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6.050J Information and Entropy (MIT) 6.050J Information and Entropy (MIT)

Description

6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university.  6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university. 

Subjects

information and entropy | information and entropy | computing | computing | communications | communications | thermodynamics | thermodynamics | digital signals and streams | digital signals and streams | codes | codes | compression | compression | noise | noise | probability | probability | reversible operations | reversible operations | irreversible operations | irreversible operations | information in biological systems | information in biological systems | channel capacity | channel capacity | aximum-entropy formalism | aximum-entropy formalism | thermodynamic equilibrium | thermodynamic equilibrium | temperature | temperature | second law of thermodynamics quantum computation | second law of thermodynamics quantum computation | maximum-entropy formalism | maximum-entropy formalism | second law of thermodynamics | second law of thermodynamics | quantum computation | quantum computation | biological systems | biological systems | unified theory of information | unified theory of information | digital signals | digital signals | digital streams | digital streams | bits | bits | errors | errors | processes | processes | inference | inference | maximum entropy | maximum entropy | physical systems | physical systems | energy | energy | quantum information | quantum information | 6.050 | 6.050 | 2.110 | 2.110

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6.050J Information and Entropy (MIT) 6.050J Information and Entropy (MIT)

Description

Includes audio/video content: AV selected lectures. This course explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include: information and computation, digital signals, codes and compression, applications such as biological representations of information, logic circuits, computer architectures, and algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, and quantum computation. The concept of entropy applied to channel capacity and to the second law of thermodynamics. Includes audio/video content: AV selected lectures. This course explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include: information and computation, digital signals, codes and compression, applications such as biological representations of information, logic circuits, computer architectures, and algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, and quantum computation. The concept of entropy applied to channel capacity and to the second law of thermodynamics.

Subjects

information and entropy | information and entropy | computing | computing | communications | communications | thermodynamics | thermodynamics | digital signals and streams | digital signals and streams | codes | codes | compression | compression | noise | noise | probability | probability | reversible operations | reversible operations | irreversible operations | irreversible operations | information in biological systems | information in biological systems | channel capacity | channel capacity | maximum-entropy formalism | maximum-entropy formalism | thermodynamic equilibrium | thermodynamic equilibrium | temperature | temperature | second law of thermodynamics quantum computation | second law of thermodynamics quantum computation

License

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6.050J Information and Entropy (MIT)

Description

6.050J / 2.110J presents the unified theory of information with applications to computing, communications, thermodynamics, and other sciences. It covers digital signals and streams, codes, compression, noise, and probability, reversible and irreversible operations, information in biological systems, channel capacity, maximum-entropy formalism, thermodynamic equilibrium, temperature, the Second Law of Thermodynamics, and quantum computation. Designed for MIT freshmen as an elective, this course has been jointly developed by MIT's Departments of Electrical Engineering and Computer Science and Mechanical Engineering. There is no known course similar to 6.050J / 2.110J offered at any other university. 

Subjects

information and entropy | computing | communications | thermodynamics | digital signals and streams | codes | compression | noise | probability | reversible operations | irreversible operations | information in biological systems | channel capacity | aximum-entropy formalism | thermodynamic equilibrium | temperature | second law of thermodynamics quantum computation | maximum-entropy formalism | second law of thermodynamics | quantum computation | biological systems | unified theory of information | digital signals | digital streams | bits | errors | processes | inference | maximum entropy | physical systems | energy | quantum information | 6.050 | 2.110

License

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16.050 Thermal Energy (MIT) 16.050 Thermal Energy (MIT)

Description

This course is taught in four main parts. The first is a review of fundamental thermodynamic concepts (e.g. energy exchange in propulsion and power processes), and is followed by the second law (e.g. reversibility and irreversibility, lost work). Next are applications of thermodynamics to engineering systems (e.g. propulsion and power cycles, thermo chemistry), and the course concludes with fundamentals of heat transfer (e.g. heat exchange in aerospace devices). This course is taught in four main parts. The first is a review of fundamental thermodynamic concepts (e.g. energy exchange in propulsion and power processes), and is followed by the second law (e.g. reversibility and irreversibility, lost work). Next are applications of thermodynamics to engineering systems (e.g. propulsion and power cycles, thermo chemistry), and the course concludes with fundamentals of heat transfer (e.g. heat exchange in aerospace devices).

Subjects

energy exchange | energy exchange | propulsion | propulsion | power | power | second law | second law | thermodynamics | thermodynamics | reversible process | reversible process | irreversible process | irreversible process | irreversibility | irreversibility | lost work | lost work | first law | first law | cycles | cycles | energy transfer | energy transfer | heat exchange | heat exchange | energy conversion | energy conversion | entropy | entropy

License

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8.333 Statistical Mechanics (MIT) 8.333 Statistical Mechanics (MIT)

Description

8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory. 8.333 is the first course in a two-semester sequence on statistical mechanics. Basic principles are examined in 8.333: the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Postulates of classical statistical mechanics, micro canonical, canonical, and grand canonical distributions; applications to lattice vibrations, ideal gas, photon gas. Quantum statistical mechanics; Fermi and Bose systems. Interacting systems: cluster expansions, van der Waal's gas, and mean-field theory.

Subjects

hermodynamics | hermodynamics | entropy | entropy | mehanics | mehanics | microcanonical distributions | microcanonical distributions | canonical distributions | canonical distributions | grand canonical distributions | grand canonical distributions | lattice vibrations | lattice vibrations | ideal gas | ideal gas | photon gas | photon gas | quantum statistical mechanics | quantum statistical mechanics | Fermi systems | Fermi systems | Bose systems | Bose systems | cluster expansions | cluster expansions | van der Waal's gas | van der Waal's gas | mean-field theory | mean-field theory

License

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Kinetics (MIT) Kinetics (MIT)

Description

This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions. This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.

Subjects

thermodynamics | thermodynamics | kinetics | kinetics | equilibrium | equilibrium | macroscopic systems | macroscopic systems | state variables | state variables | law of thermodynamics | law of thermodynamics | entropy | entropy | Gibbs function | Gibbs function | reaction rates | reaction rates | clapeyron | clapeyron | enthalpy | enthalpy | clausius | clausius | adiabatic | adiabatic | Hemholtz | Hemholtz | catalysis | catalysis | oscillators | oscillators | autocatalysis | autocatalysis | carnot cycle | carnot cycle

License

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

Description

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

Subjects

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

License

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3.00 Thermodynamics of Materials (MIT) 3.00 Thermodynamics of Materials (MIT)

Description

Treatment of the laws of thermodynamics and their applications to equilibrium and the properties of materials. Provides a foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity. Develops relations pertaining to multiphase equilibria as determined by a treatment of solution thermodynamics. Develops graphical constructions that are essential for the interpretation of phase diagrams. Treatment includes electrochemical equilibria and surface thermodynamics. Introduces aspects of statistical thermodynamics as they relate to macroscopic equilibrium phenomena. Treatment of the laws of thermodynamics and their applications to equilibrium and the properties of materials. Provides a foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity. Develops relations pertaining to multiphase equilibria as determined by a treatment of solution thermodynamics. Develops graphical constructions that are essential for the interpretation of phase diagrams. Treatment includes electrochemical equilibria and surface thermodynamics. Introduces aspects of statistical thermodynamics as they relate to macroscopic equilibrium phenomena.

Subjects

thermodynamics | | thermodynamics | | First Law | | First Law | | Second Law | | Second Law | | Third Law | | Third Law | | entropy | | entropy | | state function | | state function | | Zeroth Law | | Zeroth Law | | ideal gas | | ideal gas | | phase transformation | | phase transformation | | equilibrium condition | | equilibrium condition | | Gibbs-Duhem Equation | | Gibbs-Duhem Equation | | chemical potential | chemical potential

License

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Kinetics (MIT) Kinetics (MIT)

Description

This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.AcknowledgementsThe material for 5.60 has evolved over a period of many years, and therefore several faculty members have contributed to the development of the course contents. The following are known to have assisted in preparing the lecture notes available on OCW:Emeritus Professors of Chemistry: Robert A. Alberty, Carl W. Garland, Irwin Oppenheim, John S. Waugh.Professors of Chemistry: Moungi Bawendi, John M. Deutch, Robert W. Field, Robert G. Griffin, Keith A. Nelson, Robert J. Silbey, Jeffrey I. Steinfeld.Professor of Bioengineering and Computer Science: Bruce Tidor.Professor of Chem This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.AcknowledgementsThe material for 5.60 has evolved over a period of many years, and therefore several faculty members have contributed to the development of the course contents. The following are known to have assisted in preparing the lecture notes available on OCW:Emeritus Professors of Chemistry: Robert A. Alberty, Carl W. Garland, Irwin Oppenheim, John S. Waugh.Professors of Chemistry: Moungi Bawendi, John M. Deutch, Robert W. Field, Robert G. Griffin, Keith A. Nelson, Robert J. Silbey, Jeffrey I. Steinfeld.Professor of Bioengineering and Computer Science: Bruce Tidor.Professor of Chem

Subjects

thermodynamics | thermodynamics | kinetics | kinetics | equilibrium | equilibrium | macroscopic systems | macroscopic systems | state variables | state variables | law of thermodynamics | law of thermodynamics | entropy | entropy | Gibbs function | Gibbs function | reaction rates | reaction rates

License

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6.02 Introduction to EECS II: Digital Communication Systems (MIT) 6.02 Introduction to EECS II: Digital Communication Systems (MIT)

Description

Includes audio/video content: AV lectures. An introduction to several fundamental ideas in electrical engineering and computer science, using digital communication systems as the vehicle. The three parts of the course—bits, signals, and packets—cover three corresponding layers of abstraction that form the basis of communication systems like the Internet. The course teaches ideas that are useful in other parts of EECS: abstraction, probabilistic analysis, superposition, time and frequency-domain representations, system design principles and trade-offs, and centralized and distributed algorithms. The course emphasizes connections between theoretical concepts and practice using programming tasks and some experiments with real-world communication channels. Includes audio/video content: AV lectures. An introduction to several fundamental ideas in electrical engineering and computer science, using digital communication systems as the vehicle. The three parts of the course—bits, signals, and packets—cover three corresponding layers of abstraction that form the basis of communication systems like the Internet. The course teaches ideas that are useful in other parts of EECS: abstraction, probabilistic analysis, superposition, time and frequency-domain representations, system design principles and trade-offs, and centralized and distributed algorithms. The course emphasizes connections between theoretical concepts and practice using programming tasks and some experiments with real-world communication channels.

Subjects

digital communication | digital communication | communication systems | communication systems | information | information | entropy | entropy | compression | compression | error correction | error correction | Fourier analysis | Fourier analysis | filtering | filtering | signals | signals | media access protocols | media access protocols | networks | networks | packets | packets | data transport | data transport | internet | internet

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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6.450 Principles of Digital Communication I (MIT) 6.450 Principles of Digital Communication I (MIT)

Description

The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication. The course serves as an introduction to the theory and practice behind many of today's communications systems. 6.450 forms the first of a two-course sequence on digital communication. The second class, 6.451 Principles of Digital Communication II, is offered in the spring. Topics covered include: digital communications at the block diagram level, data compression, Lempel-Ziv algorithm, scalar and vector quantization, sampling and aliasing, the Nyquist criterion, PAM and QAM modulation, signal constellations, finite-energy waveform spaces, detection, and modeling and system design for wireless communication.

Subjects

digital communication | digital communication | data compression | data compression | Lempel-Ziv algorithm | Lempel-Ziv algorithm | scalar quantization | scalar quantization | vector quantization | vector quantization | sampling | sampling | aliasing | aliasing | Nyquist criterion | Nyquist criterion | PAM modulation | PAM modulation | QAM modulation | QAM modulation | signal constellations | signal constellations | finite-energy waveform spaces | finite-energy waveform spaces | detection | detection | communication system design | communication system design | wireless | wireless | discrete source encoding | discrete source encoding | memory-less sources | memory-less sources | entropy | entropy | asymptotic equipartition property | asymptotic equipartition property | Fourier series | Fourier series | Fourier transforms | Fourier transforms | sampling theorem | sampling theorem | orthonormal expansions | orthonormal expansions | random processes | random processes | linear functionals | linear functionals | theorem of irrelevance | theorem of irrelevance | Doppler spread | Doppler spread | time spread | time spread | coherence time | coherence time | coherence frequency | coherence frequency | Rayleigh fading | Rayleigh fading | Rake receivers | Rake receivers | CDMA | CDMA | code division multiple access | code division multiple access

License

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6.047 Computational Biology: Genomes, Networks, Evolution (MIT) 6.047 Computational Biology: Genomes, Networks, Evolution (MIT)

Description

This course focuses on the algorithmic and machine learning foundations of computational biology, combining theory with practice. We study the principles of algorithm design for biological datasets, and analyze influential problems and techniques. We use these to analyze real datasets from large-scale studies in genomics and proteomics. The topics covered include: Genomes: biological sequence analysis, hidden Markov models, gene finding, RNA folding, sequence alignment, genome assembly Networks: gene expression analysis, regulatory motifs, graph algorithms, scale-free networks, network motifs, network evolution Evolution: comparative genomics, phylogenetics, genome duplication, genome rearrangements, evolutionary theory, rapid evolution This course focuses on the algorithmic and machine learning foundations of computational biology, combining theory with practice. We study the principles of algorithm design for biological datasets, and analyze influential problems and techniques. We use these to analyze real datasets from large-scale studies in genomics and proteomics. The topics covered include: Genomes: biological sequence analysis, hidden Markov models, gene finding, RNA folding, sequence alignment, genome assembly Networks: gene expression analysis, regulatory motifs, graph algorithms, scale-free networks, network motifs, network evolution Evolution: comparative genomics, phylogenetics, genome duplication, genome rearrangements, evolutionary theory, rapid evolution

Subjects

computational biology | computational biology | algorithms | algorithms | machine learning | machine learning | biology | biology | biological datasets | biological datasets | genomics | genomics | proteomics | proteomics | genomes | genomes | sequence analysis | sequence analysis | sequence alignment | sequence alignment | genome assembly | genome assembly | network motifs | network motifs | network evolution | network evolution | graph algorithms | graph algorithms | phylogenetics | phylogenetics | comparative genomics | comparative genomics | python | python | probability | probability | statistics | statistics | entropy | entropy | information | information

License

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6.050J Information and Entropy (MIT)

Description

This course explores the ultimate limits to communication and computation, with an emphasis on the physical nature of information and information processing. Topics include: information and computation, digital signals, codes and compression, applications such as biological representations of information, logic circuits, computer architectures, and algorithmic information, noise, probability, error correction, reversible and irreversible operations, physics of computation, and quantum computation. The concept of entropy applied to channel capacity and to the second law of thermodynamics.

Subjects

information and entropy | computing | communications | thermodynamics | digital signals and streams | codes | compression | noise | probability | reversible operations | irreversible operations | information in biological systems | channel capacity | maximum-entropy formalism | thermodynamic equilibrium | temperature | second law of thermodynamics quantum computation

License

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20.110J Thermodynamics of Biomolecular Systems (MIT) 20.110J Thermodynamics of Biomolecular Systems (MIT)

Description

This subject deals primarily with equilibrium properties of macroscopic and microscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and macromolecular interactions. This subject deals primarily with equilibrium properties of macroscopic and microscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and macromolecular interactions.

Subjects

thermodynamics | thermodynamics | biomolecular systems | biomolecular systems | equilibrium properties | equilibrium properties | first law of thermodynamics | first law of thermodynamics | second law of thermodynamics | second law of thermodynamics | third law of thermodynamics | third law of thermodynamics | thermochemistry | thermochemistry | entropy | entropy | Gibbs function | Gibbs function | chemical equilibrium | chemical equilibrium | macromolecular structure | macromolecular structure | binding cooperativity | binding cooperativity

License

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1.020 Ecology II: Engineering for Sustainability (MIT) 1.020 Ecology II: Engineering for Sustainability (MIT)

Description

This course covers the use of ecological and thermodynamic principles to examine interactions between humans and the natural environment. Topics include conservation and constitutive laws, box models, feedback, thermodynamic concepts, energy in natural and engineered systems, basic transport concepts, life cycle analysis and related economic methods.Topics such as renewable energy, sustainable agriculture, green buildings, and mitigation of climate change are illustrated with quantitative case studies. Case studies are team-oriented and may include numerical simulations and design exercises. Some programming experience is desirable but not a prerequisite. Instruction and practice in oral and written communication are provided. This course covers the use of ecological and thermodynamic principles to examine interactions between humans and the natural environment. Topics include conservation and constitutive laws, box models, feedback, thermodynamic concepts, energy in natural and engineered systems, basic transport concepts, life cycle analysis and related economic methods.Topics such as renewable energy, sustainable agriculture, green buildings, and mitigation of climate change are illustrated with quantitative case studies. Case studies are team-oriented and may include numerical simulations and design exercises. Some programming experience is desirable but not a prerequisite. Instruction and practice in oral and written communication are provided.

Subjects

systems | systems | conservation laws | conservation laws | constitutive laws | constitutive laws | box models | box models | mass conservation | mass conservation | perturbation methods | perturbation methods | thermodymanics | thermodymanics | heat transfer | heat transfer | enthalpy | enthalpy | entropy | entropy | multiphase systems | multiphase systems | mass and energy balances | mass and energy balances | energy supply options | energy supply options | economic value | economic value | natural resources | natural resources | multiobjective analysis | multiobjective analysis | life cycle analysis | life cycle analysis | mass and energy transport | mass and energy transport | green buildings | green buildings | transportation modeling | transportation modeling | renewable energy | renewable energy | climate modeling | climate modeling

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8.821 String Theory and Holographic Duality (MIT) 8.821 String Theory and Holographic Duality (MIT)

Description

Includes audio/video content: AV lectures. This string theory course focuses on holographic duality (also known as gauge / gravity duality or AdS / CFT) as a novel method of approaching and connecting a range of diverse subjects, including quantum gravity / black holes, QCD at extreme conditions, exotic condensed matter systems, and quantum information. Includes audio/video content: AV lectures. This string theory course focuses on holographic duality (also known as gauge / gravity duality or AdS / CFT) as a novel method of approaching and connecting a range of diverse subjects, including quantum gravity / black holes, QCD at extreme conditions, exotic condensed matter systems, and quantum information.

Subjects

string theory | string theory | holographic duality | holographic duality | Weinberg-Witten | Weinberg-Witten | AdS/CFT duality | AdS/CFT duality | black holes | black holes | Holographic principle | Holographic principle | Wilson loops | Wilson loops | Entanglement entropy | Entanglement entropy | Quark-gluon plasmas | Quark-gluon plasmas | quantum gravity | quantum gravity | Hamilton-Jacobi | Hamilton-Jacobi | D-branes | D-branes | Large-N Expansion | Large-N Expansion | Light-Cone Gauge | Light-Cone Gauge

License

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

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8.333 Statistical Mechanics I: Statistical Mechanics of Particles (MIT) 8.333 Statistical Mechanics I: Statistical Mechanics of Particles (MIT)

Description

Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles. Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.

Subjects

Thermodynamics | Thermodynamics | entropy. mehanics | entropy. mehanics | microcanonical distributions | microcanonical distributions | canonical distributions | canonical distributions | grand canonical distributions; lattice vibrations | grand canonical distributions; lattice vibrations | ideal gas | ideal gas | photon gas. | photon gas. | quantum statistical mechanics; Fermi systems | quantum statistical mechanics; Fermi systems | Bose systems | Bose systems | cluster expansions | cluster expansions | van der Waal's gas | van der Waal's gas | mean-field theory. | mean-field theory.

License

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

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6.441 Information Theory (MIT)

Description

This is a graduate-level introduction to mathematics of information theory. We will cover both classical and modern topics, including information entropy, lossless data compression, binary hypothesis testing, channel coding, and lossy data compression.

Subjects

properties of information | entropy | divergence | information measures | mutual information | sufficient statistic | probability of error | entropy rate | lossless data compression | fixed-length compression | ergodic sources | universal compression | binary hypothesis testing | information projection | channel coding | achievability bounds | linear codes | gaussian channels | input constraints | lattice codes | energy-per-bit | source-channel separation | feedback | forney concatenation | lossy compression | distortion | multiple-access channel | random number generator | source coding theorem | noisy communication | channel coding theorem | source channel separation theorem | broadcast channels | Gaussian noise | time-varying channels

License

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6.047 Computational Biology (MIT) 6.047 Computational Biology (MIT)

Description

This course covers the algorithmic and machine learning foundations of computational biology combining theory with practice. We cover both foundational topics in computational biology, and current research frontiers. We study fundamental techniques, recent advances in the field, and work directly with current large-scale biological datasets. This course covers the algorithmic and machine learning foundations of computational biology combining theory with practice. We cover both foundational topics in computational biology, and current research frontiers. We study fundamental techniques, recent advances in the field, and work directly with current large-scale biological datasets.

Subjects

Genomes | Genomes | Networks | Networks | Evolution | Evolution | computational biology | computational biology | genomics | genomics | comparative genomics | comparative genomics | epigenomics | epigenomics | functional genomics | motifs | functional genomics | motifs | phylogenomics | phylogenomics | personal genomics | personal genomics | algorithms | algorithms | machine learning | machine learning | biology | biology | biological datasets | biological datasets | proteomics | proteomics | sequence analysis | sequence analysis | sequence alignment | sequence alignment | genome assembly | genome assembly | network motifs | network motifs | network evolution | network evolution | graph algorithms | graph algorithms | phylogenetics | phylogenetics | python | python | probability | probability | statistics | statistics | entropy | entropy | information | information

License

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

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8.333 Statistical Mechanics I: Statistical Mechanics of Particles (MIT) 8.333 Statistical Mechanics I: Statistical Mechanics of Particles (MIT)

Description

Includes audio/video content: AV lectures. Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: Thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles. Includes audio/video content: AV lectures. Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: Thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.

Subjects

thermodynamics | thermodynamics | entropy | entropy | mehanics | mehanics | microcanonical distributions | microcanonical distributions | canonical distributions | canonical distributions | grand canonical distributions | grand canonical distributions | lattice vibrations | lattice vibrations | ideal gas | ideal gas | photon gas | photon gas | quantum statistical mechanics | quantum statistical mechanics | Fermi systems | Fermi systems | Bose systems | Bose systems | cluster expansions | cluster expansions | van der Waal's gas | van der Waal's gas | mean-field theory | mean-field theory

License

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

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10.40 Chemical Engineering Thermodynamics (MIT) 10.40 Chemical Engineering Thermodynamics (MIT)

Description

This course aims to connect the principles, concepts, and laws/postulates of classical and statistical thermodynamics to applications that require quantitative knowledge of thermodynamic properties from a macroscopic to a molecular level. It covers their basic postulates of classical thermodynamics and their application to transient open and closed systems, criteria of stability and equilibria, as well as constitutive property models of pure materials and mixtures emphasizing molecular-level effects using the formalism of statistical mechanics. Phase and chemical equilibria of multicomponent systems are covered. Applications are emphasized through extensive problem work relating to practical cases. This course aims to connect the principles, concepts, and laws/postulates of classical and statistical thermodynamics to applications that require quantitative knowledge of thermodynamic properties from a macroscopic to a molecular level. It covers their basic postulates of classical thermodynamics and their application to transient open and closed systems, criteria of stability and equilibria, as well as constitutive property models of pure materials and mixtures emphasizing molecular-level effects using the formalism of statistical mechanics. Phase and chemical equilibria of multicomponent systems are covered. Applications are emphasized through extensive problem work relating to practical cases.

Subjects

thermodynamics | thermodynamics | first law | first law | second law | second law | entropy | entropy | Carnot | Carnot | Gibbs | Gibbs | energy | energy | free energy | free energy | equilibrium | equilibrium | ideal gas | ideal gas | statistical mechanics | statistical mechanics | ensemble | ensemble | Hamiltonian | Hamiltonian | fugacity | fugacity | fluids | fluids | phase | phase | stability | stability

License

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16.55 Ionized Gases (MIT) 16.55 Ionized Gases (MIT)

Description

This course highlights the properties and behavior of low-temperature plasmas in relation to energy conversion, plasma propulsion, and gas lasers. The course includes material on the equilibrium (energy states, statistical mechanics, and relationship to thermodynamics) and kinetic theory of ionized gases (motion of charged particles, distribution function, collisions, characteristic lengths and times, cross sections, and transport properties). In addition, the course discusses gas surface interactions (thermionic emission, sheaths, and probe theory) and radiation in plasmas and diagnostics. This course highlights the properties and behavior of low-temperature plasmas in relation to energy conversion, plasma propulsion, and gas lasers. The course includes material on the equilibrium (energy states, statistical mechanics, and relationship to thermodynamics) and kinetic theory of ionized gases (motion of charged particles, distribution function, collisions, characteristic lengths and times, cross sections, and transport properties). In addition, the course discusses gas surface interactions (thermionic emission, sheaths, and probe theory) and radiation in plasmas and diagnostics.

Subjects

Ionized gases | Ionized gases | plasma physics | plasma physics | motion of charges | motion of charges | drift | drift | adiabatic invariants | adiabatic invariants | collision theory | collision theory | kinetic theory | kinetic theory | H theorem | H theorem | entropy | entropy | Maxwellian distribution | Maxwellian distribution | Boltzmann equation | Boltzmann equation | plasma sheath | plasma sheath | electrostatic probe | electrostatic probe | orbital motion limit | orbital motion limit | equilibrium statistical mechanics | equilibrium statistical mechanics | radiation transport | radiation transport

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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Kinetics (MIT) Kinetics (MIT)

Description

This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.AcknowledgementsThe material for 5.60 has evolved over a period of many years, and therefore several faculty members have contributed to the development of the course contents. The following are known to have assisted in preparing the lecture notes available on OCW:Emeritus Professors of Chemistry: Robert A. Alberty, Carl W. Garland, Irwin Oppenheim, John S. Waugh.Professors of Chemistry: Moungi Bawendi, John M. Deutch, Robert W. Field, Robert G. Griffin, Keith A. Nelson, Robert J. Silbey, Jeffrey I. Steinfeld.Professor of Bioengineering and Computer Science: Bruce Tidor.Professor of Chemistry, Ri This subject deals primarily with equilibrium properties of macroscopic systems, basic thermodynamics, chemical equilibrium of reactions in gas and solution phase, and rates of chemical reactions.AcknowledgementsThe material for 5.60 has evolved over a period of many years, and therefore several faculty members have contributed to the development of the course contents. The following are known to have assisted in preparing the lecture notes available on OCW:Emeritus Professors of Chemistry: Robert A. Alberty, Carl W. Garland, Irwin Oppenheim, John S. Waugh.Professors of Chemistry: Moungi Bawendi, John M. Deutch, Robert W. Field, Robert G. Griffin, Keith A. Nelson, Robert J. Silbey, Jeffrey I. Steinfeld.Professor of Bioengineering and Computer Science: Bruce Tidor.Professor of Chemistry, Ri

Subjects

thermodynamics | thermodynamics | kinetics | kinetics | equilibrium | equilibrium | macroscopic systems | macroscopic systems | state variables | state variables | law of thermodynamics | law of thermodynamics | entropy | entropy | Gibbs function | Gibbs function | reaction rates | reaction rates | clapeyron | clapeyron | enthalpy | enthalpy | clausius | clausius | adiabatic | adiabatic | Hemholtz | Hemholtz | catalysis | catalysis | oscillators | oscillators | autocatalysis | autocatalysis | carnot cycle | carnot cycle

License

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16.36 Communication Systems Engineering (MIT) 16.36 Communication Systems Engineering (MIT)

Description

This course will cover fundamentals of digital communications and networking. We will study the basics of information theory, sampling and quantization, coding, modulation, signal detection and system performance in the presence of noise. The study of data networking will include multiple access, reliable packet transmission, routing and protocols of the internet. The concepts taught in class will be discussed in the context of aerospace communication systems: aircraft communications, satellite communications, and deep space communications. This course will cover fundamentals of digital communications and networking. We will study the basics of information theory, sampling and quantization, coding, modulation, signal detection and system performance in the presence of noise. The study of data networking will include multiple access, reliable packet transmission, routing and protocols of the internet. The concepts taught in class will be discussed in the context of aerospace communication systems: aircraft communications, satellite communications, and deep space communications.

Subjects

digital communications | digital communications | networking | networking | information theory | information theory | sampling | sampling | quantization | quantization | coding | coding | modulation | modulation | signal detection | signal detection | data networking | data networking | multiple access | multiple access | packet transmission | packet transmission | routing | routing | aerospace communication | aerospace communication | aircraft communication | aircraft communication | satellite communication | satellite communication | deep space communication | deep space communication | communication systems haykin | communication systems haykin | computer networks tanenbaum | computer networks tanenbaum | communication systems engineering proakis | communication systems engineering proakis | sampling theorem | sampling theorem | entropy | entropy | signal detection in noise | signal detection in noise | delay models | delay models

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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