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16.07 Dynamics (MIT) 16.07 Dynamics (MIT)

Description

Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.

Subjects

Curvilinear motion | Curvilinear motion | carteian coordinates | carteian coordinates | dynamics | dynamics | equations of motion | equations of motion | intrinsic coordinates | intrinsic coordinates | coordinate systems | coordinate systems | work | work | energy | energy | conservative forces | conservative forces | potential energy | potential energy | linear impulse | linear impulse | mommentum | mommentum | angular impulse | angular impulse | relative motion | relative motion | rotating axes | rotating axes | translating axes | translating axes | Newton's second law | Newton's second law | inertial forces | inertial forces | accelerometers | accelerometers | Newtonian relativity | Newtonian relativity | gravitational attraction | gravitational attraction | 2D rigid body kinematics | 2D rigid body kinematics | conservation laws for systems of particles | conservation laws for systems of particles | 2D rigid body dynamics | 2D rigid body dynamics | pendulums | pendulums | 3D rigid body kinematics | 3D rigid body kinematics | 3d rigid body dynamics | 3d rigid body dynamics | inertia tensor | inertia tensor | gyroscopic motion | gyroscopic motion | torque-free motion | torque-free motion | spin stabilization | spin stabilization | variable mass systems | variable mass systems | rocket equation | rocket equation | central foce motion | central foce motion | Keppler's laws | Keppler's laws | orbits | orbits | orbit transfer | orbit transfer | vibration | vibration | spring mass systems | spring mass systems | forced vibration | forced vibration | isolation | isolation | coupled oscillators | coupled oscillators | normal modes | normal modes | wave propagation | wave propagation | cartesian coordinates | cartesian coordinates | momentum | momentum | central force motion | central force motion

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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis Introduction to Astronomy provides a quantitative introduction to physics of the solar system, stars, interstellar medium, the galaxy, and universe, as determined from a variety of astronomical observations and models.Topics include: planets, planet formation; stars, the Sun, "normal" stars, star formation; stellar evolution, supernovae, compact objects (white dwarfs, neutron stars, and black holes), plusars, binary X-ray sources; star clusters, globular and open clusters; interstellar medium, gas, dust, magnetic fields, cosmic rays; distance ladder; galaxies, normal and active galaxies, jets; gravitational lensing; large scaling structure; Newtonian cosmology, dynamical expansion and thermal history of the Universe; cosmic microwave background radiation; big-bang nucleosynthesis

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402

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6.252J Nonlinear Programming (MIT) 6.252J Nonlinear Programming (MIT)

Description

6.252J is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems. 6.252J is a course in the department's "Communication, Control, and Signal Processing" concentration. This course provides a unified analytical and computational approach to nonlinear optimization problems. The topics covered in this course include: unconstrained optimization methods, constrained optimization methods, convex analysis, Lagrangian relaxation, nondifferentiable optimization, and applications in integer programming. There is also a comprehensive treatment of optimality conditions, Lagrange multiplier theory, and duality theory. Throughout the course, applications are drawn from control, communications, power systems, and resource allocation problems.

Subjects

nonlinear programming | nonlinear programming | non-linear programming | non-linear programming | nonlinear optimization | nonlinear optimization | unconstrained optimization | unconstrained optimization | gradient | gradient | conjugate direction | conjugate direction | Newton | Newton | quasi-Newton methods | quasi-Newton methods | constrained optimization | constrained optimization | feasible directions | feasible directions | projection | projection | interior point | interior point | Lagrange multiplier | Lagrange multiplier | convex analysis | convex analysis | Lagrangian relaxation | Lagrangian relaxation | nondifferentiable optimization | nondifferentiable optimization | integer programming | integer programming | optimality conditions | optimality conditions | Lagrange multiplier theory | Lagrange multiplier theory | duality theory | duality theory | control | control | communications | communications | power systems | power systems | resource allocation | resource allocation | 6.252 | 6.252 | 15.084 | 15.084

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8.01X Physics I: Classical Mechanics with an Experimental Focus (MIT) 8.01X Physics I: Classical Mechanics with an Experimental Focus (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. This course has a hands-on focus, and approaches mechanics through take-home experiments. Topics include: kinematics, Newton's laws of motion, universal gravitation, statics, conservation laws, energy, work, momentum, and special relativity. Physics I is a first-year physics course which introduces students to classical mechanics. This course has a hands-on focus, and approaches mechanics through take-home experiments. Topics include: kinematics, Newton's laws of motion, universal gravitation, statics, conservation laws, energy, work, momentum, and special relativity.

Subjects

Newton | Newton | mechanics | mechanics | Newtonian mechanics | Newtonian mechanics | experiments | experiments | 8.01 | 8.01

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8.282J Introduction to Astronomy (MIT) 8.282J Introduction to Astronomy (MIT)

Description

Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models. Introduction to Astronomy provides a quantitative introduction to the physics of the solar system, stars, the interstellar medium, the galaxy, and the universe, as determined from a variety of astronomical observations and models.

Subjects

solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system; stars; interstellar medium; the Galaxy; the Universe; planets; planet formation; star formation; stellar evolution; supernovae; compact objects; white dwarfs; neutron stars; black holes; plusars | binary X-ray sources; star clusters; globular and open clusters; interstellar medium | gas | dust | magnetic fields | cosmic rays; distance ladder; | solar system | solar system | stars | stars | interstellar medium | interstellar medium | the Galaxy | the Galaxy | the Universe | the Universe | planets | planets | planet formation | planet formation | star formation | star formation | stellar evolution | stellar evolution | supernovae | supernovae | compact objects | compact objects | white dwarfs | white dwarfs | neutron stars | neutron stars | black holes | black holes | plusars | binary X-ray sources | plusars | binary X-ray sources | star clusters | star clusters | globular and open clusters | globular and open clusters | interstellar medium | gas | dust | magnetic fields | cosmic rays | interstellar medium | gas | dust | magnetic fields | cosmic rays | distance ladder | distance ladder | galaxies | normal and active galaxies | jets | galaxies | normal and active galaxies | jets | gravitational lensing | gravitational lensing | large scaling structure | large scaling structure | Newtonian cosmology | dynamical expansion and thermal history of the Universe | Newtonian cosmology | dynamical expansion and thermal history of the Universe | cosmic microwave background radiation | cosmic microwave background radiation | big-bang nucleosynthesis | big-bang nucleosynthesis | pulsars | pulsars | binary X-ray sources | binary X-ray sources | gas | gas | dust | dust | magnetic fields | magnetic fields | cosmic rays | cosmic rays | galaxy | galaxy | universe | universe | astrophysics | astrophysics | Sun | Sun | supernova | supernova | globular clusters | globular clusters | open clusters | open clusters | jets | jets | Newtonian cosmology | Newtonian cosmology | dynamical expansion | dynamical expansion | thermal history | thermal history | normal galaxies | normal galaxies | active galaxies | active galaxies | Greek astronomy | Greek astronomy | physics | physics | Copernicus | Copernicus | Tycho | Tycho | Kepler | Kepler | Galileo | Galileo | classical mechanics | classical mechanics | circular orbits | circular orbits | full kepler orbit problem | full kepler orbit problem | electromagnetic radiation | electromagnetic radiation | matter | matter | telescopes | telescopes | detectors | detectors | 8.282 | 8.282 | 12.402 | 12.402 | plusars | plusars | galaxies | galaxies | normal and active galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe | dynamical expansion and thermal history of the Universe

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8.01 Physics I (MIT) 8.01 Physics I (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics. Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.

Subjects

classical mechanics | classical mechanics | Space and time | Space and time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | experimental basis of Newton's laws | experimental basis of Newton's laws | particle dynamics | particle dynamics | universal gravitation | universal gravitation | collisions and conservation laws | collisions and conservation laws | work and potential energy | work and potential energy | vibrational motion | vibrational motion | conservative forces | conservative forces | central force motions | central force motions | inertial forces and non-inertial frames | inertial forces and non-inertial frames | rigid bodies and rotational dynamics | rigid bodies and rotational dynamics | forces and equilibrium | forces and equilibrium | space | space | time | time | space-time | space-time | planar motion | planar motion | forces | forces | equilibrium | equilibrium | Newton?s laws | Newton?s laws | collisions | collisions | conservation laws | conservation laws | work | work | potential energy | potential energy | inertial forces | inertial forces | non-inertial forces | non-inertial forces | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics

License

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Física (Preparación para la Universidad) Física (Preparación para la Universidad)

Description

Esta asignatura está pensada para alumnos que estudian su primer año en la Universidad o que están a punto de hacerlo y quieren prepararse desde su último curso en la Enseñanza no Universitaria. En la asignatura se realiza una revisión de los conceptos físicos básicos para la preparación de los estudios en cualquiera de las titulaciones del ámbito de la Ingeniería y de la Arquitectura. Está estructurada en seis bloques temáticos: Mecánica, Oscilaciones y ondas, Termodinámica, Electromagnetismo, Optica y Física Moderna, además de un primer Bloque que trata sobre algunas cuestiones básicas de la Física, como son los sistemas de unidades, la incertidumbre de una medida y los vectores. Cada Bloque temático está estructurado en Unidades independientes, de modo que cada e Esta asignatura está pensada para alumnos que estudian su primer año en la Universidad o que están a punto de hacerlo y quieren prepararse desde su último curso en la Enseñanza no Universitaria. En la asignatura se realiza una revisión de los conceptos físicos básicos para la preparación de los estudios en cualquiera de las titulaciones del ámbito de la Ingeniería y de la Arquitectura. Está estructurada en seis bloques temáticos: Mecánica, Oscilaciones y ondas, Termodinámica, Electromagnetismo, Optica y Física Moderna, además de un primer Bloque que trata sobre algunas cuestiones básicas de la Física, como son los sistemas de unidades, la incertidumbre de una medida y los vectores. Cada Bloque temático está estructurado en Unidades independientes, de modo que cada e

Subjects

Ondas armónicas | Ondas armónicas | Interacción gravitatoria | Interacción gravitatoria | Sistemas de unidades | Sistemas de unidades | Termodinámica | Termodinámica | Temperatura y gases ideales | Temperatura y gases ideales | Oscilaciones | Oscilaciones | Núcleo atómico | Núcleo atómico | Ondas sonoras | Ondas sonoras | Fenómenos ondulatorios | Fenómenos ondulatorios | Cinemática | Cinemática | Naturaleza de la luz | Naturaleza de la luz | Aplicaciones de las leyes de Newton | Aplicaciones de las leyes de Newton | Resolución de problemas de física | Resolución de problemas de física | Introducción a la Física cuántica | Introducción a la Física cuántica | Movimiento circular | Movimiento circular | Física Moderna | Física Moderna | Corriente eléctrica | Corriente eléctrica | Campo eléctrico | Campo eléctrico | Trabajo y energía | Trabajo y energía | Campo magnético | Campo magnético | Teoría dde la relatividad | Teoría dde la relatividad | Inducción electromagnética | Inducción electromagnética | Medida e incertidumbre | Medida e incertidumbre | Ondas electromagnéticas | Ondas electromagnéticas | Optica | Optica | Leyes de Newton | Leyes de Newton | Movimiento parabólico | Movimiento parabólico | Optica geométrica | Optica geométrica | Oscilaciones armónicas | Oscilaciones armónicas | Vectores | Vectores | Trabajo | calor y principios de la Termodinámica | Trabajo | calor y principios de la Termodinámica | Física aplicada | Física aplicada | Mecánica | Mecánica

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3.044 Materials Processing (MIT) 3.044 Materials Processing (MIT)

Description

This course is focused on physical understanding of materials processing, and the scaling laws that govern process speed, volume, and material quality. In particular, this course will cover the transport of heat and matter as these topics apply to materials processing. This course is focused on physical understanding of materials processing, and the scaling laws that govern process speed, volume, and material quality. In particular, this course will cover the transport of heat and matter as these topics apply to materials processing.

Subjects

materials processing | materials processing | heat conduction | heat conduction | heat transfer | heat transfer | Biot number | Biot number | glass fibers | glass fibers | thermal spray | thermal spray | 2D analysis | 2D analysis | friction welding | friction welding | radiation | radiation | black bodies | black bodies | emessivity | emessivity | solidification | solidification | sand casting | sand casting | lost foam | lost foam | molds | molds | binary solidification | binary solidification | microstructures | microstructures | fluid flow | fluid flow | glass production | glass production | Pilkington glass | Pilkington glass | drag force | drag force | Newtonian | Newtonian | non-Newtonian | non-Newtonian | blow molding | blow molding | compressive forming | compressive forming | powder | powder | sintering | sintering | slurry | slurry | and colloid processing | and colloid processing | steel making | steel making | electronics manufacturing | electronics manufacturing

License

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21H.141 Renaissance To Revolution: Europe, 1300-1800 (MIT) 21H.141 Renaissance To Revolution: Europe, 1300-1800 (MIT)

Description

This course provides an introduction to major political, social, cultural and intellectual changes in Europe from the beginnings of the Renaissance in Italy around 1300 to the outbreak of the French Revolution at the end of the 1700s. It focuses on the porous boundaries between categories of theology, magic and science, as well as print. It examines how developments in these areas altered European political institutions, social structures, and cultural practices. It also studies men and women, nobles and commoners, as well as Europeans and some non-Europeans with whom they came into contact. This course provides an introduction to major political, social, cultural and intellectual changes in Europe from the beginnings of the Renaissance in Italy around 1300 to the outbreak of the French Revolution at the end of the 1700s. It focuses on the porous boundaries between categories of theology, magic and science, as well as print. It examines how developments in these areas altered European political institutions, social structures, and cultural practices. It also studies men and women, nobles and commoners, as well as Europeans and some non-Europeans with whom they came into contact.

Subjects

renaissance | renaissance | revolution | revolution | Europe | Europe | Italy | Italy | French Revolution | French Revolution | theology | theology | magic | magic | science | science | England | England | censorship | censorship | Rene Descartes | Rene Descartes | Italian humanism | Italian humanism | Copernicus | Copernicus | Constantine | Constantine | printing | printing | rare books | rare books | paper-making | paper-making | Erasmus of Rotterdam | Erasmus of Rotterdam | The Paraclesis | The Paraclesis | free will | free will | Luther | Luther | German Peasants War | German Peasants War | The Cheese and the Worms | The Cheese and the Worms | Protestant revolution | Protestant revolution | Catholic renewal | Catholic renewal | radical reform movements | radical reform movements | religion | religion | Menocchio | Menocchio | skepticism | skepticism | the occult | the occult | Michel de Montaigne | Michel de Montaigne | astrology | astrology | Cardano | Cardano | Cartesian Method | Cartesian Method | Discourse on Method | Discourse on Method | English Civil War | English Civil War | interregnum | Putney debates | interregnum | Putney debates | Wallington's World | Wallington's World | The Mad Hatter | The Mad Hatter | Isaac Newton | Isaac Newton | Newtonianism | Newtonianism | Principia | Principia | The Encyclopedie | The Encyclopedie | Diderot | Diderot | d'Alembert | d'Alembert | metric system | metric system

License

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2.57 Nano-to-Macro Transport Processes (MIT) 2.57 Nano-to-Macro Transport Processes (MIT)

Description

This course provides parallel treatments of photons, electrons, phonons, and molecules as energy carriers, aiming at fundamental understanding and descriptive tools for energy and heat transport processes from nanoscale continuously to macroscale. Topics include the energy levels, the statistical behavior and internal energy, energy transport in the forms of waves and particles, scattering and heat generation processes, Boltzmann equation and derivation of classical laws, deviation from classical laws at nanoscale and their appropriate descriptions, with applications in nano- and microtechnology. This course provides parallel treatments of photons, electrons, phonons, and molecules as energy carriers, aiming at fundamental understanding and descriptive tools for energy and heat transport processes from nanoscale continuously to macroscale. Topics include the energy levels, the statistical behavior and internal energy, energy transport in the forms of waves and particles, scattering and heat generation processes, Boltzmann equation and derivation of classical laws, deviation from classical laws at nanoscale and their appropriate descriptions, with applications in nano- and microtechnology.

Subjects

nanotechnology | nanotechnology | nanoscale | nanoscale | transport phenomena | transport phenomena | photons | photons | electrons | electrons | phonons | phonons | energy carriers | energy carriers | energy transport | energy transport | heat transport | heat transport | energy levels | energy levels | statistical behavior | statistical behavior | internal energy | internal energy | waves and particles | waves and particles | scattering | scattering | heat generation | heat generation | Boltzmann equation | Boltzmann equation | classical laws | classical laws | microtechnology | microtechnology | crystal | crystal | lattice | lattice | quantum oscillator | quantum oscillator | laudaurer | laudaurer | nanotube | nanotube | Louiville equation | Louiville equation | X-ray | X-ray | blackbody | blackbody | quantum well | quantum well | Fourier | Fourier | Newton | Newton | Ohm | Ohm | thermoelectric effect | thermoelectric effect | Brownian motion | Brownian motion | surface tension | surface tension | van der Waals potential. | van der Waals potential. | van der Waals potential | van der Waals potential

License

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15.093 Optimization Methods (SMA 5213) (MIT) 15.093 Optimization Methods (SMA 5213) (MIT)

Description

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5213 (Optimisation Methods). This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include the simplex method, network flow methods, branch and bound and cutting plane methods for discrete optimization, optimality conditions for nonlinear optimization, interior point methods for convex optimization, Newton's method, heuristic methods, and dynamic programming and optimal control methods. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5213 (Optimisation Methods).

Subjects

principal algorithms | principal algorithms | linear | linear | network | network | discrete | discrete | nonlinear | nonlinear | dynamic optimization | dynamic optimization | optimal control | optimal control | methodology and the underlying mathematical structures | methodology and the underlying mathematical structures | simplex method | simplex method | network flow methods | network flow methods | branch and bound and cutting plane methods for discrete optimization | branch and bound and cutting plane methods for discrete optimization | optimality conditions for nonlinear optimization | optimality conditions for nonlinear optimization | interior point methods for convex optimization | interior point methods for convex optimization | Newton's method | Newton's method | heuristic methods | heuristic methods | dynamic programming | dynamic programming | optimal control methods | optimal control methods | SMA 5213 | SMA 5213

License

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8.012 Physics I: Classical Mechanics (MIT) 8.012 Physics I: Classical Mechanics (MIT)

Description

This class is an introduction to classical mechanics for students who are comfortable with calculus. The main topics are: Vectors, Kinematics, Forces, Motion, Momentum, Energy, Angular Motion, Angular Momentum, Gravity, Planetary Motion, Moving Frames, and the Motion of Rigid Bodies. This class is an introduction to classical mechanics for students who are comfortable with calculus. The main topics are: Vectors, Kinematics, Forces, Motion, Momentum, Energy, Angular Motion, Angular Momentum, Gravity, Planetary Motion, Moving Frames, and the Motion of Rigid Bodies.

Subjects

elementary mechanics | elementary mechanics | Newton's laws | Newton's laws | momentum | momentum | energy | energy | angular momentum | angular momentum | rigid body motion | rigid body motion | non-inertial systems | non-inertial systems | classical mechanics | classical mechanics

License

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8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay. Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.

Subjects

Einstein's postulates | Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects and paradoxes | relativistic effects and paradoxes | Minkowski diagrams | Minkowski diagrams | invariants and four-vectors | invariants and four-vectors | momentum | energy and mass | momentum | energy and mass | particle collisions | particle collisions | Relativity and electricity | Relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | General Relativity | General Relativity | principle of equivalence | principle of equivalence | the Schwarzchild metric | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | gravitational red shift | particle trajectories | particle trajectories | light trajectories | light trajectories | invariants | invariants | four-vectors | four-vectors | momentum | momentum | energy | energy | mass | mass | relativistic effects | relativistic effects | paradoxes | paradoxes | electricity | electricity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Schwarzchild metric | Schwarzchild metric | geodesics | geodesics | Shaprio delay | Shaprio delay | relativistic kinematics | relativistic kinematics | relativistic dynamics | relativistic dynamics | electromagnetism | electromagnetism | hubble expansion | hubble expansion | universe | universe | equivalence principle | equivalence principle | curved space time | curved space time | Ether Theory | Ether Theory | constants | constants | speed of light | speed of light | c | c | graph | graph | pythagorem theorem | pythagorem theorem | triangle | triangle | arrows | arrows

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18.335J Numerical Methods of Applied Mathematics I (MIT) 18.335J Numerical Methods of Applied Mathematics I (MIT)

Description

IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. Quadrature.Technical RequirementsFile decompression software, such as Winzip or StuffIt, is required to open the .tar files found on this course site. The .tar files contain additional files which require software as well. MATLAB® software is required to run the .m files.Postscript viewer software, such as Ghostscript/Ghostview, can be used to view the .ps files.Ghostscript/Ghostview, Adobe Photoshop, and Adobe Illustrator are among the software tools that can be used to view the .ep IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. Quadrature.Technical RequirementsFile decompression software, such as Winzip or StuffIt, is required to open the .tar files found on this course site. The .tar files contain additional files which require software as well. MATLAB® software is required to run the .m files.Postscript viewer software, such as Ghostscript/Ghostview, can be used to view the .ps files.Ghostscript/Ghostview, Adobe Photoshop, and Adobe Illustrator are among the software tools that can be used to view the .ep

Subjects

IEEE-standard | IEEE-standard | iterative and direct linear system solution methods | iterative and direct linear system solution methods | eigendecomposition and model-order reduction | eigendecomposition and model-order reduction | fast Fourier transforms | fast Fourier transforms | multigrid | multigrid | wavelets | wavelets | other multiresolution methods | other multiresolution methods | matrix sparsification | matrix sparsification | Nonlinear root finding (Newton's method) | Nonlinear root finding (Newton's method) | Numerical interpolation | Numerical interpolation | Numerical extrapolation | Numerical extrapolation | Quadrature | Quadrature | 18.335 | 18.335 | 6.337 | 6.337

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13.013J Dynamics and Vibration (MIT) 13.013J Dynamics and Vibration (MIT)

Description

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-energy (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. 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-energy (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.

Subjects

umped-parameter models | umped-parameter models | lumped-parameter models | lumped-parameter models | mechanical systems | mechanical systems | Three-dimensional particle kinematics | Three-dimensional particle kinematics | Force-momentum formulation | Force-momentum formulation | Newton-Euler equations | Newton-Euler equations | Work-enery (variational) formulation | Work-enery (variational) formulation | systems particles | systems particles | rigid bodies (indirect method) | rigid bodies (indirect method) | Virtual displacements | Virtual displacements | Lagrange's equations | Lagrange's equations | Linear stability analysis | Linear stability analysis | 1.053J | 1.053J | 13.013 | 13.013 | 1.053 | 1.053

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8.012 Physics I (MIT) 8.012 Physics I (MIT)

Description

Elementary mechanics, presented at greater depth than in 8.01(Calculus). Newton's laws, concepts of momentum, energy, angular momentum, rigid body motion, and non-inertial systems. Uses elementary calculus freely. Concurrent registration in a math subject more advanced than 18.01 is recommended. In addition to the theoretical subject matter, several experiments in classical mechanics are performed by the students in the laboratory. Elementary mechanics, presented at greater depth than in 8.01(Calculus). Newton's laws, concepts of momentum, energy, angular momentum, rigid body motion, and non-inertial systems. Uses elementary calculus freely. Concurrent registration in a math subject more advanced than 18.01 is recommended. In addition to the theoretical subject matter, several experiments in classical mechanics are performed by the students in the laboratory.

Subjects

elementary mechanics | elementary mechanics | Newton's laws | Newton's laws | momentum | momentum | energy | energy | angular momentum | angular momentum | rigid body motion | rigid body motion | non-inertial systems | non-inertial systems | classical mechanics | classical mechanics

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18.S997 Introduction To MATLAB Programming (MIT) 18.S997 Introduction To MATLAB Programming (MIT)

Description

Includes audio/video content: AV lectures. This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular. Includes audio/video content: AV lectures. This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.

Subjects

MATLAB | programming | MATLAB | programming | variables | variables | plotting | plotting | scripts | scripts | functions | functions | flow control | flow control | statistics | statistics | data structures | data structures | images | images | vectors | vectors | matrices | matrices | root-finding | root-finding | Newton's Method | Newton's Method | Secant Method | Secant Method | Basins of Attraction | Basins of Attraction | Conway Game of Life | Conway Game of Life | Game of Life | Game of Life | vectorization | vectorization | debugging | debugging | scope | scope | function block | function block

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15.084J Nonlinear Programming (MIT) 15.084J Nonlinear Programming (MIT)

Description

Includes audio/video content: AV selected lectures. This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods. Includes audio/video content: AV selected lectures. This course introduces students to the fundamentals of nonlinear optimization theory and methods. Topics include unconstrained and constrained optimization, linear and quadratic programming, Lagrange and conic duality theory, interior-point algorithms and theory, Lagrangian relaxation, generalized programming, and semi-definite programming. Algorithmic methods used in the class include steepest descent, Newton's method, conditional gradient and subgradient optimization, interior-point methods and penalty and barrier methods.

Subjects

unconstrained and constrained optimization | unconstrained and constrained optimization | Lagrangean relaxation | Lagrangean relaxation | generalized programming | generalized programming | Newton's method | Newton's method | conditional gradient and subgradient optimization | conditional gradient and subgradient optimization | linear and quadratic programming | linear and quadratic programming | lagrange and conic duality theory | lagrange and conic duality theory | interior-point algorithms and theory | interior-point algorithms and theory | semi-definite programming | semi-definite programming | Algorithmic methods include steepest descent | Algorithmic methods include steepest descent | interior-point methods and penalty and barrier methods | interior-point methods and penalty and barrier methods | 15.084 | 15.084 | 6.252 | 6.252

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8.01 Physics I: Classical Mechanics (MIT)

Description

8.01 is a first-semester freshman physics class in Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory. In addition to the basic concepts of Newtonian Mechanics, Fluid Mechanics, and Kinetic Gas Theory, a variety of interesting topics are covered in this course: Binary Stars, Neutron Stars, Black Holes, Resonance Phenomena, Musical Instruments, Stellar Collapse, Supernovae, Astronomical observations from very high flying balloons (lecture 35), and you will be allowed a peek into the intriguing Quantum World. Also by Walter Lewin Courses: Electricity and Magnetism (8.02) - with a complete set of 36 video lectures from the Spring of 2002 Vibrations and Waves (8.03) - with a complete set of 23 video lectures from the Fall of 2004 Talks: For The Love Of Physics - Profes

Subjects

units of measurement | powers of ten | dimensional analysis | measurement uncertainty | scaling arguments | velocity | speed | acceleration | acceleration of gravity | vectors | motion | vector product | scalar product | projectiles | projectile trajectory | circular motion | centripetal motion | artifical gravity | force | Newton's Three Laws | eight | weightlessness | tension | friction | frictionless forces | static friction | dot products | cross products | kinematics | springs | pendulum | mechanical energy | kinetic energy | universal gravitation | resistive force | drag force | air drag | viscous terminal velocity | potential energy | heat; energy consumption | heat | energy consumption | collisions | center of mass | momentum | Newton's Cradle | impulse and impact | rocket thrust | rocket velocity | flywheels | inertia | torque | spinning rod | elliptical orbits | Kepler's Laws | Doppler shift | stellar dynamics | sound waves | electromagnets | binary star | black holes | rope tension | elasticity | speed of sound | pressure in fluid | Pascal's Principle | hydrostatic pressure | barometric pressure | submarines | buoyant force | Bernoulli's Equations | Archimede's Principle | floating | baloons | resonance | wind instruments | thermal expansion | shrink fitting | particles and waves | diffraction

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2.003J Dynamics and Vibration (13.013J) (MIT) 2.003J Dynamics and Vibration (13.013J) (MIT)

Description

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-energy (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. This subject was originally offered in Course 13 (Departm 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-energy (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. This subject was originally offered in Course 13 (Departm

Subjects

umped-parameter models | umped-parameter models | lumped-parameter models | lumped-parameter models | mechanical systems | mechanical systems | Three-dimensional particle kinematics | Three-dimensional particle kinematics | Force-momentum formulation | Force-momentum formulation | Newton-Euler equations | Newton-Euler equations | Work-enery (variational) formulation | Work-enery (variational) formulation | systems particles | systems particles | rigid bodies (indirect method) | rigid bodies (indirect method) | Virtual displacements | Virtual displacements | Lagrange's equations | Lagrange's equations | Linear stability analysis | Linear stability analysis | 13.013J | 13.013J | 13.013 | 13.013 | 1.053 | 1.053

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6.336J Introduction to Numerical Simulation (SMA 5211) (MIT) 6.336J Introduction to Numerical Simulation (SMA 5211) (MIT)

Description

6.336J is an introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5211 (Introduction to Numerical Simulation). 6.336J is an introduction to computational techniques for the simulation of a large variety of engineering and physical systems. Applications are drawn from aerospace, mechanical, electrical, chemical and biological engineering, and materials science. Topics include: mathematical formulations; network problems; sparse direct and iterative matrix solution techniques; Newton methods for nonlinear problems; discretization methods for ordinary, time-periodic and partial differential equations, fast methods for partial differential and integral equations, techniques for dynamical system model reduction and approaches for molecular dynamics. This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5211 (Introduction to Numerical Simulation).

Subjects

Numerical Simulation | Numerical Simulation | simulation | simulation | mathematics | mathematics | network problems | network problems | matrix solution | matrix solution | Newton method | Newton method | nonlinear problems | nonlinear problems | discretization methods | discretization methods | differential equations | differential equations | integral equations | integral equations | model-order reduction | model-order reduction | Monte Carlo | Monte Carlo | 6.336 | 6.336 | 2.096 | 2.096 | 16.910 | 16.910

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8.012 Physics I: Classical Mechanics (MIT) 8.012 Physics I: Classical Mechanics (MIT)

Description

This class is an introduction to classical mechanics for students who are comfortable with calculus. The main topics are: Vectors, Kinematics, Forces, Motion, Momentum, Energy, Angular Motion, Angular Momentum, Gravity, Planetary Motion, Moving Frames, and the Motion of Rigid Bodies. This class is an introduction to classical mechanics for students who are comfortable with calculus. The main topics are: Vectors, Kinematics, Forces, Motion, Momentum, Energy, Angular Motion, Angular Momentum, Gravity, Planetary Motion, Moving Frames, and the Motion of Rigid Bodies.

Subjects

elementary mechanics | elementary mechanics | Newton's laws | Newton's laws | momentum | momentum | energy | energy | angular momentum | angular momentum | rigid body motion | rigid body motion | non-inertial | non-inertial

License

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8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year. Topics include Einstein's postulates, the Lorentz transformation, relativistic effects and paradoxes, and applications involving electromagnetism and particle physics. This course also provides a brief introduction to some concepts of general relativity, including the principle of equivalence, the Schwartzschild metric and black holes, and the FRW metric and cosmology. This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year. Topics include Einstein's postulates, the Lorentz transformation, relativistic effects and paradoxes, and applications involving electromagnetism and particle physics. This course also provides a brief introduction to some concepts of general relativity, including the principle of equivalence, the Schwartzschild metric and black holes, and the FRW metric and cosmology.

Subjects

relativity | relativity | special relativity | special relativity | Einstein's postulates | Einstein's postulates | simultaneity | simultaneity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects | relativistic effects | Minkowski diagrams | Minkowski diagrams | relativistic invariants | relativistic invariants | four-vectors | four-vectors | relativitistic particle collisions | relativitistic particle collisions | relativity and electricity | relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | general relativity | general relativity | Schwarzchild metric | Schwarzchild metric | gravitational | gravitational | red shift | red shift | light trajectories | light trajectories | geodesics | geodesics | Shapiro delay | Shapiro delay

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8.01T Physics I (MIT) 8.01T Physics I (MIT)

Description

This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation.

Subjects

classical mechanics | classical mechanics | Space and time | Space and time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | forces and equilibrium | forces and equilibrium | experimental basis of Newton's laws | experimental basis of Newton's laws | particle dynamics | particle dynamics | universal gravitation | universal gravitation | collisions and conservation laws | collisions and conservation laws | work and potential energy | work and potential energy | vibrational motion | vibrational motion | conservative forces | conservative forces | inertial forces and non-inertial frames | inertial forces and non-inertial frames | central force motions | central force motions | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics | rigid bodies and rotational dynamics | rigid bodies and rotational dynamics

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8.902 Astrophysics II (MIT) 8.902 Astrophysics II (MIT)

Description

This is the second course in a two-semester sequence on astrophysics. Topics include galactic dynamics, groups and clusters on galaxies, phenomenological cosmology, Newtonian cosmology, Roberston-Walker models, and galaxy formation. This is the second course in a two-semester sequence on astrophysics. Topics include galactic dynamics, groups and clusters on galaxies, phenomenological cosmology, Newtonian cosmology, Roberston-Walker models, and galaxy formation.

Subjects

Galactic dynamics | Galactic dynamics | potential theory | potential theory | orbits | orbits | collisionless Boltzmann equations | collisionless Boltzmann equations | Galaxy interactions | Galaxy interactions | Groups and clusters | Groups and clusters | dark matter | dark matter | Intergalactic medium | Intergalactic medium | x-ray clusters | x-ray clusters | Active galactic nuclei | Active galactic nuclei | unified models | unified models | black hole accretion | black hole accretion | radio and optical jets | radio and optical jets | Homogeneity and isotropy | Homogeneity and isotropy | redshift | redshift | galaxy distance ladder | galaxy distance ladder | Newtonian cosmology | Newtonian cosmology | Roberston-Walker models and cosmography | Roberston-Walker models and cosmography | Early universe | Early universe | primordial nucleosynthesis | primordial nucleosynthesis | recombination | recombination | Cosmic microwave background radiation | Cosmic microwave background radiation | Large-scale structure | Large-scale structure | galaxy formation | galaxy formation

License

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