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3.016 Mathematics for Materials Scientists and Engineers (MIT) 3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site. The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.

Subjects

energetics | energetics | materials structure and symmetry: applied fields | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | mechanics and physics of solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalues | eigenvalues | eigenvectors | eigenvectors | quadratic forms | quadratic forms | tensor operations | tensor operations | symmetry operations | symmetry operations | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walks | random walks | mathematical technicques | mathematical technicques | materials science | materials science | materials engineering | materials engineering | materials structure | materials structure | symmetry | symmetry | applied fields | applied fields | materials response | materials response | solids mechanics | solids mechanics | solids physics | solids physics | soft materials | soft materials | multi-variable calculus | multi-variable calculus | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | applied mathematics | applied mathematics | mathematical techniques | mathematical techniques

License

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5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.

Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scattering

License

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5.068 Physical Methods in Inorganic Chemistry (MIT) 5.068 Physical Methods in Inorganic Chemistry (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.

Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scattering

License

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3.016 Mathematics for Materials Scientists and Engineers (MIT) 3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor C This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor C

Subjects

energetics | energetics | visualization | visualization | graph | graph | plot | plot | chart | chart | materials science | materials science | DMSE | DMSE | structure | structure | symmetry | symmetry | mechanics | mechanics | physicss | physicss | solids and soft materials | solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalue | eigenvalue | eigenvector | eigenvector | quadratic form | quadratic form | tensor operation | tensor operation | symmetry operation | symmetry operation | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | ODE | ODE | solution | solution | vector | vector | matrix | matrix | determinant | determinant | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walk | random walk | Mathematica | Mathematica | simulation | simulation

License

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5.069 Crystal Structure Analysis (MIT) 5.069 Crystal Structure Analysis (MIT)

Description

This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases. This course covers the following topics: X-ray diffraction: symmetry, space groups, geometry of diffraction, structure factors, phase problem, direct methods, Patterson methods, electron density maps, structure refinement, how to grow good crystals, powder methods, limits of X-ray diffraction methods, and structure data bases.

Subjects

crystallography | crystallography | inorganic chemistry | inorganic chemistry | physical methods | physical methods | crystal structure determination | crystal structure determination | 3D structure | 3D structure | x-ray crystallagraphy | x-ray crystallagraphy | diffraction | diffraction | x-rays | x-rays | symmetry | symmetry | phasing | phasing | crystal structure | crystal structure | symmetry operations | symmetry operations | crystal lattice | crystal lattice | structure refinement | structure refinement | electron density maps | electron density maps | space group determination | space group determination | anomalous scattering | anomalous scattering

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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5.04 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 | LCAO

License

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6.055J The Art of Approximation in Science and Engineering (MIT) 6.055J The Art of Approximation in Science and Engineering (MIT)

Description

This course teaches simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications are drawn from the physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis is on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world. This course teaches simple reasoning techniques for complex phenomena: divide and conquer, dimensional analysis, extreme cases, continuity, scaling, successive approximation, balancing, cheap calculus, and symmetry. Applications are drawn from the physical and biological sciences, mathematics, and engineering. Examples include bird and machine flight, neuron biophysics, weather, prime numbers, and animal locomotion. Emphasis is on low-cost experiments to test ideas and on fostering curiosity about phenomena in the world.

Subjects

approximation | approximation | science | science | engineering | engineering | managing complexity | managing complexity | divide and conquer | divide and conquer | heterogeneous hierarchies | heterogeneous hierarchies | homogeneous hierarchies | homogeneous hierarchies | proportional reasoning | proportional reasoning | conservation/box models | conservation/box models | dimensional analysis | dimensional analysis | special cases | special cases | extreme cases | extreme cases | discretization | discretization | spring models | spring models | symmetry | symmetry | invariance | invariance | discarding information | discarding information | oil imports | oil imports | tree representations | tree representations | gold | gold | random walks | random walks | UNIX | UNIX | triangle bisection | triangle bisection | pentagonal heat flow | pentagonal heat flow | jump heights | jump heights | simple calculus | simple calculus | drag | drag | cycling | cycling | swimming | swimming | flying | flying | flight | flight | algebraic symmetry | algebraic symmetry | densities | densities | hydrogen size | hydrogen size | bending of light | bending of light | Buckingham Pi Theorem | Buckingham Pi Theorem | pulley acceleration | pulley acceleration | waves | waves

License

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8.324 Relativistic Quantum Field Theory II (MIT) 8.324 Relativistic Quantum Field Theory II (MIT)

Description

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material.

Subjects

Quantum Field Theory | Quantum Field Theory | nonabelian gauge theories | nonabelian gauge theories | BRST symmetry | BRST symmetry | Perturbation theory anomalies | Perturbation theory anomalies | Renormalization | Renormalization | symmetry breaking | symmetry breaking | Critical exponents | Critical exponents | scalar field theory | scalar field theory | Conformal field theory | Conformal field theory

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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8.321 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

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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8.322 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

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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8.324 Relativistic Quantum Field Theory II (MIT) 8.324 Relativistic Quantum Field Theory II (MIT)

Description

This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics include functional path integrals, renormalization and renormalization groups, quantization of nonabelian gauge theories, BRST symmetry, renormalization and symmetry breaking, critical exponents and scalar field theory, and perturbation theory anomalies. This course is the second course of the quantum field theory trimester sequence beginning with Relativistic Quantum Field Theory I (8.323) and ending with Relativistic Quantum Field Theory III (8.325). It develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics include functional path integrals, renormalization and renormalization groups, quantization of nonabelian gauge theories, BRST symmetry, renormalization and symmetry breaking, critical exponents and scalar field theory, and perturbation theory anomalies.

Subjects

Quantum Field Theory | Quantum Field Theory | nonabelian gauge theories | nonabelian gauge theories | BRST symmetry | BRST symmetry | Perturbation theory anomalies | Perturbation theory anomalies | Renormalization | Renormalization | symmetry breaking | symmetry breaking | Critical exponents | Critical exponents | scalar field theory | scalar field theory | Conformal field theory | Conformal field theory

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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3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.

Subjects

energetics | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | linear algebra | orthonormal basis | eigenvalues | eigenvectors | quadratic forms | tensor operations | symmetry operations | calculus | complex analysis | differential equations | theory of distributions | fourier analysis | random walks | mathematical technicques | materials science | materials engineering | materials structure | symmetry | applied fields | materials response | solids mechanics | solids physics | soft materials | multi-variable calculus | ordinary differential equations | partial differential equations | applied mathematics | mathematical techniques

License

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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 groups

License

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5.04 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. The electronic structure of molecules will be developed. Against this backdrop, the optical, vibrational, and magnetic properties of transition metal complexes are presented and their investigation by the appropriate spectroscopy is 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. The electronic structure of molecules will be developed. Against this backdrop, the optical, vibrational, and magnetic properties of transition metal complexes are presented and their investigation by the appropriate spectroscopy is described.

Subjects

inorganic chemistry | inorganic chemistry | group theory | group theory | transition metal complexes | transition metal complexes | symmetry element | symmetry element | point group | point group | LCAO | LCAO | metal metal bonding | metal metal bonding | vibrational spectroscopy | vibrational spectroscopy | character tables | character tables | sandwich compounds | sandwich compounds

License

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

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18.701 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 groups

License

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18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics (MIT) 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics (MIT)

Description

This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.

Subjects

linear algebra | linear algebra | eigensystems for Maxwell's equations | eigensystems for Maxwell's equations | symmetry groups | symmetry groups | representation theory | representation theory | Bloch's theorem | Bloch's theorem | numerical eigensolver methods | numerical eigensolver methods | time and frequency-domain computation | time and frequency-domain computation | perturbation theory | perturbation theory | coupled-mode theories | coupled-mode theories | waveguide theory | waveguide theory | adiabatic transitions | adiabatic transitions | Optical phenomena | Optical phenomena | photonic crystals | photonic crystals | band gaps | band gaps | anomalous diffraction | anomalous diffraction | mechanisms for optical confinement | mechanisms for optical confinement | optical fibers | optical fibers | integrated optical devices | integrated optical devices

License

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5.841 Crystal Structure Refinement (MIT) 5.841 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

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8.231 Physics of Solids I (MIT) 8.231 Physics of Solids I (MIT)

Description

The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetism The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetism

Subjects

periodic structure and symmetry of crystals | periodic structure and symmetry of crystals | diffraction | diffraction | reciprocal lattice | reciprocal lattice | chemical bonding | chemical bonding | phonons | phonons | thermal properties | thermal properties | free electron gas | free electron gas | model of metals | model of metals | Bloch theorem and band structure | Bloch theorem and band structure | nearly free electron approximation | nearly free electron approximation | tight binding method | tight binding method | Fermi surface | Fermi surface | semiconductors | semiconductors | electrons | electrons | holes | holes | impurities | impurities | optical properties | optical properties | excitons | excitons | magnetism | magnetism

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8.811 Particle Physics II (MIT) 8.811 Particle Physics II (MIT)

Description

8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments.  Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories, 8.811, Particle Physics II, describes essential research in High Energy Physics. We derive the Standard Model (SM) first using a bottom up method based on Unitarity, in addition to the usual top down method using SU3xSU2xU1. We describe and analyze several classical experiments, which established the SM, as examples on how to design experiments.  Further topics include heavy flavor physics, high-precision tests of the Standard Model, neutrino oscillations, searches for new phenomena (compositeness, supersymmetry, technical color, and GUTs), and discussion of expectations from future accelerators (B factory, LHC, large electron-positron linear colliders, etc). The term paper requires the students to have constant discussions with the instructor throughout the semester on theories,

Subjects

electron-positron and proton-antiproton collisions | electron-positron and proton-antiproton collisions | electroweak phenomena | electroweak phenomena | heavy flavor physics | and high-precision tests of the Standard Model | heavy flavor physics | and high-precision tests of the Standard Model | compositeness | supersymmetry | and GUTs | compositeness | supersymmetry | and GUTs | Top Quark | and expectations from future accelerators (B factory | LHC) | Top Quark | and expectations from future accelerators (B factory | LHC)

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3.012 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 all

Subjects

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 | entropy

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8.324 Quantum Field Theory II (MIT) 8.324 Quantum Field Theory II (MIT)

Description

8.324 is the second term of the quantum field theory trimester sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: Functional path integrals. Renormalization and renormalization group. Quantization of nonabelian gauge theories. BRST symmetry. Renormalization and symmetry breaking. Critical exponents and scalar field theory. Perturbation theory anomalies. 8.324 is the second term of the quantum field theory trimester sequence. Develops in depth some of the topics discussed in 8.323 and introduces some advanced material. Topics: Functional path integrals. Renormalization and renormalization group. Quantization of nonabelian gauge theories. BRST symmetry. Renormalization and symmetry breaking. Critical exponents and scalar field theory. Perturbation theory anomalies.

Subjects

Quantum Field Theory | Quantum Field Theory | nonabelian gauge theories | nonabelian gauge theories | BRST symmetry | BRST symmetry | Nonabelian Gauge Theories | Nonabelian Gauge Theories | Perturbation Theory Anomalies | Perturbation Theory Anomalies | Renormalization | Renormalization | Symmetry Breaking | Symmetry Breaking | Critical Exponents | Critical Exponents | Scalar Field Theory | Scalar Field Theory | Conformal Field Theory | Conformal Field Theory

License

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3.21 Kinetic Processes in Materials (MIT) 3.21 Kinetic Processes in Materials (MIT)

Description

This course presents a unified treatment of phenomenological and atomistic kinetic processes in materials. It provides the foundation for the advanced understanding of processing, microstructural evolution, and behavior for a broad spectrum of materials. The course emphasizes analysis and development of rigorous comprehension of fundamentals. Topics include: irreversible thermodynamics; diffusion; nucleation; phase transformations; fluid and heat transport; morphological instabilities; gas-solid, liquid-solid, and solid-solid reactions. This course presents a unified treatment of phenomenological and atomistic kinetic processes in materials. It provides the foundation for the advanced understanding of processing, microstructural evolution, and behavior for a broad spectrum of materials. The course emphasizes analysis and development of rigorous comprehension of fundamentals. Topics include: irreversible thermodynamics; diffusion; nucleation; phase transformations; fluid and heat transport; morphological instabilities; gas-solid, liquid-solid, and solid-solid reactions.

Subjects

Thermodynamics | Thermodynamics | field | field | gradient | gradient | continuity equation | continuity equation | irreversible thermodynamics | irreversible thermodynamics | entropy | entropy | Onsager's symmetry principle | Onsager's symmetry principle | diffusion | diffusion | capillarity | capillarity | stress | stress | diffusion equation | diffusion equation | crystal | crystal | jump process | jump process | jump rate | jump rate | diffusivity | diffusivity | interstitial | interstitial | Kroger-Vink | Kroger-Vink | grain boundary | grain boundary | isotropic | isotropic | Rayleigh instability | Rayleigh instability | Gibbs-Thomson | Gibbs-Thomson | particle coarsening | particle coarsening | growth kinetics | growth kinetics | phase transformation | phase transformation | nucleation | nucleation | spinoldal decomposition | spinoldal decomposition

License

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5.067 Crystal Structure Refinement (MIT) 5.067 Crystal Structure Refinement (MIT)

Description

This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules. This course in crystal structure refinement examines the practical aspects of crystal structure determination from data collection strategies to data reduction and basic and advanced refinement problems of organic and inorganic molecules.

Subjects

chemistry | chemistry | crystal structure refinement | crystal structure refinement | practical aspects | practical aspects | crystal structure determination | crystal structure determination | data collection | data collection | strategies | strategies | data reduction | data reduction | refinement problems | refinement problems | organic | organic | inorganic | inorganic | molecules | molecules | SHELXL | SHELXL | hydrogen atoms | hydrogen atoms | disorder | disorder | pseudo symmetry | pseudo symmetry | merohedral twins | merohedral twins | pseudo-merohedral twins | pseudo-merohedral twins | twinning | twinning | non-merohedral twins | non-merohedral twins | PLATON | PLATON

License

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6.856J Randomized Algorithms (MIT) 6.856J Randomized Algorithms (MIT)

Description

This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms. This course examines how randomization can be used to make algorithms simpler and more efficient via random sampling, random selection of witnesses, symmetry breaking, and Markov chains. Topics covered include: randomized computation; data structures (hash tables, skip lists); graph algorithms (minimum spanning trees, shortest paths, minimum cuts); geometric algorithms (convex hulls, linear programming in fixed or arbitrary dimension); approximate counting; parallel algorithms; online algorithms; derandomization techniques; and tools for probabilistic analysis of algorithms.

Subjects

Randomized Algorithms | Randomized Algorithms | algorithms | algorithms | efficient in time and space | efficient in time and space | randomization | randomization | computational problems | computational problems | data structures | data structures | graph algorithms | graph algorithms | optimization | optimization | geometry | geometry | Markov chains | Markov chains | sampling | sampling | estimation | estimation | geometric algorithms | geometric algorithms | parallel and distributed algorithms | parallel and distributed algorithms | parallel and ditributed algorithm | parallel and ditributed algorithm | parallel and distributed algorithm | parallel and distributed algorithm | random sampling | random sampling | random selection of witnesses | random selection of witnesses | symmetry breaking | symmetry breaking | randomized computational models | randomized computational models | hash tables | hash tables | skip lists | skip lists | minimum spanning trees | minimum spanning trees | shortest paths | shortest paths | minimum cuts | minimum cuts | convex hulls | convex hulls | linear programming | linear programming | fixed dimension | fixed dimension | arbitrary dimension | arbitrary dimension | approximate counting | approximate counting | parallel algorithms | parallel algorithms | online algorithms | online algorithms | derandomization techniques | derandomization techniques | probabilistic analysis | probabilistic analysis | computational number theory | computational number theory | simplicity | simplicity | speed | speed | design | design | basic probability theory | basic probability theory | application | application | randomized complexity classes | randomized complexity classes | game-theoretic techniques | game-theoretic techniques | Chebyshev | Chebyshev | moment inequalities | moment inequalities | limited independence | limited independence | coupon collection | coupon collection | occupancy problems | occupancy problems | tail inequalities | tail inequalities | Chernoff bound | Chernoff bound | conditional expectation | conditional expectation | probabilistic method | probabilistic method | random walks | random walks | algebraic techniques | algebraic techniques | probability amplification | probability amplification | sorting | sorting | searching | searching | combinatorial optimization | combinatorial optimization | approximation | approximation | counting problems | counting problems | distributed algorithms | distributed algorithms | 6.856 | 6.856 | 18.416 | 18.416

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