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14.126 Game Theory (MIT) 14.126 Game Theory (MIT)

Description

This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available. This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available.

Subjects

extensive-form games | extensive-form games | Nash equilibria | Nash equilibria | evolutionary equilibria | evolutionary equilibria | bargaining with incomplete information | bargaining with incomplete information | rationalizability | rationalizability | non-cooperative games | non-cooperative games

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14.462 Advanced Macroeconomics II (MIT) 14.462 Advanced Macroeconomics II (MIT)

Description

14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information 14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information

Subjects

macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research | macroeconomics research | analytical tools | analytical tools | analysis | analysis | endogenous growth | endogenous growth | coordintation | coordintation | incomplete markets | incomplete markets | technolgy | technolgy | distribution | distribution | employment | employment | intellectual property rights | intellectual property rights | bounded rationality | bounded rationality | demographics | demographics | complementarities | complementarities | amplification | amplification | recursive equilibria | recursive equilibria | uncertainty | uncertainty | morris | morris | shin | shin | global games | global games | policy | policy | price | price | aggregation | aggregation | social learning | social learning | dynamic adjustment | dynamic adjustment | business cycle | business cycle | heterogeneous agents | heterogeneous agents | savings | savings | utility | utility | aiyagari | aiyagari | steady state | steady state | krusell | krusell | smith | smith | idiosyncratic investment risk | idiosyncratic investment risk | growth | growth | fluctuations | fluctuations | heterogeneity | heterogeneity | optimal fiscal policy | optimal fiscal policy | time inconsistency | time inconsistency | reputation | reputation | information | information | coordination games | coordination games

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14.126 Game Theory (MIT) 14.126 Game Theory (MIT)

Description

This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available. This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available.

Subjects

extensive-form games | extensive-form games | Nash equilibria | Nash equilibria | evolutionary equilibria | evolutionary equilibria | bargaining with incomplete information | bargaining with incomplete information | rationalizability | rationalizability | non-cooperative games | non-cooperative games

License

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6.972 Game Theory and Mechanism Design (MIT) 6.972 Game Theory and Mechanism Design (MIT)

Description

This course is offered to graduates and is an introduction to fundamentals of game theory and mechanism design with motivations drawn from various applications including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, and pricing. Emphasis is placed on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notions in different environments. Topics covered include: normal form games, learning in games, supermodular games, potential games, dynamic games, subgame perfect equilibrium, bargaining, repeated games, auctions, mechanism design, cooperative game theory, network and congestion games, and price of anarchy. This course is offered to graduates and is an introduction to fundamentals of game theory and mechanism design with motivations drawn from various applications including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, and pricing. Emphasis is placed on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notions in different environments. Topics covered include: normal form games, learning in games, supermodular games, potential games, dynamic games, subgame perfect equilibrium, bargaining, repeated games, auctions, mechanism design, cooperative game theory, network and congestion games, and price of anarchy.

Subjects

game theory | game theory | mechanism design | mechanism design | mathematical tools | mathematical tools | normal form games | normal form games | existence and computation of equilibria | existence and computation of equilibria | supermodular games | supermodular games | potential games | potential games | subgame perfect equilibrium | subgame perfect equilibrium | dynamic games | dynamic games | bargaining | bargaining | repeated games | repeated games | games with incomplete/imperfect information | games with incomplete/imperfect information | auctions | auctions | cooperative game theory | cooperative game theory | network and congestion games | network and congestion games | pricing | pricing | price of anarchy | price of anarchy

License

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12.480 Thermodynamics for Geoscientists (MIT) 12.480 Thermodynamics for Geoscientists (MIT)

Description

Principles of thermodynamics are used to infer the physical conditions of formation and modification of igneous and metamorphic rocks. It includes phase equilibria of homogeneous and heterogeneous systems and thermodynamic modelling of non-ideal crystalline solutions. It also surveys the processes that lead to the formation of metamorphic and igneous rocks in the major tectonic environments in the Earth's crust and mantle. Principles of thermodynamics are used to infer the physical conditions of formation and modification of igneous and metamorphic rocks. It includes phase equilibria of homogeneous and heterogeneous systems and thermodynamic modelling of non-ideal crystalline solutions. It also surveys the processes that lead to the formation of metamorphic and igneous rocks in the major tectonic environments in the Earth's crust and mantle.

Subjects

Principles of thermodynamics | Principles of thermodynamics | formation and modification of igneous and metamorphic rocks | formation and modification of igneous and metamorphic rocks | phase equilibria of homogeneous and heterogeneous systems | phase equilibria of homogeneous and heterogeneous systems | thermodynamic modelling of non-ideal crystalline solutions | thermodynamic modelling of non-ideal crystalline solutions | tectonic environments | tectonic environments | crust | crust | mantle | mantle | Ideal Solutions | Ideal Solutions | Non-ideal Solutions | Non-ideal Solutions | Pyroxene Thermometry | Pyroxene Thermometry | Plagioclase Feldspars Solution Models | Plagioclase Feldspars Solution Models | Alkali Feldspars Solution Models | Alkali Feldspars Solution Models | Multi-site Mineral Solutions | Multi-site Mineral Solutions | Homogeneous Equilibria | Homogeneous Equilibria | Quad | Quad | Spinels | Spinels | Rhombohedral Oxides | Rhombohedral Oxides | T-?O2 Relations | T-?O2 Relations | Heterogeneous Equilibria | Heterogeneous Equilibria | Multi-Component Systems | Multi-Component Systems | Liquidus Diagrams | Liquidus Diagrams | Schreinemaker's Analysis | Schreinemaker's Analysis | Composition Space | Composition Space | Gibbs Method | Gibbs Method | Silicate Melts | Silicate Melts | Mixed Volatile Equilibria P-T-XCO2-XH2O | Mixed Volatile Equilibria P-T-XCO2-XH2O | thermodynamic models | thermodynamic models | thermodynamics | thermodynamics

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18.385 Nonlinear Dynamics and Chaos (MIT) 18.385 Nonlinear Dynamics and Chaos (MIT)

Description

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Phase plane | Phase plane | limit cycles | limit cycles | Poincare-Bendixson theory | Poincare-Bendixson theory | Time-dependent systems | Time-dependent systems | Floquet theory | Floquet theory | Poincare maps | Poincare maps | averaging | averaging | Stability of equilibria | Stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | Center manifolds | Center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal forms | chaos | chaos

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8.08 Statistical Physics II (MIT) 8.08 Statistical Physics II (MIT)

Description

Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations. Probability distributions for classical and quantum systems. Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Conditions of thermodynamic equilibrium for homogenous and heterogenous systems. Applications: non-interacting Bose and Fermi gases; mean field theories for real gases, binary mixtures, magnetic systems, polymer solutions; phase and reaction equilibria, critical phenomena. Fluctuations, correlation functions and susceptibilities, and Kubo formulae. Evolution of distribution functions: Boltzmann and Smoluchowski equations.

Subjects

Probability distributions | Probability distributions | quantum systems | quantum systems | Microcanonical | Microcanonical | canonical | canonical | grand canonical partition-functions | grand canonical partition-functions | thermodynamic potentials | thermodynamic potentials | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | non-interacting Bose and Fermi gases | non-interacting Bose and Fermi gases | mean field theories for real gases | mean field theories for real gases | binary mixtures | binary mixtures | magnetic systems | magnetic systems | polymer solutions | polymer solutions | phase and reaction equilibria | phase and reaction equilibria | critical phenomena | critical phenomena | Fluctuations | Fluctuations | correlation functions and susceptibilities | correlation functions and susceptibilities | Kubo formulae | Kubo formulae | Evolution of distribution functions | Evolution of distribution functions | Boltzmann and Smoluchowski equations | Boltzmann and Smoluchowski equations | correlation functions | correlation functions | susceptibilities | susceptibilities

License

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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

License

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1.725J Chemicals in the Environment: Fate and Transport (MIT) 1.725J Chemicals in the Environment: Fate and Transport (MIT)

Description

This core class in the Environmental M.Eng. program is for all students interested in the behavior of chemicals in the environment. The emphasis is on man-made chemicals; their movement through water, air, and soil; and their eventual fate. Physical transport, as well as chemical and biological sources and sinks, are discussed. Linkages to health effects, sources and control, and policy aspects are discussed and debated. This core class in the Environmental M.Eng. program is for all students interested in the behavior of chemicals in the environment. The emphasis is on man-made chemicals; their movement through water, air, and soil; and their eventual fate. Physical transport, as well as chemical and biological sources and sinks, are discussed. Linkages to health effects, sources and control, and policy aspects are discussed and debated.

Subjects

control volumes | control volumes | mass balance | mass balance | advective/dispersive transport | advective/dispersive transport | chemical equilibria | chemical equilibria | mass action | mass action | electroneutrality | electroneutrality | mass conservation | mass conservation | chemical kinetics and partitioning | chemical kinetics and partitioning | river transport | river transport | lakes and wetlands and estuaries | lakes and wetlands and estuaries | sediment transport | sediment transport | bottom sediments | bottom sediments | paleolimnology | paleolimnology | air-water exchange | air-water exchange | major ion chemistry of natural waters | major ion chemistry of natural waters | D'Arcy's Law | D'Arcy's Law | 1.725 | 1.725

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3.012 Fundamentals of Materials Science (MIT) 3.012 Fundamentals of Materials Science (MIT)

Description

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and s This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and 3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and s

Subjects

bonding | bonding | energetics | energetics | structure | structure | antibonding | antibonding | hydrogen | hydrogen | Quantum mechanics | Quantum mechanics | electron | electron | atom | atom | molecule | molecule | molecular dynamics | molecular dynamics | MD | MD | Symmetry properties | Symmetry properties | solid | solid | gas | gas | liquid | liquid | phase | phase | matter; molecular geometry | matter; molecular geometry | complex and disordered materials | complex and disordered materials | thermodynamics | thermodynamics | equilibrium property | equilibrium property | macroscopic behavior | macroscopic behavior | molecular model | molecular model | heat capacity | heat capacity | phase transformation | phase transformation | multiphase equilibria | multiphase equilibria | chemical reaction | chemical reaction | magnetism | magnetism | engineered alloy | engineered alloy | electronic and magnetic material | electronic and magnetic material | ionic solid | ionic solid | network solid | network solid | polymer | polymer | biomaterial | biomaterial | glass | glass | liquid crystal | liquid crystal | LCD | LCD | matter | matter | molecular geometry | molecular geometry

License

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6.243J Dynamics of Nonlinear Systems (MIT) 6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems. This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Subjects

nonlinear systems | nonlinear systems | deterministic dynamical systems | deterministic dynamical systems | ordinary differential equations | ordinary differential equations | planar autonomous systems | planar autonomous systems | Picard iteration | Picard iteration | contraction mapping theorem | contraction mapping theorem | Bellman-Gronwall lemma | Bellman-Gronwall lemma | Lyapunov methods | Lyapunov methods | feedback linearization | feedback linearization | nonlinear circuits | nonlinear circuits | control systems | control systems | local controllability | local controllability | volume evolution | volume evolution | system analysis | system analysis | singular perturbations | singular perturbations | averaging | averaging | local behavior | local behavior | trajectories | trajectories | equilibria | equilibria | storage functions | storage functions | stability analysis | stability analysis | continuity | continuity | differential equations | differential equations | system models | system models | parameters | parameters | input/output | input/output | state-space | state-space | 16.337 | 16.337

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8.08 Statistical Physics II (MIT) 8.08 Statistical Physics II (MIT)

Description

This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Also discussed are conditions of thermodynamic equilibrium for homogenous and heterogenous systems. The course follows 8.044, Statistical Physics I, and is second in this series of undergraduate Statistical Physics courses. This course covers probability distributions for classical and quantum systems. Topics include: Microcanonical, canonical, and grand canonical partition-functions and associated thermodynamic potentials. Also discussed are conditions of thermodynamic equilibrium for homogenous and heterogenous systems. The course follows 8.044, Statistical Physics I, and is second in this series of undergraduate Statistical Physics courses.

Subjects

Probability distributions | Probability distributions | quantum systems | quantum systems | Microcanonical | canonical | and grand canonical partition-functions | Microcanonical | canonical | and grand canonical partition-functions | thermodynamic potentials | thermodynamic potentials | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | Conditions of thermodynamic equilibrium for homogenous and heterogenous systems | non-interacting Bose and Fermi gases | non-interacting Bose and Fermi gases | mean field theories for real gases | mean field theories for real gases | binary mixtures | binary mixtures | magnetic systems | magnetic systems | polymer solutions | polymer solutions | phase and reaction equilibria | phase and reaction equilibria | critical phenomena | critical phenomena | Fluctuations | Fluctuations | correlation functions and susceptibilities | and Kubo formulae | correlation functions and susceptibilities | and Kubo formulae | Evolution of distribution functions: Boltzmann and Smoluchowski equations | Evolution of distribution functions: Boltzmann and Smoluchowski equations

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10.32 Separation Processes (MIT) 10.32 Separation Processes (MIT)

Description

This course covers the general principles of separation by equilibrium and rate processes. Topics include staged cascades and applications to distillation, absorption, adsorption, and membrane processes. Phase equilibria and the role of diffusion are also covered. This course covers the general principles of separation by equilibrium and rate processes. Topics include staged cascades and applications to distillation, absorption, adsorption, and membrane processes. Phase equilibria and the role of diffusion are also covered.

Subjects

separation process | separation process | chemical mixtures | chemical mixtures | biological mixtures | biological mixtures | distillation | distillation | membrane processes | membrane processes | chromatography | chromatography | adsorption | adsorption | precipitation | precipitation | crystallization | crystallization | filtration | filtration | membrane filtration | membrane filtration | fixed bed adsorption | fixed bed adsorption | reverse osmosis | reverse osmosis | McCabe-Thiele | McCabe-Thiele | stripping | stripping | equilibrium | equilibrium | rate processes | rate processes | staged cascades | staged cascades | absorption | absorption | phase equilibria | phase equilibria | diffusion | diffusion

License

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12.480 Thermodynamics for Geoscientists (MIT) 12.480 Thermodynamics for Geoscientists (MIT)

Description

In this course, principles of thermodynamics are used to infer the physical conditions of formation and modification of igneous and metamorphic rocks. The course includes phase equilibria of homogeneous and heterogeneous systems and thermodynamic modeling of non-ideal crystalline solutions. It also surveys the processes that lead to the formation of metamorphic and igneous rocks in the major tectonic environments in the Earth's crust and mantle. In this course, principles of thermodynamics are used to infer the physical conditions of formation and modification of igneous and metamorphic rocks. The course includes phase equilibria of homogeneous and heterogeneous systems and thermodynamic modeling of non-ideal crystalline solutions. It also surveys the processes that lead to the formation of metamorphic and igneous rocks in the major tectonic environments in the Earth's crust and mantle.

Subjects

Principles of thermodynamics | Principles of thermodynamics | formation and modification of igneous and metamorphic rocks | formation and modification of igneous and metamorphic rocks | phase equilibria of homogeneous and heterogeneous systems | phase equilibria of homogeneous and heterogeneous systems | thermodynamic modelling of non-ideal crystalline solutions | thermodynamic modelling of non-ideal crystalline solutions | tectonic environments | tectonic environments | crust | crust | mantle | mantle | Ideal Solutions | Ideal Solutions | Non-ideal Solutions | Non-ideal Solutions | Pyroxene Thermometry | Pyroxene Thermometry | Plagioclase Feldspars Solution Models | Plagioclase Feldspars Solution Models | Alkali Feldspars Solution Models | Alkali Feldspars Solution Models | Multi-site Mineral Solutions | Multi-site Mineral Solutions | Homogeneous Equilibria | Homogeneous Equilibria | Quad | Quad | Spinels | Spinels | Rhombohedral Oxides | Rhombohedral Oxides | T-?O2 Relations | T-?O2 Relations | Heterogeneous Equilibria | Heterogeneous Equilibria | Multi-Component Systems | Multi-Component Systems | Liquidus Diagrams | Liquidus Diagrams | Schreinemaker's Analysis | Schreinemaker's Analysis | Composition Space | Composition Space | Gibbs Method | Gibbs Method | Silicate Melts | Silicate Melts | Mixed Volatile Equilibria P-T-XCO2-XH2O | Mixed Volatile Equilibria P-T-XCO2-XH2O | thermodynamic models | thermodynamic models | thermodynamics | thermodynamics

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14.461 Advanced Macroeconomics I (MIT) 14.461 Advanced Macroeconomics I (MIT)

Description

14.461 is an advanced course in macroeconomics that seeks to bring students to the research frontier. The course is divided into two sections. The first half is taught by Prof. Iván Werning and covers topics such as how to formulate and solve optimal problems. Students will study fiscal and monetary policy, among other issues. The second half, taught by Prof. George-Marios Angeletos, covers recent work on multiple equilibria, global games, and informational fictions. 14.461 is an advanced course in macroeconomics that seeks to bring students to the research frontier. The course is divided into two sections. The first half is taught by Prof. Iván Werning and covers topics such as how to formulate and solve optimal problems. Students will study fiscal and monetary policy, among other issues. The second half, taught by Prof. George-Marios Angeletos, covers recent work on multiple equilibria, global games, and informational fictions.

Subjects

macroeconomics | macroeconomics | macroeconomic theory | macroeconomic theory | policy | policy | fiscal policy | fiscal policy | monetary policy | monetary policy | research | research | business cycles | business cycles | financial crisis | financial crisis | global games | global games | multiple equilibria | multiple equilibria | informational fictions | informational fictions

License

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18.385J Nonlinear Dynamics and Chaos (MIT) 18.385J Nonlinear Dynamics and Chaos (MIT)

Description

This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software. This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.

Subjects

Phase plane | Phase plane | limit cycles | limit cycles | Poincare-Bendixson theory | Poincare-Bendixson theory | Time-dependent systems | Time-dependent systems | Floquet theory | Floquet theory | Poincare maps | Poincare maps | averaging | averaging | Stability of equilibria | Stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | Center manifolds | Center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal forms | chaos | chaos | 18.385 | 18.385 | 2.036 | 2.036

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22.615 MHD Theory of Fusion Systems (MIT) 22.615 MHD Theory of Fusion Systems (MIT)

Description

This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta. This course discusses MHD equilibria in cylindrical, toroidal, and noncircular tokamaks. It covers derivation of the basic MHD model from the Boltzmann equation, use of MHD equilibrium theory in poloidal field design, MHD stability theory including the Energy Principle, interchange instability, ballooning modes, second region of stability, and external kink modes. Emphasis is on discovering configurations capable of achieving good confinement at high beta.

Subjects

Magnetohydrodynamics | Magnetohydrodynamics | plasma | plasma | transport theory | transport theory | Boltzmann-Maxwell equations | Boltzmann-Maxwell equations | tokamaks | tokamaks | MHD equilibria | MHD equilibria | poloidal field design | poloidal field design | MHD stability theory | MHD stability theory | Energy Principle | Energy Principle | interchange instability | interchange instability | ballooning modes | ballooning modes | second region of stability | second region of stability | external kink modes | external kink modes | MHD instabilities | MHD instabilities

License

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18.385J Nonlinear Dynamics and Chaos (MIT) 18.385J Nonlinear Dynamics and Chaos (MIT)

Description

This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software. This graduate level course focuses on nonlinear dynamics with applications. It takes an intuitive approach with emphasis on geometric thinking, computational and analytical methods and makes extensive use of demonstration software.

Subjects

chaos | chaos | Floquet theory | Floquet theory | Poincare-Bendixson theory | Poincare-Bendixson theory | phase plane | phase plane | limit cycles | limit cycles | time-dependent systems | time-dependent systems | Poincare maps | Poincare maps | stability of equilibria | stability of equilibria | near-equilibrium dynamics | near-equilibrium dynamics | center manifolds | center manifolds | elementary bifurcations | elementary bifurcations | normal forms | normal forms

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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14.462 Advanced Macroeconomics II (MIT)

Description

14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information

Subjects

macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research | analytical tools | analysis | endogenous growth | coordintation | incomplete markets | technolgy | distribution | employment | intellectual property rights | bounded rationality | demographics | complementarities | amplification | recursive equilibria | uncertainty | morris | shin | global games | policy | price | aggregation | social learning | dynamic adjustment | business cycle | heterogeneous agents | savings | utility | aiyagari | steady state | krusell | smith | idiosyncratic investment risk | growth | fluctuations | heterogeneity | optimal fiscal policy | time inconsistency | reputation | information | coordination games

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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14.126 Game Theory (MIT)

Description

This course provides a rigorous treatment of non-cooperative solution concepts in game theory, including rationalizability and Nash, sequential, and stable equilibria. It covers topics such as epistemic foundations, higher order beliefs, bargaining, repeated games, reputation, supermodular games, and global games. It also introduces cooperative solution concepts—Nash bargaining solution, core, Shapley value—and develops corresponding non-cooperative foundations.

Subjects

extensive-form games | Nash equilibria | evolutionary equilibria | bargaining with incomplete information | rationalizability | non-cooperative games

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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14.126 Game Theory (MIT)

Description

This course is a rigorous investigation of the evolutionary and epistemic foundations of solution concepts, such as rationalizability and Nash equilibrium. It covers classical topics, such as repeated games, bargaining, and supermodular games as well as new topics such as global games, heterogeneous priors, psychological games, and games without expected utility maximization. Applications are provided when available.

Subjects

extensive-form games | Nash equilibria | evolutionary equilibria | bargaining with incomplete information | rationalizability | non-cooperative games

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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6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Subjects

nonlinear systems | deterministic dynamical systems | ordinary differential equations | planar autonomous systems | Picard iteration | contraction mapping theorem | Bellman-Gronwall lemma | Lyapunov methods | feedback linearization | nonlinear circuits | control systems | local controllability | volume evolution | system analysis | singular perturbations | averaging | local behavior | trajectories | equilibria | storage functions | stability analysis | continuity | differential equations | system models | parameters | input/output | state-space | 16.337

License

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6.972 Game Theory and Mechanism Design (MIT)

Description

This course is offered to graduates and is an introduction to fundamentals of game theory and mechanism design with motivations drawn from various applications including distributed control of wireline and wireless communication networks, incentive-compatible/dynamic resource allocation, and pricing. Emphasis is placed on the foundations of the theory, mathematical tools, as well as modeling and the equilibrium notions in different environments. Topics covered include: normal form games, learning in games, supermodular games, potential games, dynamic games, subgame perfect equilibrium, bargaining, repeated games, auctions, mechanism design, cooperative game theory, network and congestion games, and price of anarchy.

Subjects

game theory | mechanism design | mathematical tools | normal form games | existence and computation of equilibria | supermodular games | potential games | subgame perfect equilibrium | dynamic games | bargaining | repeated games | games with incomplete/imperfect information | auctions | cooperative game theory | network and congestion games | pricing | price of anarchy

License

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

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12.480 Thermodynamics for Geoscientists (MIT)

Description

Principles of thermodynamics are used to infer the physical conditions of formation and modification of igneous and metamorphic rocks. It includes phase equilibria of homogeneous and heterogeneous systems and thermodynamic modelling of non-ideal crystalline solutions. It also surveys the processes that lead to the formation of metamorphic and igneous rocks in the major tectonic environments in the Earth's crust and mantle.

Subjects

Principles of thermodynamics | formation and modification of igneous and metamorphic rocks | phase equilibria of homogeneous and heterogeneous systems | thermodynamic modelling of non-ideal crystalline solutions | tectonic environments | crust | mantle | Ideal Solutions | Non-ideal Solutions | Pyroxene Thermometry | Plagioclase Feldspars Solution Models | Alkali Feldspars Solution Models | Multi-site Mineral Solutions | Homogeneous Equilibria | Quad | Spinels | Rhombohedral Oxides | T-?O2 Relations | Heterogeneous Equilibria | Multi-Component Systems | Liquidus Diagrams | Schreinemaker's Analysis | Composition Space | Gibbs Method | Silicate Melts | Mixed Volatile Equilibria P-T-XCO2-XH2O | thermodynamic models | 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 https://ocw.mit.edu/terms/index.htm

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18.385 Nonlinear Dynamics and Chaos (MIT)

Description

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear coupled oscillators in biology and physics. Perturbation, averaging theory. Parametric resonances, Floquet theory. Relaxation oscillations. Hysterises. Phase locking. Chaos: Lorenz model, iterated mappings, period doubling, renormalization. Fractals. Hamiltonian systems, area preserving maps; KAM theory.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Phase plane | limit cycles | Poincare-Bendixson theory | Time-dependent systems | Floquet theory | Poincare maps | averaging | Stability of equilibria | near-equilibrium dynamics | Center manifolds | elementary bifurcations | normal forms | chaos

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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