore platforms. Geophysical fluid dynamics will also be addressed including distributions of salinity, temperature, and density; heat balance in the ocean; major ocean circulations and geostrophic flows; and the influence of wind stress. Experimental projects conducted in ocean engineering laboratories illustrating concepts taught in class, including ship resistance and model testing, lift and drag forces on submerged bodies, and vehicle propulsion.

Selection of material from the following topics: calculus of variations (the first variation and the second variation); integral equations (Volterra equations; Fredholm equations, the Hilbert-Schmidt theorem); the Hilbert Problem and singular integral equations of Cauchy type; Wiener-Hopf Method and partial differential equations; Wiener-Hopf Method and integral equations; group theory.

This graduate-level course covers fluid systems dominated by the influence of interfacial tension. The roles of curvature pressure and Marangoni stress are elucidated in a variety of fluid systems. Particular attention is given to drops and bubbles, soap films and minimal surfaces, wetting phenomena, water-repellency, surfactants, Marangoni flows, capillary origami and contact line dynamics.

In this course the fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering. The various topics covered are: Transport theorem and conservation principles, Navier-Stokes' equation, dimensional analysis, ideal and potential flows, vorticity and Kelvin's theorem, hydrodynamic forces in potential flow, D'Alembert's paradox, added-mass, slender-body theory, viscous-fluid flow, laminar and turbulent boundary layers, model testing, scaling laws, application of potential theory to surface waves, energy transport, wave/body forces, linearized theory of lifting surfaces, and experimental project in the towing tank or propeller tunnel.

Molecular-level engineering and analysis of chemical processes. Use of chemical bonding, reactivity, and other key concepts in the design and tailoring of organic systems. Application and development of structure-property relationships. Descriptions of the chemical forces and structural factors that govern supramolecular and interfacial phenomena for molecular and polymeric systems. This course is an advanced subject in fluid and continuum mechanics. The course content includes kinematics, macroscopic balances for linear and angular momentum, stress tensors, creeping flows and the lubrication approximation, the boundary layer approximation, linear stability theory, and some simple turbulent flows.

Modelling is about understanding the nature: our world, ourselves and our work. Everything that we observe has a cause (typically several) and has the effect thereof. The heart of modelling lies in identifying, understanding and quantifying these cause-and-effect relationships.

A model can be treated as a (selective) representation of a system. We create the model by defining a mapping from the system space to the model space, thus we can map system state and behaviour to model state and behaviour. By defining the inverse mapping, we may map results from the study of the model back to the system. In this course, using an overarching modelling paradigm, students will become familiar with several instances of modelling, e.g., mechanics, thermal dynamics, fluid mechanics, etc.

" This subject is designed for upper level undergraduates and graduate students as an introduction to politics and the policy process in modern Japan. The semester is divided into two parts. After a two-week general introduction to Japan and to the dominant approaches to the study of Japanese history, politics and society, we will begin exploring five aspects of Japanese politics: party politics, electoral politics, interest group politics, bureaucratic politics, and policy, which will be broken up into seven additional sections. We will try to understand the ways in which the actors and institutions identified in the first part of the semester affect the policy process across a variety of issues areas."

Introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory and optimization techniques. Emphasis on basic ideas and on applications in mechanical engineering. Selection will change every year. This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This course deals with the transfer of work, energy, and material via gases and liquids. These fluids may undergo changes in temperature, pressure, density, and chemical composition during the transfer process and may act on or be acted on by external systems. Engineers must fully understand these processes in order to analyze, troubleshoot, or improve existing processes and/or innovate and design new ones. Upon successful completion of this course, the student will be able to: Interpret and use scientific notation and engineering units for the description of fluid flow and energy transfer; Interpret measurements of thermodynamic quantities for description of fluid flow and energy transfer; Use concepts of continuum fluid dynamics to interpret physical situations; Determine the interrelationship of variables in pumping and piping operations; Analyze heat-exchanger performance and understand design considerations; Apply thermodynamics to the analysis of energy conversion and cooling/heating situations; Communicate technical information in written and graphical form. (Mechanical Engineering 303)

The basic objective of Unified is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics and Propulsion (T); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, we seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year we will endeavor to point out the connections among the disciplines.