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18.238 Geometry and Quantum Field Theory (MIT) 18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory. Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | perturbative quantum field theory | classical field theory | classical field theory | free quantum theories | free quantum theories | Feynman diagrams | Feynman diagrams | Renormalization theory | Renormalization theory | Local operators | Local operators | Operator product expansion | Operator product expansion | Renormalization group equation | Renormalization group equation | classical | classical | field | field | theory | theory | Feynman | Feynman | diagrams | diagrams | free | free | quantum | quantum | theories | theories | local | local | operators | operators | product | product | expansion | expansion | perturbative | perturbative | renormalization | renormalization | group | group | equations | equations | functional | functional | function | function | intergrals | intergrals | operator | operator | QFT | QFT | string | string | physics | physics | mathematics | mathematics | geometry | geometry | geometric | geometric | algebraic | algebraic | topology | topology | number | number | 0-dimensional | 0-dimensional | 1-dimensional | 1-dimensional | d-dimensional | d-dimensional | supergeometry | supergeometry | supersymmetry | supersymmetry | conformal | conformal | stationary | stationary | phase | phase | formula | formula | calculus | calculus | combinatorics | combinatorics | matrix | matrix | mechanics | mechanics | lagrangians | lagrangians | hamiltons | hamiltons | least | least | action | action | principle | principle | limits | limits | formalism | formalism | Feynman-Kac | Feynman-Kac | current | current | charges | charges | Noether?s | Noether?s | theorem | theorem | path | path | integral | integral | approach | approach | divergences | divergences | functional integrals | functional integrals | fee quantum theories | fee quantum theories | renormalization theory | renormalization theory | local operators | local operators | operator product expansion | operator product expansion | renormalization group equation | renormalization group equation | mathematical language | mathematical language | string theory | string theory | 0-dimensional QFT | 0-dimensional QFT | Stationary Phase Formula | Stationary Phase Formula | Matrix Models | Matrix Models | Large N Limits | Large N Limits | 1-dimensional QFT | 1-dimensional QFT | Classical Mechanics | Classical Mechanics | Least Action Principle | Least Action Principle | Path Integral Approach | Path Integral Approach | Quantum Mechanics | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Operator Formalism | Feynman-Kac Formula | Feynman-Kac Formula | d-dimensional QFT | d-dimensional QFT | Formalism of Classical Field Theory | Formalism of Classical Field Theory | Currents | Currents | Noether?s Theorem | Noether?s Theorem | Path Integral Approach to QFT | Path Integral Approach to QFT | Perturbative Expansion | Perturbative Expansion | Renormalization Theory | Renormalization Theory | Conformal Field Theory | Conformal Field Theory | algebraic topology | algebraic topology | algebraic geometry | algebraic geometry | number theory | number theory

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8.05 Quantum Physics II (MIT) 8.05 Quantum Physics II (MIT)

Description

This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen

Subjects

General formalism of quantum mechanics: states | General formalism of quantum mechanics: states | operators | operators | Dirac notation | Dirac notation | representations | representations | measurement theory | measurement theory | Harmonic oscillator: operator algebra | Harmonic oscillator: operator algebra | states | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | bound and scattering states | qualitative analysis of wavefunctions | qualitative analysis of wavefunctions | Angular momentum: operators | Angular momentum: operators | commutator algebra | commutator algebra | eigenvalues and eigenstates | eigenvalues and eigenstates | spherical harmonics | spherical harmonics | Spin: Stern-Gerlach devices and measurements | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | nuclear magnetic resonance | spin and statistics | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | spin systems | allotropic forms of hydrogen | allotropic forms of hydrogen | Angular momentum | Angular momentum | Harmonic oscillator | Harmonic oscillator | operator algebra | operator algebra | Spin | Spin | Stern-Gerlach devices and measurements | Stern-Gerlach devices and measurements | central potentials and the radial equation | central potentials and the radial equation | Clebsch-Gordan series and coefficients | Clebsch-Gordan series and coefficients | quantum physics | quantum physics

License

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8.05 Quantum Physics II (MIT) 8.05 Quantum Physics II (MIT)

Description

Together, this course and 8.06: Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum. Together, this course and 8.06: Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

Subjects

General formalism of quantum mechanics: states | General formalism of quantum mechanics: states | operators | operators | Dirac notation | Dirac notation | representations | representations | measurement theory | measurement theory | Harmonic oscillator: operator algebra | Harmonic oscillator: operator algebra | states | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | bound and scattering states | qualitative analysis of wavefunctions | qualitative analysis of wavefunctions | Angular momentum: operators | Angular momentum: operators | commutator algebra | commutator algebra | eigenvalues and eigenstates | eigenvalues and eigenstates | spherical harmonics | spherical harmonics | Spin: Stern-Gerlach devices and measurements | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | nuclear magnetic resonance | spin and statistics | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | spin systems | allotropic forms of hydrogen | allotropic forms of hydrogen | Angular momentum | Angular momentum | Harmonic oscillator | Harmonic oscillator | operator algebra | operator algebra | Spin | Spin | Stern-Gerlach devices and measurements | Stern-Gerlach devices and measurements | central potentials and the radial equation | central potentials and the radial equation | Clebsch-Gordan series and coefficients | Clebsch-Gordan series and coefficients | quantum physics | quantum physics | 8. Quantum mechanics in three-dimensions: central potentials and the radial equation | 8. Quantum mechanics in three-dimensions: central potentials and the radial equation | and allotropic forms of hydrogen | and allotropic forms of hydrogen

License

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18.238 Geometry and Quantum Field Theory (MIT)

Description

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of classical field theory, free quantum theories and Feynman diagrams. The goal is to discuss, using mathematical language, a number of basic notions and results of QFT that are necessary to understand talks and papers in QFT and String Theory.

Subjects

perturbative quantum field theory | classical field theory | free quantum theories | Feynman diagrams | Renormalization theory | Local operators | Operator product expansion | Renormalization group equation | classical | field | theory | Feynman | diagrams | free | quantum | theories | local | operators | product | expansion | perturbative | renormalization | group | equations | functional | function | intergrals | operator | QFT | string | physics | mathematics | geometry | geometric | algebraic | topology | number | 0-dimensional | 1-dimensional | d-dimensional | supergeometry | supersymmetry | conformal | stationary | phase | formula | calculus | combinatorics | matrix | mechanics | lagrangians | hamiltons | least | action | principle | limits | formalism | Feynman-Kac | current | charges | Noether?s | theorem | path | integral | approach | divergences | functional integrals | fee quantum theories | renormalization theory | local operators | operator product expansion | renormalization group equation | mathematical language | string theory | 0-dimensional QFT | Stationary Phase Formula | Matrix Models | Large N Limits | 1-dimensional QFT | Classical Mechanics | Least Action Principle | Path Integral Approach | Quantum Mechanics | Perturbative Expansion using Feynman Diagrams | Operator Formalism | Feynman-Kac Formula | d-dimensional QFT | Formalism of Classical Field Theory | Currents | Noether?s Theorem | Path Integral Approach to QFT | Perturbative Expansion | Renormalization Theory | Conformal Field Theory | algebraic topology | algebraic geometry | number 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 https://ocw.mit.edu/terms/index.htm

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8.05 Quantum Physics II (MIT)

Description

Together, this course and 8.06: Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

Subjects

General formalism of quantum mechanics: states | operators | Dirac notation | representations | measurement theory | Harmonic oscillator: operator algebra | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | qualitative analysis of wavefunctions | Angular momentum: operators | commutator algebra | eigenvalues and eigenstates | spherical harmonics | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | allotropic forms of hydrogen | Angular momentum | Harmonic oscillator | operator algebra | Spin | Stern-Gerlach devices and measurements | central potentials and the radial equation | Clebsch-Gordan series and coefficients | quantum physics | 8. Quantum mechanics in three-dimensions: central potentials and the radial equation | and allotropic forms of hydrogen

License

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8.05 Quantum Physics II (MIT)

Description

Together, this course and 8.06: Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

Subjects

General formalism of quantum mechanics: states | operators | Dirac notation | representations | measurement theory | Harmonic oscillator: operator algebra | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | qualitative analysis of wavefunctions | Angular momentum: operators | commutator algebra | eigenvalues and eigenstates | spherical harmonics | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | allotropic forms of hydrogen | Angular momentum | Harmonic oscillator | operator algebra | Spin | Stern-Gerlach devices and measurements | central potentials and the radial equation | Clebsch-Gordan series and coefficients | quantum physics | 8. Quantum mechanics in three-dimensions: central potentials and the radial equation | and allotropic forms of hydrogen

License

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

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8.05 Quantum Physics II (MIT)

Description

This course, along with the next course in this sequence (8.06, Quantum Physics III) in a two-course sequence covering quantum physics with applications drawn from modern physics. General formalism of quantum mechanics: states, operators, Dirac notation, representations, measurement theory. Harmonic oscillator: operator algebra, states. Quantum mechanics in three-dimensions: central potentials and the radial equation, bound and scattering states, qualitative analysis of wavefunctions. Angular momentum: operators, commutator algebra, eigenvalues and eigenstates, spherical harmonics. Spin: Stern-Gerlach devices and measurements, nuclear magnetic resonance, spin and statistics. Addition of angular momentum: Clebsch-Gordan series and coefficients, spin systems, and allotropic forms of hydrogen

Subjects

General formalism of quantum mechanics: states | operators | Dirac notation | representations | measurement theory | Harmonic oscillator: operator algebra | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | qualitative analysis of wavefunctions | Angular momentum: operators | commutator algebra | eigenvalues and eigenstates | spherical harmonics | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | allotropic forms of hydrogen | Angular momentum | Harmonic oscillator | operator algebra | Spin | Stern-Gerlach devices and measurements | central potentials and the radial equation | Clebsch-Gordan series and coefficients | quantum physics

License

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

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8.851 Strong Interactions (MIT) 8.851 Strong Interactions (MIT)

Description

Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects. Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.

Subjects

matching | matching | renormalization | renormalization | the operator product expansion | the operator product expansion | power counting | power counting | heavy quark decays | heavy quark decays | CP violation | CP violation | factorization in hard processes | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | chiral perturbation theory | few-nucleon systems | few-nucleon systems | strong force | strong force | quarks | quarks | relativistic quantum field theory | relativistic quantum field theory | quantum chromodynamics | quantum chromodynamics | QCD | QCD | QCD Langrangian | QCD Langrangian | asymptotic freedom | asymptotic freedom | deep inelastic scattering | deep inelastic scattering | jets | jets | QCD vacuum | QCD vacuum | instantons | instantons | U(1) proglem | U(1) proglem | lattice gauge theory | lattice gauge theory | strong interactions | strong interactions | standard model | standard model | operator product expansion | operator product expansion | factorization | factorization | hard processes | hard processes | exclusive processes | exclusive processes | non-relativistic bound states | non-relativistic bound states | QED | QED | massive particles | massive particles | effective field theory | effective field theory | soft-collinear effective theory | soft-collinear effective 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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8.05 Quantum Physics II (MIT)

Description

Together, this course and 8.06: Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.

Subjects

General formalism of quantum mechanics: states | operators | Dirac notation | representations | measurement theory | Harmonic oscillator: operator algebra | states | Quantum mechanics in three-dimensions: central potentials and the radial equation | bound and scattering states | qualitative analysis of wavefunctions | Angular momentum: operators | commutator algebra | eigenvalues and eigenstates | spherical harmonics | Spin: Stern-Gerlach devices and measurements | nuclear magnetic resonance | spin and statistics | Addition of angular momentum: Clebsch-Gordan series and coefficients | spin systems | allotropic forms of hydrogen | Angular momentum | Harmonic oscillator | operator algebra | Spin | Stern-Gerlach devices and measurements | central potentials and the radial equation | Clebsch-Gordan series and coefficients | quantum physics | 8. Quantum mechanics in three-dimensions: central potentials and the radial equation | and allotropic forms of hydrogen

License

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DH3C35 Software Development: Object-Oriented Programming

Description

This unit is designed to develop a broad knowledge of the concepts, principles, boundaries and scope of software development using an object-oriented programming language. These will be reinforced by developing the practical skills required in using the structures and features of an object-oriented programming language in the creation of software solutions to problems. Outcomes On completion of this unit, you should be able to: 1 use programming techniques to develop program modules 2 implement a solution from design 3 test the completed product 4 create technical and user documentation.

Subjects

DH3C 35 | Java | arithmetic operators | relational operators | logical operators | flow of execution | Nested loops | Array | String class | Date class | Encapsulation | Polymorphism | Java Collections Framework | SCQF Level 8

License

Licensed to colleges in Scotland only Licensed to colleges in Scotland only Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Scottish Qualification Authority (SQA), and (ii) none of these materials may be Used without the express, prior, written consent of the Colleges Open Learning Exchange Group (COLEG) and SQA, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Material. Except where expressly indicated otherwise on the face of these materials (i) copyright in these materials is owned by the Scottish Qualification Authority (SQA), and (ii) none of these materials may be Used without the express, prior, written consent of the Colleges Open Learning Exchange Group (COLEG) and SQA, except if and to the extent that such Use is permitted under COLEG's conditions of Contribution and Use of Learning Materials through COLEG’s Repository, for the purposes of which these materials are COLEG Material. http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 http://content.resourceshare.ac.uk/xmlui/bitstream/handle/10949/17761/LicenceSQAMaterialsCOLEG.pdf?sequence=1 SQA SQA

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18.152 Introduction to Partial Differential Equations (MIT) 18.152 Introduction to Partial Differential Equations (MIT)

Description

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications. This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

Subjects

diffusion | diffusion | elliptic | elliptic | hyperbolic | hyperbolic | partial differential equation | partial differential equation | Initial and boundary value problems for ordinary differential equations | Initial and boundary value problems for ordinary differential equations | Sturm-Liouville theory and eigenfunction expansions | Sturm-Liouville theory and eigenfunction expansions | initial value problems | initial value problems | wave equation;heat equation | wave equation;heat equation | Dirichlet problem | Dirichlet problem | Laplace operator and potential theory | Laplace operator and potential theory | Black-Scholes equation | Black-Scholes equation | water waves | water waves | scalar conservation laws | scalar conservation laws | first order equations | first order equations

License

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5.72 Statistical Mechanics (MIT) 5.72 Statistical Mechanics (MIT)

Description

This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes. This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes.

Subjects

statistical mechanics | statistical mechanics | quantum | quantum | statistics | statistics | atoms | atoms | materials | materials | master equations | master equations | random walk | random walk | langevin | langevin | fokker | fokker | planck | planck | probability theory | probability theory | bloch-redfield | bloch-redfield | navier-stokes | navier-stokes | hydrodynamic | hydrodynamic | scattering | scattering | projection operator | projection operator | thermodynamics | thermodynamics

License

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ía II (2014) ía II (2014)

Description

Odontopediatría es el término más común para referirse al área de conocimiento que estudia la boca del niño y sus enfermedades. Está orientada hacia la salud dental integral de un grupo muy especial como es el niño hasta convertirse en un adulto joven. La asignatura de Odontopediatría II, pretende preparar al alumno para dar la atención bucodental integral al paciente niño y adolescente colaborador o potencialmente colaborador, así como para prestar atención educativa a padres y pacientes. Así como obtener una buena exploración y pruebas complementarias cuando sea necesario, para cumplimentar una historia clínica que refleje la situación de desarrollo y salud bucodental del niño, y un plan de tratamiento de los problemas en el niño, además de promover la futura salud de Odontopediatría es el término más común para referirse al área de conocimiento que estudia la boca del niño y sus enfermedades. Está orientada hacia la salud dental integral de un grupo muy especial como es el niño hasta convertirse en un adulto joven. La asignatura de Odontopediatría II, pretende preparar al alumno para dar la atención bucodental integral al paciente niño y adolescente colaborador o potencialmente colaborador, así como para prestar atención educativa a padres y pacientes. Así como obtener una buena exploración y pruebas complementarias cuando sea necesario, para cumplimentar una historia clínica que refleje la situación de desarrollo y salud bucodental del niño, y un plan de tratamiento de los problemas en el niño, además de promover la futura salud de

Subjects

ía | ía | ón con composite | ón con composite | anestesia infiltrativa | anestesia infiltrativa | aislamiento operatorio | aislamiento operatorio | anestesia troncular | anestesia troncular

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http://creativecommons.org/licenses/by-nc-sa/3.0/

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18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics (MIT) 18.735 Double Affine Hecke Algebras in Representation Theory, Combinatorics, Geometry, and Mathematical Physics (MIT)

Description

Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems. Double affine Hecke algebras (DAHA), also called Cherednik algebras, and their representations appear in many contexts: integrable systems (Calogero-Moser and Ruijsenaars models), algebraic geometry (Hilbert schemes), orthogonal polynomials, Lie theory, quantum groups, etc. In this course we will review the basic theory of DAHA and their representations, emphasizing their connections with other subjects and open problems.

Subjects

dunkl operators | dunkl operators | cherednik | cherednik | affine algebra | affine algebra | representation theory | representation theory | hecke | hecke | knizknik-zamoldchikov | knizknik-zamoldchikov | orbifolds | orbifolds | calogero-moser space | calogero-moser space | hilbert scheme | hilbert scheme | algebra | algebra | macdonald-mehta integral | macdonald-mehta integral | integrable system | integrable system

License

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22.616 Plasma Transport Theory (MIT) 22.616 Plasma Transport Theory (MIT)

Description

This course describes the processes by which mass, momentum, and energy are transported in plasmas, with special reference to magnetic confinement fusion applications. The Fokker-Planck collision operator and its limiting forms, as well as collisional relaxation and equilibrium, are considered in detail. Special applications include a Lorentz gas, Brownian motion, alpha particles, and runaway electrons. The Braginskii formulation of classical collisional transport in general geometry based on the Fokker-Planck equation is presented. Neoclassical transport in tokamaks, which is sensitive to the details of the magnetic geometry, is considered in the high (Pfirsch-Schluter), low (banana) and intermediate (plateau) regimes of collisionality. This course describes the processes by which mass, momentum, and energy are transported in plasmas, with special reference to magnetic confinement fusion applications. The Fokker-Planck collision operator and its limiting forms, as well as collisional relaxation and equilibrium, are considered in detail. Special applications include a Lorentz gas, Brownian motion, alpha particles, and runaway electrons. The Braginskii formulation of classical collisional transport in general geometry based on the Fokker-Planck equation is presented. Neoclassical transport in tokamaks, which is sensitive to the details of the magnetic geometry, is considered in the high (Pfirsch-Schluter), low (banana) and intermediate (plateau) regimes of collisionality.

Subjects

Plasmas | Plasmas | magnetic confinement fusion | magnetic confinement fusion | Fokker-Planck collision operator | Fokker-Planck collision operator | collisional relaxation and equilibrium | collisional relaxation and equilibrium | Lorentz gas | Lorentz gas | Brownian motion | Brownian motion | alpha particles | alpha particles | runaway electrons | runaway electrons | Braginskii formulation | Braginskii formulation | tokamak | tokamak | Pfirsch-Schluter | Pfirsch-Schluter | regimes of collisionality | regimes of collisionality

License

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8.851 Strong Interactions (MIT)

Description

Strong Interactions is a course in the construction and application of effective field theories, which are a modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from heavy quark decays and CP violation, factorization in hard processes (deep inelastic scattering and exclusive processes), non-relativistic bound states in field theory (QED and QCD), chiral perturbation theory, few-nucleon systems, and possibly other Standard Model subjects.

Subjects

matching | renormalization | the operator product expansion | power counting | heavy quark decays | CP violation | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | few-nucleon systems | strong force | quarks | relativistic quantum field theory | quantum chromodynamics | QCD | QCD Langrangian | asymptotic freedom | deep inelastic scattering | jets | QCD vacuum | instantons | U(1) proglem | lattice gauge theory | strong interactions | standard model | operator product expansion | factorization | hard processes | exclusive processes | non-relativistic bound states | QED | massive particles | effective field theory | soft-collinear effective 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 https://ocw.mit.edu/terms/index.htm

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5.72 Statistical Mechanics (MIT) 5.72 Statistical Mechanics (MIT)

Description

This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes. This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes.

Subjects

statistical mechanics | statistical mechanics | quantum | quantum | statistics | statistics | atoms | atoms | materials | materials | master equations | master equations | random walk | random walk | langevin | langevin | fokker | fokker | planck | planck | probability theory | probability theory | bloch-redfield | bloch-redfield | navier-stokes | navier-stokes | hydrodynamic | hydrodynamic | scattering | scattering | projection operator | projection operator | thermodynamics | thermodynamics

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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18.155 Differential Analysis (MIT) 18.155 Differential Analysis (MIT)

Description

Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Method of characteristics. Review of Lebesgue integration. Distributions. Fourier transform. Homogeneous distributions. Asymptotic methods. Fundamental solutions for elliptic, hyperbolic and parabolic differential operators. Method of characteristics. Review of Lebesgue integration. Distributions. Fourier transform. Homogeneous distributions. Asymptotic methods.

Subjects

elliptic | elliptic | hyperbolic | hyperbolic | parabolic differential operators | parabolic differential operators | Lebesgue integration | Lebesgue integration | Distributions | Distributions | Fourier transform | Fourier transform | Homogeneous distributions | Homogeneous distributions | Asymptotic methods | Asymptotic methods

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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18.098 Street-Fighting Mathematics (MIT) 18.098 Street-Fighting Mathematics (MIT)

Description

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

Subjects

extreme-cases reasoning | extreme-cases reasoning | dimensional analysis | dimensional analysis | discretization | discretization | drag | drag | fluid mechanics | fluid mechanics | pendulum | pendulum | pictorial proofs | pictorial proofs | analogy | analogy | operators | operators | summation | summation | square roots | square roots | logarithms | logarithms | musical intervals | musical intervals | taking out the big part | taking out the big part | integration | integration | differentiation | differentiation

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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8.851 Strong Interactions: Effective Field Theories of QCD (MIT) 8.851 Strong Interactions: Effective Field Theories of QCD (MIT)

Description

This is a course in the construction and application of effective field theories, which are the modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from factorization in hard processes relevant for the LHC, heavy quark decays and CP violation, chiral perturbation theory, non-relativistic bound states in field theory (QED and QCD), nucleon effective theories with a fine-tuning, and possibly other subjects from QCD, electroweak physics, and gravity. This is a course in the construction and application of effective field theories, which are the modern tool of choice in making predictions based on the Standard Model. Concepts such as matching, renormalization, the operator product expansion, power counting, and running with the renormalization group will be discussed. Topics will be taken from factorization in hard processes relevant for the LHC, heavy quark decays and CP violation, chiral perturbation theory, non-relativistic bound states in field theory (QED and QCD), nucleon effective theories with a fine-tuning, and possibly other subjects from QCD, electroweak physics, and gravity.

Subjects

matching | matching | renormalization | renormalization | the operator product expansion | the operator product expansion | power counting | power counting | heavy quark decays | heavy quark decays | CP violation | CP violation | factorization in hard processes | factorization in hard processes | non-relativistic bound states in field theory (QED and QCD) | non-relativistic bound states in field theory (QED and QCD) | chiral perturbation theory | chiral perturbation theory | few-nucleon systems | few-nucleon systems

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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5.73 Introductory Quantum Mechanics I (MIT) 5.73 Introductory Quantum Mechanics I (MIT)

Description

5.73 covers fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Basic applications of the following are discussed: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. The course also examines approximation methods: WKB method, variational principle, and perturbation theory. Acknowledgement The instructor would like to acknowledge Peter Giunta for preparing the original version of the materials for 5.73. 5.73 covers fundamental concepts of quantum mechanics: wave properties, uncertainty principles, Schrodinger equation, and operator and matrix methods. Basic applications of the following are discussed: one-dimensional potentials (harmonic oscillator), three-dimensional centrosymetric potentials (hydrogen atom), and angular momentum and spin. The course also examines approximation methods: WKB method, variational principle, and perturbation theory. Acknowledgement The instructor would like to acknowledge Peter Giunta for preparing the original version of the materials for 5.73.

Subjects

quantum mechanics | quantum mechanics | wave properties | wave properties | uncertainty principles | uncertainty principles | Schrodinger | Schrodinger | operator method | operator method | matrix method | matrix method | one-dimensional potentials | one-dimensional potentials | harmonic oscillator | harmonic oscillator | three- dimensional centrosymetric potentials | three- dimensional centrosymetric potentials | angular momentum | angular momentum | spin | spin | approximation methods | approximation methods | WKB method | WKB method | variational principle | variational principle | perturbation theory | perturbation 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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18.155 Differential Analysis (MIT) 18.155 Differential Analysis (MIT)

Description

This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods. This is the first semester of a two-semester sequence on Differential Analysis. Topics include fundamental solutions for elliptic; hyperbolic and parabolic differential operators; method of characteristics; review of Lebesgue integration; distributions; fourier transform; homogeneous distributions; asymptotic methods.

Subjects

elliptic | elliptic | hyperbolic | hyperbolic | parabolic differential operators | parabolic differential operators | Lebesgue integration | Lebesgue integration | Distributions | Distributions | Fourier transform | Fourier transform | Homogeneous distributions | Homogeneous distributions | Asymptotic methods | Asymptotic methods

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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Programming in Java Language Programming in Java Language

Description

The course on Programming provides an introduction to basic programming techniques and paradigms. Students will learn the foundamentals of structured, procedural and object-oriented programming in the Java programming language. The course on Programming provides an introduction to basic programming techniques and paradigms. Students will learn the foundamentals of structured, procedural and object-oriented programming in the Java programming language.

Subjects

Data and operators | Data and operators | Lenguajes y Sistemas Informaticos | Lenguajes y Sistemas Informaticos | Java | Java | Components of a program | Components of a program | Programming | Programming | Introduction to classes and objects | Introduction to classes and objects | Algorithms with arrays | Algorithms with arrays | Utility classes | Utility classes | Control flow statements | Control flow statements | ía Informática | ía Informática | 2011 | 2011 | Methods | Methods

License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/

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