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12.620J Classical Mechanics: A Computational Approach (MIT) 12.620J Classical Mechanics: A Computational Approach (MIT)

Description

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overl We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overl

Subjects

classical mechanics | classical mechanics | computational classical mechanics | computational classical mechanics | structure and interpretation of classical mechanics | structure and interpretation of classical mechanics | phase space | phase space | lagrangian | lagrangian | action | action | variational principles | variational principles | equation of motion | equation of motion | hamilton principle | hamilton principle | rigid bodies | rigid bodies | Hamiltonian | Hamiltonian | canonical equations | canonical equations | surfaces of section | surfaces of section | canonical transformations | canonical transformations | liouville | liouville | Poincare | Poincare | birkhoff | birkhoff | kam theorem | kam theorem | invariant curves | invariant curves | resonance | resonance | chaos | chaos

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12.620J Classical Mechanics: A Computational Approach (MIT)

Description

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overl

Subjects

classical mechanics | computational classical mechanics | structure and interpretation of classical mechanics | phase space | lagrangian | action | variational principles | equation of motion | hamilton principle | rigid bodies | Hamiltonian | canonical equations | surfaces of section | canonical transformations | liouville | Poincare | birkhoff | kam theorem | invariant curves | resonance | chaos

License

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12.620J Classical Mechanics: A Computational Approach (MIT) 12.620J Classical Mechanics: A Computational Approach (MIT)

Description

12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov 12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov

Subjects

classical mechanics | classical mechanics | phase space | phase space | computation | computation | Lagrangian formulation | Lagrangian formulation | action | action | variational principles | variational principles | equations of motion | equations of motion | Hamilton's principle | Hamilton's principle | conserved quantities | conserved quantities | rigid bodies and tops | rigid bodies and tops | Hamiltonian formulation | Hamiltonian formulation | canonical equations | canonical equations | surfaces of section | surfaces of section | chaos | chaos | canonical transformations | canonical transformations | generating functions | generating functions | Liouville's theorem | Liouville's theorem | Poincar? integral invariants | Poincar? integral invariants | Poincar?-Birkhoff | Poincar?-Birkhoff | KAM theorem | KAM theorem | invariant curves | invariant curves | cantori | cantori | nonlinear resonances | nonlinear resonances | resonance overlap | resonance overlap | transition to chaos | transition to chaos | chaotic motion | chaotic motion | 12.620 | 12.620 | 6.946 | 6.946 | 8.351 | 8.351

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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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8.09 Classical Mechanics II (MIT) 8.09 Classical Mechanics II (MIT)

Description

This course provides a formal introduction to classical mechanics. Topics include Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also provides an extension to continuous and relativistic systems and classical electrodynamics.AcknowledgementsProfessor Wyslouch acknowledges the contributions of MIT Professor Christoph Paus to the development of the 8.09 materials. This course provides a formal introduction to classical mechanics. Topics include Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also provides an extension to continuous and relativistic systems and classical electrodynamics.AcknowledgementsProfessor Wyslouch acknowledges the contributions of MIT Professor Christoph Paus to the development of the 8.09 materials.

Subjects

classical mechanics | classical mechanics | Euler-Lagrange equations | Euler-Lagrange equations | Hamilton's equations of motion | Hamilton's equations of motion | perturbation theory | perturbation theory | Noether's theorem | Noether's theorem | continuous and relativistic systems | continuous and relativistic systems | classical electrodynamics | classical electrodynamics

License

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6.685 Electric Machines (MIT) 6.685 Electric Machines (MIT)

Description

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. 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.

Subjects

electric | electric | machine | machine | transformers | transformers | electromechanical | electromechanical | transducers | transducers | rotating | rotating | linear electric machines | linear electric machines | lumped parameter | lumped parameter | dc | dc | induction | induction | synchronous | synchronous | energy conversion | energy conversion | electromechanics | electromechanics | Mechatronics | Mechatronics | Electromechanical transducers | Electromechanical transducers | rotating electric machines | rotating electric machines | lumped-parameter elecromechanics | lumped-parameter elecromechanics | interaction electromechanics | interaction electromechanics | device characteristics | device characteristics | energy conversion density | energy conversion density | efficiency | efficiency | system interaction characteristics | system interaction characteristics | regulation | regulation | stability | stability | controllability | controllability | response | response | electric machines | electric machines | drive systems | drive systems | electric machinery | electric machinery | electromechanical systems | electromechanical systems | design | design | dynamic parameters | dynamic parameters | phenomena | phenomena | interactions | interactions | classical mechanics | classical mechanics

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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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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

License

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8.01L Physics I: Classical Mechanics (MIT) 8.01L Physics I: Classical Mechanics (MIT)

Description

8.01L is an introductory mechanics course, which covers all the topics covered in 8.01T. The class meets throughout the fall, and continues throughout the Independent Activities Period (IAP). 8.01L is an introductory mechanics course, which covers all the topics covered in 8.01T. The class meets throughout the fall, and continues throughout the Independent Activities Period (IAP).

Subjects

Introductory classical mechanics | Introductory classical mechanics | space | space | time | time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | forces | forces | static equilibrium | static equilibrium | particle dynamics | particle dynamics | conservation of momentum | conservation of momentum | relative inertial frames | relative inertial frames | non-inertial force | non-inertial force | work | work | potential energy | potential energy | conservation of energy | conservation of energy | ideal gas | ideal gas | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics | vibrational motion | vibrational motion | conservation of angular momentum | conservation of angular momentum | central force motions | central force motions | fluid mechanics | fluid mechanics | Technology-Enabled Active Learning | Technology-Enabled Active Learning

License

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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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8.01T 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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8.321 Quantum Theory I (MIT) 8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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8.322 Quantum Theory II (MIT) 8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamics

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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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8.09 Classical Mechanics (MIT) 8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics. This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | classical mechanics | Euler-Lagrange equations | Euler-Lagrange equations | Hamilton's equations of motion | Hamilton's equations of motion | perturbation theory | perturbation theory | Noether's theorem | Noether's theorem | continuous and relativistic systems | continuous and relativistic systems | classical electrodynamics | classical electrodynamics

License

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8.01SC Physics I: Classical Mechanics (MIT)

Description

Physics I is a first-year, first-semester course that provides an introduction to Classical Mechanics. It covers the basic concepts of Newtonian mechanics, fluid mechanics, and kinetic gas theory.

Subjects

classical mechanics | 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 | rotational dynamics | rigid bodies and rotational dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

License

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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.

Subjects

classical mechanics | 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 | rotational dynamics | rigid bodies and rotational dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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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.

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 | 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 | pulsars | binary X-ray sources | gas | dust | magnetic fields | cosmic rays | galaxy | universe | astrophysics | Sun | supernova | globular clusters | open clusters | jets | Newtonian cosmology | dynamical expansion | thermal history | normal galaxies | active galaxies | Greek astronomy | physics | Copernicus | Tycho | Kepler | Galileo | classical mechanics | circular orbits | full kepler orbit problem | electromagnetic radiation | matter | telescopes | detectors | 8.282 | 12.402 | plusars | galaxies | normal and active galaxies | dynamical expansion and thermal history of the Universe

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8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.

Subjects

eigenstates | uncertainty relation | observables | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

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8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.

Subjects

uncertainty relation | observables | eigenstates | eigenvalues | probabilities of the results of measurement | transformation theory | equations of motion | constants of motion | Symmetry in quantum mechanics | representations of symmetry groups | Variational and perturbation approximations | Systems of identical particles and applications | Time-dependent perturbation theory | Scattering theory: phase shifts | Born approximation | The quantum theory of radiation | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | probability | measurement | motion equations | motion constants | symmetry groups | quantum mechanics | variational approximations | perturbation approximations | identical particles | time-dependent perturbation theory | scattering theory | phase shifts | quantum theory of radiation | second quantization | many-body theory | relativistic quantum mechanics | one electron | quantization | EM radiation field | electromagnetic radiation field | adiabatic theorem | Berry?s phase | many-particle systems | Dirac equation | Hilbert spaces | time evolution | Schrodinger picture | Heisenberg picture | interaction picture | classical mechanics | path integrals | EM fields | electromagnetic fields | angular momentum | density operators | quantum measurement | quantum statistics | quantum dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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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.

Subjects

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

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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8.09 Classical Mechanics (MIT)

Description

This class provides a formal introduction to classical mechanics, Euler-Lagrange equations, Hamilton's equations of motion used to describe central force motion, scattering, perturbation theory and Noether's theorem. The course also extends to continuous and relativistic systems and classical electrodynamics.

Subjects

classical mechanics | Euler-Lagrange equations | Hamilton's equations of motion | perturbation theory | Noether's theorem | continuous and relativistic systems | classical electrodynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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12.620J Classical Mechanics: A Computational Approach (MIT)

Description

12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov

Subjects

classical mechanics | phase space | computation | Lagrangian formulation | action | variational principles | equations of motion | Hamilton's principle | conserved quantities | rigid bodies and tops | Hamiltonian formulation | canonical equations | surfaces of section | chaos | canonical transformations | generating functions | Liouville's theorem | Poincar? integral invariants | Poincar?-Birkhoff | KAM theorem | invariant curves | cantori | nonlinear resonances | resonance overlap | transition to chaos | chaotic motion | 12.620 | 6.946 | 8.351

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