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6.013 Electromagnetics and Applications (MIT) 6.013 Electromagnetics and Applications (MIT)

Description

This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.The instructors of this course extend a general acknowledgment to the many students and instructors who have made major contributions to the 6.013 course materials over the years, and apologize for any residual errors that may remain in these writ This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.The instructors of this course extend a general acknowledgment to the many students and instructors who have made major contributions to the 6.013 course materials over the years, and apologize for any residual errors that may remain in these writSubjects

electromagnetics | electromagnetics | applications | applications | wireless communications | wireless communications | circuits | circuits | computer interconnects | computer interconnects | peripherals | peripherals | optical fiber links | optical fiber links | microwave | microwave | communications | communications | radar | radar | antennas | antennas | sensors | sensors | micro-electromechanical systems | micro-electromechanical systems | power generation | power generation | power transmission | power transmission | quasistatic solutions | quasistatic solutions | dynamic solutions | dynamic solutions | Maxwell | Maxwell | Maxwell's equations | Maxwell's equations | waves | waves | radiation | radiation | diffraction | diffraction | guided waves | guided waves | unguided waves | unguided waves | resonance | resonance | forces | forces | power | power | energy | energy | microwave communications | microwave communicationsLicense

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Includes audio/video content: AV selected lectures. To prosper, firms must develop major product and service innovations. Often, though, they don't know how. Recent research into the innovation process has made it possible to develop "breakthroughs" systematically. 15.356 presents several practical concept development methods, such as the "Lead User Method," where manufacturers learn from innovative customers. Expert guest speakers present case studies that show the "art" required to implement a concept development method. 15.356 is a half-term subject. Includes audio/video content: AV selected lectures. To prosper, firms must develop major product and service innovations. Often, though, they don't know how. Recent research into the innovation process has made it possible to develop "breakthroughs" systematically. 15.356 presents several practical concept development methods, such as the "Lead User Method," where manufacturers learn from innovative customers. Expert guest speakers present case studies that show the "art" required to implement a concept development method. 15.356 is a half-term subject.Subjects

lead user method; innovations; innovation process; idea generation; brainstorming; concept development methods; prototypes; solutions; problem solving; business breakthroughs; incremental improvements; market research; focus groups; MIT Media Lab; creativity | lead user method; innovations; innovation process; idea generation; brainstorming; concept development methods; prototypes; solutions; problem solving; business breakthroughs; incremental improvements; market research; focus groups; MIT Media Lab; creativity | lead user method | lead user method | innovations | innovations | innovation process | innovation process | idea generation | idea generation | brainstorming | brainstorming | concept development methods | concept development methods | prototypes | prototypes | solutions | solutions | problem solving | problem solving | business breakthroughs | business breakthroughs | incremental improvements | incremental improvements | market research | market research | focus groups | focus groups | MIT Media Lab | MIT Media Lab | creativity | creativityLicense

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See all metadata6.013 Electromagnetics and Applications (MIT) 6.013 Electromagnetics and Applications (MIT)

Description

This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.Acknowledgments The instructors would like to thank Robert Haussman for transcribing into LaTeX the problem set and Quiz 2 solutions. This course explores electromagnetic phenomena in modern applications, including wireless communications, circuits, computer interconnects and peripherals, optical fiber links and components, microwave communications and radar, antennas, sensors, micro-electromechanical systems, motors, and power generation and transmission. Fundamentals covered include: quasistatic and dynamic solutions to Maxwell's equations; waves, radiation, and diffraction; coupling to media and structures; guided and unguided waves; resonance; and forces, power, and energy.Acknowledgments The instructors would like to thank Robert Haussman for transcribing into LaTeX the problem set and Quiz 2 solutions.Subjects

ESD.013 | ESD.013 | electromagnetics | electromagnetics | applications | applications | wireless communications | wireless communications | circuits | circuits | computer interconnects | computer interconnects | peripherals | peripherals | optical fiber links | optical fiber links | microwave communications | microwave communications | radar | radar | antennas | antennas | sensors | sensors | micro-electromechanical systems | micro-electromechanical systems | power generation | power generation | power transmission | power transmission | quasistatic solutions | quasistatic solutions | dynamic solutions | dynamic solutions | Maxwell | Maxwell | Maxwell's equations | Maxwell's equations | waves | waves | radiation | radiation | diffraction | diffraction | guided waves | guided waves | unguided waves | unguided waves | resonance | resonance | forces | forces | power | power | energy | energyLicense

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

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See all metadata14.01 Principles of Microeconomics (MIT) 14.01 Principles of Microeconomics (MIT)

Description

This introductory course teaches the fundamentals of microeconomics. Topics include consumer theory, producer theory, the behavior of firms, market equilibrium, monopoly, and the role of the government in the economy. 14.01 is a Humanities, Arts, and Social Sciences (HASS) elective and is offered both terms. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges. This introductory course teaches the fundamentals of microeconomics. Topics include consumer theory, producer theory, the behavior of firms, market equilibrium, monopoly, and the role of the government in the economy. 14.01 is a Humanities, Arts, and Social Sciences (HASS) elective and is offered both terms. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.Subjects

market | market | optimization | optimization | allocation | allocation | economic measurement | economic measurement | analysis | analysis | microeconomics | microeconomics | demand | demand | supply | supply | equilibrium | equilibrium | general equilibrium | general equilibrium | government interventions | government interventions | price elasticity of demand | price elasticity of demand | income elasticity of demand | income elasticity of demand | cross price elasticity of demand | cross price elasticity of demand | price elasticity of supply | price elasticity of supply | consumer behavior | consumer behavior | consumer preference | consumer preference | utility functions | utility functions | marginal rate of substitution | marginal rate of substitution | budget constraints | budget constraints | interior solutions | interior solutions | corner solutions | corner solutions | Engle curves | Engle curves | individual demand | individual demand | market demand | market demand | revealed preferences | revealed preferences | substitution effect | substitution effect | income effect | income effect | Giffen goods | Giffen goods | consumer surplus | consumer surplus | Irish potato famine | Irish potato famine | network externalities | network externalities | uncertainty | uncertainty | preference toward risk | preference toward risk | risk premium | risk premium | indifference curves | indifference curves | diversification | diversification | insurance | insurance | producer theory | producer theory | production functions | production functions | short run | short run | long run | long run | returns to scale | returns to scale | cost functions | cost functions | economies of scale | economies of scale | economies of scope | economies of scope | learning | learning | profit maximization | profit maximization | producer surplus | producer surplus | agricultural price support | agricultural price support | tax | tax | subsidy | subsidy | exchange economy | exchange economy | contract curves | contract curves | utility possibilities frontier | utility possibilities frontier | Edgeworth Box | Edgeworth Box | production possibilities frontier | production possibilities frontier | efficiency | efficiency | monopoly | monopoly | multiplant firm | multiplant firm | social cost | social cost | price regulation | price regulation | monopsony | monopsony | price discrimination | price discrimination | peak-load pricing | peak-load pricing | two-part tariffs | two-part tariffs | bundling | bundling | monopolistic competition | monopolistic competition | game theory | game theory | oligopoly | oligopoly | Cournot | Cournot | Stackelberg | Stackelberg | Bertrand | Bertrand | Prisoner's Dilemma | Prisoner's DilemmaLicense

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See all metadataRSC Wednesday Seminars 2011: Transnationalism: a fourth durable solution?

Description

Recorded at the Refugee Studies Centre's third Wednesday Public Seminar of Trinity Term 2011, on Wednesday 1st June 2011 at the Department of International Development, University of Oxford. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Subjects

transnationalism | refugee | forced migration | durable solutions | migration | transnationalism | refugee | forced migration | durable solutions | migrationLicense

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See all metadata2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods. This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.Subjects

numerical methods | numerical methods | interpolation | interpolation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | finite difference methods | finite difference methods | boundary integral equation panel methods | boundary integral equation panel methods | numerical lifting surface computations | numerical lifting surface computations | Fast Fourier Transforms | Fast Fourier Transforms | Numerical representation | Numerical representation | deterministic and random sea waves | deterministic and random sea waves | Integral boundary layer equations | Integral boundary layer equations | numerical solutions | numerical solutionsLicense

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See all metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods Matrix systems | Laplace transform methods Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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See all metadata6.253 Convex Analysis and Optimization (MIT) 6.253 Convex Analysis and Optimization (MIT)

Description

6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject. 6.253 develops the core analytical issues of continuous optimization, duality, and saddle point theory, using a handful of unifying principles that can be easily visualized and readily understood. The mathematical theory of convex sets and functions is discussed in detail, and is the basis for an intuitive, highly visual, geometrical approach to the subject.Subjects

affine hulls | affine hulls | recession cones | recession cones | global minima | global minima | local minima | local minima | optimal solutions | optimal solutions | hyper planes | hyper planes | minimax theory | minimax theory | polyhedral convexity | polyhedral convexity | polyhedral cones | polyhedral cones | polyhedral sets | polyhedral sets | convex analysis | convex analysis | optimization | optimization | convexity | convexity | Lagrange multipliers | Lagrange multipliers | duality | duality | continuous optimization | continuous optimization | saddle point theory | saddle point theory | linear algebra | linear algebra | real analysis | real analysis | convex sets | convex sets | convex functions | convex functions | extreme points | extreme points | subgradients | subgradients | constrained optimization | constrained optimization | directional derivatives | directional derivatives | subdifferentials | subdifferentials | conical approximations | conical approximations | Fritz John optimality | Fritz John optimality | Exact penalty functions | Exact penalty functions | conjugate duality | conjugate duality | conjugate functions | conjugate functions | Fenchel duality | Fenchel duality | exact penalty functions | exact penalty functions | dual computational methods | dual computational methodsLicense

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

Description

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

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

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See all metadata18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow. This course introduces fundamental concepts in "continuous'' applied mathematics, with an emphasis on nonlinear partial differential equations (PDEs). Topics include linear and nonlinear waves: kinematic waves, method of characteristics, expansion fans, wave breaking, shock dynamics, shock structure; linear and nonlinear diffusion: Green functions, Fourier transform, similarity solutions, boundary layers, Nernst-Planck equations. Applications include traffic flow, gas dynamics, and granular flow.Subjects

Linear and nonlinear waves | Linear and nonlinear waves | hyperbolic waves | hyperbolic waves | kinematic waves | kinematic waves | expansion fans | expansion fans | shock dynamics | shock dynamics | shock structure | shock structure | Linear diffusion | Linear diffusion | nonlinear diffusion | nonlinear diffusion | Green functions | Green functions | Fourier transform | Fourier transform | dimensional analysis | dimensional analysis | similarity solutions | similarity solutions | boundary layers | boundary layers | traffic flow | traffic flow | gas dynamics | gas dynamics | tsunamis | tsunamis | heat transfer | heat transfer | ion transport | ion transport | granular flow | granular flowLicense

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See all metadata12.480 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 | thermodynamicsLicense

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See all metadata12.815 Atmospheric Radiation (MIT) 12.815 Atmospheric Radiation (MIT)

Description

This is an introduction to the physics of atmospheric radiation and remote sensing including use of computer codes. Subjects covered include: radiative transfer equation including emission and scattering, spectroscopy, Mie theory, and numerical solutions. We examine the solution of inverse problems in remote sensing of atmospheric temperature and composition. This is an introduction to the physics of atmospheric radiation and remote sensing including use of computer codes. Subjects covered include: radiative transfer equation including emission and scattering, spectroscopy, Mie theory, and numerical solutions. We examine the solution of inverse problems in remote sensing of atmospheric temperature and composition.Subjects

atmospheric radiation | atmospheric radiation | remote sensing | remote sensing | atmospheric physics | atmospheric physics | computer codes | computer codes | Radiative transfer equation | Radiative transfer equation | emission and scattering | emission and scattering | spectroscopy | spectroscopy | Mie theory | Mie theory | numerical solutions | numerical solutions | inverse problems | inverse problems | atmospheric temperature | atmospheric temperature | atmospheric composition | atmospheric compositionLicense

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An introduction to the formulation, methodology, and techniques for numerical solution of engineering problems. Fundamental principles of digital computing and the implications for algorithm accuracy and stability. Error propagation and stability. The solution of systems of linear equations, including direct and iterative techniques. Roots of equations and systems of equations. Numerical interpolation, differentiation and integration. Fundamentals of finite-difference solutions to ordinary differential equations. Error and convergence analysis. Subject taught first half of term.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. An introduction to the formulation, methodology, and techniques for numerical solution of engineering problems. Fundamental principles of digital computing and the implications for algorithm accuracy and stability. Error propagation and stability. The solution of systems of linear equations, including direct and iterative techniques. Roots of equations and systems of equations. Numerical interpolation, differentiation and integration. Fundamentals of finite-difference solutions to ordinary differential equations. Error and convergence analysis. Subject taught first half of term.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.Subjects

digital computing | digital computing | algorithm accuracy | algorithm accuracy | error propagation | error propagation | linear equations | linear equations | iterative techniques | iterative techniques | roots of equations | roots of equations | systems of equations | systems of equations | numerical interpolation | numerical interpolation | differentiation | differentiation | integration | integration | finite-difference solutions | finite-difference solutions | differential equations | differential equations | 10.002J | 10.002J | 13.002 | 13.002 | 10.002 | 10.002License

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This course is  a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas. This course is  a foundational study of the effects of single and multiple interactions on neutron distributions and their applications to problems across the Nuclear Engineering department - fission, fusion, and RST. Particle simulation methods are introduced to deal with complex processes that cannot be studied only experimentally or by numerical solutions of equations. Treatment will emphasize basic concepts and understanding, as well as showing the underlying scientific connections with current research areas.Subjects

neutron distributions | neutron distributions | fission | fission | fusion | fusion | RST | RST | Particle simulation methods | Particle simulation methods | complex processes | complex processes | numerical solutions of equations | numerical solutions of equations | basic concepts | basic concepts | underlying scientific connections | underlying scientific connections | current research areas | current research areas | angular distributions | angular distributions | energy distributions | energy distributions | single collision | single collision | multiple collisions | multiple collisions | neutron interactions | neutron interactions | elastic scattering | elastic scattering | inelastic scattering | inelastic scattering | MCNP | MCNP | Monte Carlo | Monte Carlo | molecular dynamics | molecular dynamicsLicense

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See all metadata13.024 Numerical Marine Hydrodynamics (MIT) 13.024 Numerical Marine Hydrodynamics (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™ This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects | 2.29 | 2.29License

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See all metadata8.08 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 | susceptibilitiesLicense

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See all metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams | constant coefficients | constant coefficients | complex numbers | complex numbers | exponentials | exponentials | eigenvalues | eigenvalues | eigenvectors | eigenvectorsLicense

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This workshop is designed to introduce students to different perspectives on international politics in the 21st century. Students will explore how advances in information technology are changing international relations and global governance through opening new channels of communication, creating new methods of education, and new potentials for democratization. We will consider the positive and negative externalities associated with applications of such technologies. Students will be encouraged to look at alternative futures, and/or to frame solutions to problems that they define. The class will include guest lectures, discussions, and a final project and presentation. This workshop is designed to introduce students to different perspectives on international politics in the 21st century. Students will explore how advances in information technology are changing international relations and global governance through opening new channels of communication, creating new methods of education, and new potentials for democratization. We will consider the positive and negative externalities associated with applications of such technologies. Students will be encouraged to look at alternative futures, and/or to frame solutions to problems that they define. The class will include guest lectures, discussions, and a final project and presentation.Subjects

Political science | Political science | global | global | Twenty-first Century | Twenty-first Century | innovation | innovation | challenges | challenges | information technology | information technology | workshop | workshop | international politics | international politics | international relations | international relations | global governance | global governance | communication | communication | education | education | democratization | democratization | alternative futures | alternative futures | solutions | solutionsLicense

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

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See all metadata14.01SC Principles of Microeconomics (MIT) 14.01SC Principles of Microeconomics (MIT)

Description

Includes audio/video content: AV lectures. 14.01 Principles of Microeconomics is an introductory undergraduate course that teaches the fundamentals of microeconomics. This course introduces microeconomic concepts and analysis, supply and demand analysis, theories of the firm and individual behavior, competition and monopoly, and welfare economics. Students will also be introduced to the use of microeconomic applications to address problems in current economic policy throughout the semester. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmen Includes audio/video content: AV lectures. 14.01 Principles of Microeconomics is an introductory undergraduate course that teaches the fundamentals of microeconomics. This course introduces microeconomic concepts and analysis, supply and demand analysis, theories of the firm and individual behavior, competition and monopoly, and welfare economics. Students will also be introduced to the use of microeconomic applications to address problems in current economic policy throughout the semester. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmenSubjects

Microeconomics | Microeconomics | prices | prices | normative economics | normative economics | positive economics | positive economics | microeconomic applications | microeconomic applications | supply | supply | demand | demand | equilibrium | equilibrium | demand shift | demand shift | supply shift | supply shift | government interference | government interference | elasticity | elasticity | revenue | revenue | empirical economics | empirical economics | consumer theory | consumer theory | preference assumptions | preference assumptions | indifference curves | indifference curves | utility functions | utility functions | marginal utility | marginal utility | budget constraints | budget constraints | marginal rate of transformation | marginal rate of transformation | opportunity cost | opportunity cost | constrained utility maximization | constrained utility maximization | corner solutions | corner solutions | Engel curves | Engel curves | income effect | income effect | substitution effect | substitution effect | Giffin good | Giffin good | labor economics | labor economics | child labor | child labor | producer theory | producer theory | variable inputs | variable inputs | fixed inputs | fixed inputs | firm production functions | firm production functions | marginal rate of technical substitution | marginal rate of technical substitution | returns to scale | returns to scale | productivity | productivity | perfect competition | perfect competition | search theory | search theory | residual demand | residual demand | shutdown decisions | shutdown decisions | market equilibrium | market equilibrium | agency problem | agency problem | welfare economics | welfare economics | consumer surplus | consumer surplus | producer surplus | producer surplus | dead weight loss | dead weight loss | monopoly | monopoly | oligopoly | oligopoly | market power | market power | price discrimination | price discrimination | price regulation | price regulation | antitrust policy | antitrust policy | mergers | mergers | cartel | cartel | game theory | game theory | Nash equilibrium | Nash equilibrium | Cournot model | Cournot model | duopoly | duopoly | non-cooperative competition | non-cooperative competition | Bertrand competition | Bertrand competition | factor markets | factor markets | international trade | international trade | uncertainty | uncertainty | capital markets | capital markets | intertemporal choice | intertemporal choice | real interest rate | real interest rate | compounding | compounding | inflation | inflation | investment | investment | discount rate | discount rate | net present value | net present value | income distribution | income distribution | social welfare function | social welfare function | Utilitarianism | Utilitarianism | Raulsian criteria | Raulsian criteria | Nozickian | Nozickian | commodity egalitarianism | commodity egalitarianism | isowelfare curves | isowelfare curves | social insurance | social insurance | social security | social security | moral hazard | moral hazard | taxation | taxation | EITC | EITC | healthcare | healthcare | PPACA | PPACALicense

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See all metadata18.03SC Differential Equations (MIT) 18.03SC Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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

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See all metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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

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Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (DepartmentSubjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objectsLicense

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

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See all metadata12.000 Solving Complex Problems (MIT) 12.000 Solving Complex Problems (MIT)

Description

Includes audio/video content: AV faculty introductions. Solving Complex Problems provides an opportunity for entering freshmen to gain first-hand experience with working as part of a team to develop effective approaches to complex problems in Earth system science and engineering that do not have straightforward solutions. The subject includes training in a variety of skills, ranging from library research to Web Design. Each year's course explores a different problem in detail through the study of complimentary case histories and the development of creative solution strategies. Beginning in 2000 as an educational experiment sponsored by MIT's Committee on the Undergraduate Program, and receiving major financial support from the Alex and Britt d'Arbeloff Fund for Excellence in Includes audio/video content: AV faculty introductions. Solving Complex Problems provides an opportunity for entering freshmen to gain first-hand experience with working as part of a team to develop effective approaches to complex problems in Earth system science and engineering that do not have straightforward solutions. The subject includes training in a variety of skills, ranging from library research to Web Design. Each year's course explores a different problem in detail through the study of complimentary case histories and the development of creative solution strategies. Beginning in 2000 as an educational experiment sponsored by MIT's Committee on the Undergraduate Program, and receiving major financial support from the Alex and Britt d'Arbeloff Fund for Excellence inSubjects

small teams | small teams | effective solutions | effective solutions | complex problems | complex problems | Earth system science and engineering | Earth system science and engineering | complementary case histories | complementary case histories | creative solution strategies | creative solution strategies | Web site development | Web site development | effective written and oral communication | effective written and oral communication | team building | team buildingLicense

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See all metadata3.20 Materials at Equilibrium (SMA 5111) (MIT) 3.20 Materials at Equilibrium (SMA 5111) (MIT)

Description

Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium). Material covered in this course includes the following topics: Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams Computation of phase diagrams Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions Applications to phase stability and properties of mixtures Computational modeling Interfaces This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium).Subjects

thermodynamics | thermodynamics | mechanical | mechanical | electromagnetic and electrochemical systems | electromagnetic and electrochemical systems | phase diagrams | phase diagrams | Statistical thermodynamics | Statistical thermodynamics | microscopic and macroscopic properties | microscopic and macroscopic properties | ensembles | ensembles | gases | gases | crystal lattices | crystal lattices | phase transitions | phase transitions | phase stability | phase stability | properties of mixtures | properties of mixtures | Computational modeling | Computational modeling | Interfaces | Interfaces | mechanical | electromagnetic and electrochemical systems | mechanical | electromagnetic and electrochemical systems | Computational modeling; Interfaces | Computational modeling; Interfaces | mechanical systems | mechanical systems | electromagnetic systems | electromagnetic systems | electrochemical systems | electrochemical systems | laws of thermodynamics | laws of thermodynamics | solutions | solutions | microscopic properties | microscopic properties | macroscopic properties | macroscopic propertiesLicense

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

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This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineering This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.002J. In 2005, ocean engineeringSubjects

digital computing | digital computing | algorithm accuracy | algorithm accuracy | error propagation | error propagation | linear equations | linear equations | iterative techniques | iterative techniques | roots of equations | roots of equations | systems of equations | systems of equations | numerical interpolation | numerical interpolation | differentiation | differentiation | integration | integration | finite-difference solutions | finite-difference solutions | differential equations | differential equations | convergence analysis | convergence analysisLicense

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