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18.701 Algebra I (MIT) 18.701 Algebra I (MIT)

Description

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups. This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.Subjects

Group Theory | Group Theory | Linear Algebra | and Geometry | Linear Algebra | and Geometry | groups | groups | vector spaces | vector spaces | linear transformations | linear transformations | symmetry groups | symmetry groups | bilinear | bilinear | bilinear forms | and linear groups | bilinear forms | and linear groupsLicense

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See all metadata3.40J Physical Metallurgy (MIT) 3.40J Physical Metallurgy (MIT)

Description

This course examines how the presence of 1-, 2- and 3D defects and second phases control the mechanical, electromagnetic and chemical behavior of metals and alloys. It considers point, line and interfacial defects in the context of structural transformations including annealing, spinodal decomposition, nucleation, growth, and particle coarsening. In addition, it concentrates on structure-function relationships, and in particular how grain size, interstitial and substitutional solid solutions, and second-phase particles impact mechanical and other properties. Examples include microelectronic circuitry, magnetic memory and drug delivery applications. This course examines how the presence of 1-, 2- and 3D defects and second phases control the mechanical, electromagnetic and chemical behavior of metals and alloys. It considers point, line and interfacial defects in the context of structural transformations including annealing, spinodal decomposition, nucleation, growth, and particle coarsening. In addition, it concentrates on structure-function relationships, and in particular how grain size, interstitial and substitutional solid solutions, and second-phase particles impact mechanical and other properties. Examples include microelectronic circuitry, magnetic memory and drug delivery applications.Subjects

1- | 2- and 3D defects | 1- | 2- and 3D defects | second phases | second phases | mechanical | electromagnetic and chemical behavior of metals and alloys | mechanical | electromagnetic and chemical behavior of metals and alloys | point | line and interfacial defects | point | line and interfacial defects | structural transformations | structural transformations | annealing | annealing | spinodal decomposition | spinodal decomposition | nucleation | nucleation | growth | growth | particle coarsening | particle coarsening | structure-function relationships | structure-function relationships | grain size | grain size | interstitial and substitutional solid solutions | interstitial and substitutional solid solutions | second-phase particles | second-phase particles | microelectronic circuitry | microelectronic circuitry | magnetic memory | magnetic memory | drug delivery applications | drug delivery applications | 3.40 | 3.40 | 22.71 | 22.71License

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See all metadata3.14 Physical Metallurgy (MIT) 3.14 Physical Metallurgy (MIT)

Description

The central point of this course is to provide a physical basis that links the structure of metals with their properties. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals. The central point of this course is to provide a physical basis that links the structure of metals with their properties. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals.Subjects

processing | structure | and properties of metals and alloys | processing | structure | and properties of metals and alloys | strength | stiffness | and ductility | strength | stiffness | and ductility | crystallography | defects | microstructure | crystallography | defects | microstructure | phase transformations | phase transformations | microstructural evolution | microstructural evolution | alloy thermodynamics and kinetics | alloy thermodynamics and kinetics | structural engineering alloys | structural engineering alloys | steel | steel | aluminum | aluminumLicense

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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 ovSubjects

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 | 8.351License

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See all metadata18.701 Algebra I (MIT) 18.701 Algebra I (MIT)

Description

The subjects to be covered include groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups. The subjects to be covered include groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.Subjects

Group Theory | Group Theory | Linear Algebra | and Geometry | Linear Algebra | and Geometry | groups | groups | vector spaces | vector spaces | linear transformations | linear transformations | symmetry groups | symmetry groups | bilinear | bilinear | bilinear forms | and linear groups | bilinear forms | and linear groupsLicense

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.htmSite sourced from

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This course explores materials and materials processes from the perspective of thermodynamics and kinetics. The thermodynamics aspect includes laws of thermodynamics, solution theory and equilibrium diagrams. The kinetics aspect includes diffusion, phase transformations, and the development of microstructure. This course explores materials and materials processes from the perspective of thermodynamics and kinetics. The thermodynamics aspect includes laws of thermodynamics, solution theory and equilibrium diagrams. The kinetics aspect includes diffusion, phase transformations, and the development of microstructure.Subjects

Laws of thermodynamics | Laws of thermodynamics | solution theory | solution theory | equilibrium diagrams | equilibrium diagrams | kinetics of processes | kinetics of processes | diffusion | diffusion | phase transformations | phase transformations | microstructure development. | microstructure development. | microstructure development | microstructure developmentLicense

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See all metadata8.20 Introduction to Special Relativity (MIT) 8.20 Introduction to Special Relativity (MIT)

Description

Introduces the basic ideas and equations of Einstein's Special Theory of Relativity. Topics include: Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of General Relativity. Introduces the basic ideas and equations of Einstein's Special Theory of Relativity. Topics include: Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of General Relativity.Subjects

Einstein's Special Theory of Relativity | Einstein's Special Theory of Relativity | Lorentz transformations | Lorentz transformations | length contraction | length contraction | ime dilation | ime dilation | time dilation | time dilation | four vectors | four vectors | Lorentz invariants | Lorentz invariants | relativistic energy and momentum | relativistic energy and momentum | relativistic kinematics | relativistic kinematics | Doppler shift | Doppler shift | space-time diagrams | space-time diagrams | relativity paradoxes | relativity paradoxes | General Relativity | General RelativityLicense

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Neural structures and mechanisms mediating the detection, localization and recognition of sounds. We will discuss how acoustic signals are coded by auditory neurons, the impact of these codes on behavioral performance, and the circuitry and cellular mechanisms underlying signal transformations. Topics include temporal coding, neural maps and feature detectors, learning and plasticity, and feedback control. General principles are conveyed by theme discussions of auditory masking, sound localization, musical pitch, speech coding, and cochlear implants. Neural structures and mechanisms mediating the detection, localization and recognition of sounds. We will discuss how acoustic signals are coded by auditory neurons, the impact of these codes on behavioral performance, and the circuitry and cellular mechanisms underlying signal transformations. Topics include temporal coding, neural maps and feature detectors, learning and plasticity, and feedback control. General principles are conveyed by theme discussions of auditory masking, sound localization, musical pitch, speech coding, and cochlear implants.Subjects

hearing | hearing | neural structures | neural structures | auditory masking | auditory masking | acoustics | acoustics | signal transformations | signal transformations | temporal coding | temporal coding | neural maps | neural maps | feature detectors | feature detectors | learning | learning | plasticity | plasticity | feedback control | feedback control | sound localization | sound localization | musical pitch | musical pitch | speech coding | speech coding | cochlear implants | cochlear implantsLicense

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See all metadata3.012 Fundamentals of Materials Science (MIT) 3.012 Fundamentals of Materials Science (MIT)

Description

This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered all This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered allSubjects

fundamentals of bonding | energetics | and structure | fundamentals of bonding | energetics | and structure | Quantum mechanical descriptions of interacting electrons and atoms | Quantum mechanical descriptions of interacting electrons and atoms | Symmetry properties of molecules and solids | Symmetry properties of molecules and solids | complex and disordered materials | complex and disordered materials | thermodynamic functions | thermodynamic functions | equilibrium properties | equilibrium properties | macroscopic behavior | macroscopic behavior | molecular models | molecular models | heat capacities | heat capacities | phase transformations | phase transformations | multiphase equilibria | multiphase equilibria | chemical reactions | chemical reactions | magnetism | magnetism | engineered alloys | engineered alloys | electronic and magnetic materials | electronic and magnetic materials | ionic and network solids | ionic and network solids | polymers | polymers | biomaterials | biomaterials | energetics | energetics | structure | structure | materials science | materials science | electrons | electrons | silicon | silicon | DNA | DNA | electronic bonding | electronic bonding | energy | energy | stability | stability | quantum mechanics | quantum mechanics | atoms | atoms | interactions | interactions | symmetry | symmetry | molecules | molecules | solids | solids | complex material | complex material | disorderd materials | disorderd materials | thermodynamic laws | thermodynamic laws | electronic materials | electronic materials | magnetic materials | magnetic materials | ionic solids | ionic solids | network solids | network solids | statistical mechanics | statistical mechanics | microstates | microstates | microscopic complexity | microscopic complexity | entropy | entropyLicense

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This course offers a critical analysis of contending theories of international relations. Focus is on alternative theoretical assumptions, different analytical structures, and a common core of concepts and content. It also focuses on a comparative analysis of realism(s), liberalism(s), institutionalism(s), and new emergent theories. It also presents a discussion of connections between theories of international relations and major changes in international relations. This course offers a critical analysis of contending theories of international relations. Focus is on alternative theoretical assumptions, different analytical structures, and a common core of concepts and content. It also focuses on a comparative analysis of realism(s), liberalism(s), institutionalism(s), and new emergent theories. It also presents a discussion of connections between theories of international relations and major changes in international relations.Subjects

21st century | 21st century | political theory | political theory | international relations | international relations | realism | realism | liberalism | liberalism | institutionalism | institutionalism | constructivism | constructivism | conflict | conflict | war | war | globalization | globalization | critical analysis | critical analysis | theoretical assumptions | theoretical assumptions | analytical structures | analytical structures | comparative analysis | comparative analysis | neo-realism | neo-realism | neo-liberalism | neo-liberalism | neo-institutionalism | neo-institutionalism | contentions | contentions | environmentalism | environmentalism | emergent dynamics | emergent dynamics | evolutionary dynamics | evolutionary dynamics | warfare | warfare | transformations | transformations | structures | structures | processes | processesLicense

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See all metadata3.40J Physical Metallurgy (MIT) 3.40J Physical Metallurgy (MIT)

Description

The central point of this course is to provide a physical basis that links the structure of materials with their properties, focusing primarily on metals. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals. The central point of this course is to provide a physical basis that links the structure of materials with their properties, focusing primarily on metals. With this understanding in hand, the concepts of alloy design and microstructural engineering are also discussed, linking processing and thermodynamics to the structure and properties of metals.Subjects

point | point | line and interfacial defects | line and interfacial defects | stereographic projection | stereographic projection | annealing | annealing | spinodal decomposition | spinodal decomposition | nucleation | nucleation | growth | growth | particle coarsening | particle coarsening | structure-function relationships | structure-function relationships | interstitial and substitutional solid solutions | interstitial and substitutional solid solutions | processing and structure of metals | processing and structure of metals | strength | strength | stiffness | stiffness | and ductility | and ductility | crystallography | crystallography | phase transformations | phase transformations | microstructural evolution | microstructural evolution | steel | steel | aluminum | aluminumLicense

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This course explores materials and materials processes from the perspective of thermodynamics and kinetics. The thermodynamics aspect includes laws of thermodynamics, solution theory and equilibrium diagrams. The kinetics aspect includes diffusion, phase transformations, and the development of microstructure. This course explores materials and materials processes from the perspective of thermodynamics and kinetics. The thermodynamics aspect includes laws of thermodynamics, solution theory and equilibrium diagrams. The kinetics aspect includes diffusion, phase transformations, and the development of microstructure.Subjects

Laws of thermodynamics | Laws of thermodynamics | solution theory | solution theory | equilibrium diagrams | equilibrium diagrams | kinetics of processes | kinetics of processes | diffusion | diffusion | phase transformations | phase transformations | microstructure development | microstructure developmentLicense

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See all metadata5.04 Principles of Inorganic Chemistry II (MIT) 5.04 Principles of Inorganic Chemistry II (MIT)

Description

This course provides a systematic presentation of the chemical applications of group theory with emphasis on the formal development of the subject and its applications to the physical methods of inorganic chemical compounds. Against the backdrop of electronic structure, the electronic, vibrational, and magnetic properties of transition metal complexes are presented and their investigation by the appropriate spectroscopy described. This course provides a systematic presentation of the chemical applications of group theory with emphasis on the formal development of the subject and its applications to the physical methods of inorganic chemical compounds. Against the backdrop of electronic structure, the electronic, vibrational, and magnetic properties of transition metal complexes are presented and their investigation by the appropriate spectroscopy described.Subjects

inorganic chemistry | inorganic chemistry | group theory | group theory | electronic structure of molecules | electronic structure of molecules | transition metal complexes | transition metal complexes | spectroscopy | spectroscopy | symmetry elements | symmetry elements | mathematical groups | mathematical groups | character tables | character tables | molecular point groups | molecular point groups | Huckel Theory | Huckel Theory | N-Dimensional cyclic systems | N-Dimensional cyclic systems | solid state theory | solid state theory | band theory | band theory | frontier molecular orbitals | frontier molecular orbitals | similarity transformations | similarity transformations | complexes | complexes | organometallic complexes | organometallic complexes | two electron bond | two electron bond | vibrational spectroscopy | vibrational spectroscopy | symmetry | symmetry | overtones | overtones | normal coordinat analysis | normal coordinat analysis | AOM | AOM | single electron CFT | single electron CFT | tanabe-sugano diagram | tanabe-sugano diagram | ligand | ligand | crystal field theory | crystal field theory | LCAO | LCAOLicense

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This course covers the concepts and physical pictures behind various phenomena that appear in interacting many-body systems. Visualization occurs through concentration on path integral, mean-field theories and semi-classical picture of fluctuations around mean-field state. This course covers the concepts and physical pictures behind various phenomena that appear in interacting many-body systems. Visualization occurs through concentration on path integral, mean-field theories and semi-classical picture of fluctuations around mean-field state.Subjects

second quantization | second quantization | path-integrals | path-integrals | condensed matter | condensed matter | Goldstone modes | Goldstone modes | rigidity | rigidity | topological defects | topological defects | Mean field theory | Mean field theory | Landau Fermi Liquid Theory | Landau Fermi Liquid Theory | BCS superconductivity | BCS superconductivity | Quantum Phase Transitions | Quantum Phase Transitions | Renormalization group | Renormalization group | Duality transformations | Duality transformations | Luttinger Liquid Theory | Luttinger Liquid Theory | bosonization | bosonization | broken symmetry | broken symmetry | fractionalization | fractionalization | Fractional quantum Hall effect | Fractional quantum Hall effect | spin liquids | spin liquids | gauge theories in condensed matter | gauge theories in condensed matterLicense

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See all metadata8.20 Introduction to Special Relativity (MIT) 8.20 Introduction to Special Relativity (MIT)

Description

This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.AcknowledgementsProf. Knuteson wishes to acknowledge that this course was originally designed and taught by Prof. Robert Jaffe. This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.AcknowledgementsProf. Knuteson wishes to acknowledge that this course was originally designed and taught by Prof. Robert Jaffe.Subjects

Einstein's Special Theory of Relativity | Einstein's Special Theory of Relativity | Lorentz transformations | Lorentz transformations | length contraction | length contraction | time dilation | time dilation | four vectors | four vectors | Lorentz invariants | Lorentz invariants | relativistic energy and momentum | relativistic energy and momentum | relativistic kinematics | relativistic kinematics | Doppler shift | Doppler shift | space-time diagrams | space-time diagrams | relativity paradoxes | relativity paradoxes | General Relativity | General RelativityLicense

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See all metadata9.85 Infant and Early Childhood Cognition (MIT) 9.85 Infant and Early Childhood Cognition (MIT)

Description

This course is an introduction to cognitive development focusing on children's understanding of objects, agents, and causality. It develops a critical understanding of experimental design. The course discusses how developmental research might address philosophical questions about the origins of knowledge, appearance and reality, and the problem of other minds. It provides instruction and practice in written communication as needed for cognitive science research (including critical reviews of journal papers, a literature review and an original research proposal), as well as instruction and practice in oral communication in the form of a poster presentation of a journal paper. This course is an introduction to cognitive development focusing on children's understanding of objects, agents, and causality. It develops a critical understanding of experimental design. The course discusses how developmental research might address philosophical questions about the origins of knowledge, appearance and reality, and the problem of other minds. It provides instruction and practice in written communication as needed for cognitive science research (including critical reviews of journal papers, a literature review and an original research proposal), as well as instruction and practice in oral communication in the form of a poster presentation of a journal paper.Subjects

infant cognition | infant cognition | early childhood cognition | early childhood cognition | cognitive development | cognitive development | developmental psychology | developmental psychology | psychology | psychology | developmental research | developmental research | Piaget | Piaget | object knowledge | object knowledge | object individuation | object individuation | object concept | object concept | agents | agents | causal knowledge | causal knowledge | theory of mind | theory of mind | causation | causation | causal transformations | causal transformationsLicense

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See all metadata10.626 Electrochemical Energy Systems (MIT) 10.626 Electrochemical Energy Systems (MIT)

Description

10.626 introduces principles and mathematical models of electrochemical energy conversion and storage. Students study equivalent circuits, thermodynamics, reaction kinetics, transport phenomena, electrostatics, porous media, and phase transformations. In addition, this course includes applications to batteries, fuel cells, supercapacitors, and electrokinetics. 10.626 introduces principles and mathematical models of electrochemical energy conversion and storage. Students study equivalent circuits, thermodynamics, reaction kinetics, transport phenomena, electrostatics, porous media, and phase transformations. In addition, this course includes applications to batteries, fuel cells, supercapacitors, and electrokinetics.Subjects

energy | energy | electrochemical energy conversion | electrochemical energy conversion | electrochemical energy storage | electrochemical energy storage | transport phenomena | transport phenomena | diffuse charge | diffuse charge | Faradaic reactions | Faradaic reactions | statistical thermodynamics | statistical thermodynamics | phase transformations | phase transformations | rechargeable batteries | rechargeable batteries | fuel cells | fuel cells | supercapacitors | supercapacitors | solar cells | solar cells | desalination | desalination | electrokinetic energy conversion | electrokinetic energy conversionLicense

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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 overlSubjects

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 | chaosLicense

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See all metadata16.61 Aerospace Dynamics (MIT) 16.61 Aerospace Dynamics (MIT)

Description

This undergraduate course builds upon the dynamics content of Unified Engineering, a sophomore course taught in the Department of Aeronautics and Astronautics at MIT. Vector kinematics are applied to translation and rotation of rigid bodies. Newtonian and Lagrangian methods are used to formulate and solve equations of motion. Additional numerical methods are presented for solving rigid body dynamics problems. Examples and problems describe applications to aircraft flight dynamics and spacecraft attitude dynamics. This undergraduate course builds upon the dynamics content of Unified Engineering, a sophomore course taught in the Department of Aeronautics and Astronautics at MIT. Vector kinematics are applied to translation and rotation of rigid bodies. Newtonian and Lagrangian methods are used to formulate and solve equations of motion. Additional numerical methods are presented for solving rigid body dynamics problems. Examples and problems describe applications to aircraft flight dynamics and spacecraft attitude dynamics.Subjects

aerospace dynamics | aerospace dynamics | Newtonian dynamics | Newtonian dynamics | 3D motion | 3D motion | gyroscopic | gyroscopic | rotational | rotational | dynamics | dynamics | coordinate transformations | coordinate transformations | Lagrangian | Lagrangian | motion | motion | aircraft | aircraft | flight | flight | stability | stability | spacecraft | spacecraftLicense

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See all metadata18.S996 Category Theory for Scientists (MIT) 18.S996 Category Theory for Scientists (MIT)

Description

The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields. The goal of this class is to prove that category theory is a powerful language for understanding and formalizing common scientific models. The power of the language will be tested by its ability to penetrate into taken-for-granted ideas, either by exposing existing weaknesses or flaws in our understanding, or by highlighting hidden commonalities across scientific fields.Subjects

Sets | Sets | functions | functions | commutative diagrams | commutative diagrams | products | products | coproducts | coproducts | finite limits | finite limits | monoids | monoids | groups | groups | graphs | graphs | orders | orders | schemas | schemas | instances | instances | databases | databases | categories | categories | functors | functors | mathematics | mathematics | natural transformations | natural transformations | limits | limits | colimits | colimits | adjoint functors | adjoint functors | monads | monads | operads | operads | isomorphism | isomorphism | molecular dynamics | molecular dynamics | olog | ologLicense

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.htmSite sourced from

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See all metadata18.701 Algebra I (MIT) 18.701 Algebra I (MIT)

Description

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups. This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.Subjects

Group Theory | Group Theory | Linear Algebra | Linear Algebra | Geometry | Geometry | groups | groups | vector spaces | vector spaces | linear transformations | linear transformations | symmetry groups | symmetry groups | bilinear forms | bilinear forms | linear groups | linear groupsLicense

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.htmSite sourced from

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This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications. This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.Subjects

Random matrix theory | Random matrix theory | Matrix Jacobians | Matrix Jacobians | Wishart Matrices | Wishart Matrices | Wigner's Semi-Circular laws | Wigner's Semi-Circular laws | Matrix beta ensembles | Matrix beta ensembles | free probability | free probability | spherical coordinates | spherical coordinates | wedging | wedging | Plucker coordinates | Plucker coordinates | matrix factorizations | matrix factorizations | householder transformations | householder transformations | Stiefel manifold | Stiefel manifold | Cauchey-Binet theorem | Cauchey-Binet theorem | Telatar's paper | Telatar's paper | level densities | level densities | orthogonal polynomials | orthogonal polynomials | matrix integrals | matrix integrals | hypergeometric functions | hypergeometric functions | wireless communictions | wireless communictions | eigenvalue density | eigenvalue density | sample covariance matrices | sample covariance matrices | Marcenko-Pastur theorem | Marcenko-Pastur theorem | wireless communications | wireless communicationsLicense

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.htmSite sourced from

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See all metadata21L.015 Introduction to Media Studies (MIT) 21L.015 Introduction to Media Studies (MIT)

Description

Introduction to Media Studies is designed for students who have grown up in a rapidly changing global multimedia environment and want to become more literate and critical consumers and producers of culture. Through an interdisciplinary comparative and historical lens, the course defines "media" broadly as including oral, print, theatrical, photographic, broadcast, cinematic, and digital cultural forms and practices. The course looks at the nature of mediated communication, the functions of media, the history of transformations in media and the institutions that help define media's place in society. Over the course of the semester we explore different theoretical perspectives on the role and power of media in society in influencing our social values, political beliefs, identities Introduction to Media Studies is designed for students who have grown up in a rapidly changing global multimedia environment and want to become more literate and critical consumers and producers of culture. Through an interdisciplinary comparative and historical lens, the course defines "media" broadly as including oral, print, theatrical, photographic, broadcast, cinematic, and digital cultural forms and practices. The course looks at the nature of mediated communication, the functions of media, the history of transformations in media and the institutions that help define media's place in society. Over the course of the semester we explore different theoretical perspectives on the role and power of media in society in influencing our social values, political beliefs, identitiesSubjects

literature | literature | comparative mass media | comparative mass media | communication | communication | modern culture | modern culture | social values | social values | politics | politics | radio | radio | television | television | film | film | print | print | digital techonology | digital techonology | history | history | storytelling | storytelling | advertising | advertising | oral | oral | culture | culture | photography | photography | oral culture | oral culture | cultural forms | cultural forms | political beliefs | political beliefs | economics | economics | mediated communication | mediated communication | class politics | class politics | gender | gender | race | race | identity | identity | behavior | behavior | criticism | criticism | global multimedia environment | global multimedia environment | consumers | consumers | theatrical | theatrical | photographic | photographic | broadcast | broadcast | cinematic | cinematic | cinema | cinema | theatre | theatre | printing | printing | publishing | publishing | books | books | electronic | electronic | transformations | transformations | narrative | narrativeLicense

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.htmSite sourced from

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See all metadata21L.007J After Columbus (MIT) 21L.007J After Columbus (MIT)

Description

Sometime after 1492, the concept of the New World or America came into being, and this concept appeared differently - as an experience or an idea - for different people and in different places. This semester, we will read three groups of texts: first, participant accounts of contact between native Americans and French or English speaking Europeans, both in North America and in the Caribbean and Brazil; second, transformations of these documents into literary works by contemporaries; third, modern texts which take these earlier materials as a point of departure for rethinking the experience and aftermath of contact. The reading will allow us to compare perspectives across time and space, across the cultural geographies of religion, nation and ethnicity, and finally across a range of genres Sometime after 1492, the concept of the New World or America came into being, and this concept appeared differently - as an experience or an idea - for different people and in different places. This semester, we will read three groups of texts: first, participant accounts of contact between native Americans and French or English speaking Europeans, both in North America and in the Caribbean and Brazil; second, transformations of these documents into literary works by contemporaries; third, modern texts which take these earlier materials as a point of departure for rethinking the experience and aftermath of contact. The reading will allow us to compare perspectives across time and space, across the cultural geographies of religion, nation and ethnicity, and finally across a range of genresSubjects

21L.007 | 21L.007 | 21G.020 | 21G.020 | columbus | columbus | literature | literature | north | america | north | america | french | french | history | history | europe | europe | caribbean | caribbean | brazil | brazil | modern | modern | religion | religion | ethnicity | ethnicity | culture | culture | shakespeare | shakespeare | defoe | defoe | rowlandson | rowlandson | walcott | walcott | montaigne | montaigne | de lery | de lery | coetzee | coetzee | essay | essay | narrative | narrative | novel | novel | poetry | poetry | drama | drama | film | film | report | report | north america | north america | New World | New World | America | America | Native Americans | Native Americans | English | English | Europeans | Europeans | North America | North America | literary transformations | literary transformations | nation | nation | captivity narratives | captivity narratives | Michel Montaigne | Michel Montaigne | William Shakespeare | William Shakespeare | Jean de L?ry | Jean de L?ry | Daniel Defoe | Daniel Defoe | Mary Rowlandson | Mary Rowlandson | Derek Walcott | Derek Walcott | J. M. Coetzee | J. M. Coetzee | Christopher Columbus | Christopher Columbus | 21F.020J | 21F.020J | 21F.020 | 21F.020License

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.htmSite sourced from

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See all metadataMAS.962 Digital Typography (MIT) MAS.962 Digital Typography (MIT)

Description

This class introduces studies in the algorithmic manipulation of type as word, symbol, and form. Problems covered will include semantic filtering, inherently unstable letterforms, and spoken letters. The history and traditions of typography, and their entry into the digital age, will be studied. Weekly assignments using Java® will explore new ways of looking at and manipulating type. This class introduces studies in the algorithmic manipulation of type as word, symbol, and form. Problems covered will include semantic filtering, inherently unstable letterforms, and spoken letters. The history and traditions of typography, and their entry into the digital age, will be studied. Weekly assignments using Java® will explore new ways of looking at and manipulating type.Subjects

digital typography | digital typography | design | design | type | type | text | text | visual arts | visual arts | computation | computation | digital artworks | digital artworks | java | java | interactive design | interactive design | interactive media | interactive media | aesthetics | aesthetics | signal processing | signal processing | interaction design | interaction design | programming | programming | transformations | transformations | communication | communication | typographic design | typographic designLicense

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.htmSite sourced from

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