Searching for variation : 80 results found | RSS Feed for this search

3.987 Human Origins and Evolution (MIT) 3.987 Human Origins and Evolution (MIT)

Description

This course examines the dynamic interrelations among physical and behavioral traits of humans, environment, and culture to provide an integrated framework for studying human biological evolution and modern diversity. Topics include issues in morphological evolution and adaptation; fossil and cultural evidence for human evolution from earliest times through the Pleistocene; evolution of tool use and social behavior; modern human variation and concepts of race. The class also studies stone artifacts and fossil specimens. This course examines the dynamic interrelations among physical and behavioral traits of humans, environment, and culture to provide an integrated framework for studying human biological evolution and modern diversity. Topics include issues in morphological evolution and adaptation; fossil and cultural evidence for human evolution from earliest times through the Pleistocene; evolution of tool use and social behavior; modern human variation and concepts of race. The class also studies stone artifacts and fossil specimens.Subjects

cultural evolution | pre-hominid | hominid | Pleistocene adaptations | morphological variation | race | agriculture | urbanization | paleontology | archaeology | Oligocene | Miocene | Homo | Homo erectus | Homo heidelbergensis | Homo neanderthalensis | Homo sapiens | fossil | cultural evolution | pre-hominid | hominid | Pleistocene adaptations | morphological variation | race | agriculture | urbanization | paleontology | archaeology | Oligocene | Miocene | Homo | Homo erectus | Homo heidelbergensis | Homo neanderthalensis | Homo sapiens | fossil | cultural evolution | cultural evolution | pre-hominid | pre-hominid | hominid | hominid | Pleistocene adaptations | Pleistocene adaptations | morphological variation | morphological variation | race | race | agriculture | agriculture | urbanization | urbanization | paleontology | paleontology | archaeology | archaeology | Oligocene | Oligocene | Miocene | Miocene | Homo | Homo | Homo erectus | Homo erectus | Homo heidelbergensis | Homo heidelbergensis | Homo neanderthalensis | Homo neanderthalensis | Homo sapiens | Homo sapiens | fossil | fossilLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-3.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes. This course focuses on dynamic optimization methods, both in discrete and in continuous time. We approach these problems from a dynamic programming and optimal control perspective. We also study the dynamic systems that come from the solutions to these problems. The course will illustrate how these techniques are useful in various applications, drawing on many economic examples. However, the focus will remain on gaining a general command of the tools so that they can be applied later in other classes.Subjects

vector spaces | vector spaces | principle of optimality | principle of optimality | concavity of the value function | concavity of the value function | differentiability of the value function | differentiability of the value function | Euler equations | Euler equations | deterministic dynamics | deterministic dynamics | models with constant returns to scale | models with constant returns to scale | nonstationary models | nonstationary models | stochastic dynamic programming | stochastic dynamic programming | stochastic Euler equations | stochastic Euler equations | stochastic dynamics | stochastic dynamics | calculus of variations | calculus of variations | the maximum principle | the maximum principle | discounted infinite-horizon optimal control | discounted infinite-horizon optimal control | saddle-path stability | saddle-path stabilityLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata14.121 Microeconomic Theory I (MIT) 14.121 Microeconomic Theory I (MIT)

Description

This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered. This half-semester course provides an introduction to microeconomic theory designed to meet the needs of students in the economics Ph.D. program. Some parts of the course are designed to teach material that all graduate students should know. Others are used to introduce methodologies. Topics include consumer and producer theory, markets and competition, general equilibrium, and tools of comparative statics and their application to price theory. Some topics of recent interest may also be covered.Subjects

microeconomic theory | microeconomic theory | demand theory | demand theory | producer theory; partial equilibrium | producer theory; partial equilibrium | competitive markets | competitive markets | general equilibrium | general equilibrium | externalities | externalities | Afriat's theorem | Afriat's theorem | pricing | pricing | robust comparative statics | robust comparative statics | utility theory | utility theory | properties of preferences | properties of preferences | choice as primitive | choice as primitive | revealed preference | revealed preference | classical demand theory | classical demand theory | Kuhn-Tucker necessary conditions | Kuhn-Tucker necessary conditions | implications of Walras?s law | implications of Walras?s law | indirect utility functions | indirect utility functions | theorem of the maximum (Berge?s theorem) | theorem of the maximum (Berge?s theorem) | expenditure minimization problem | expenditure minimization problem | Hicksian demands | Hicksian demands | compensated law of demand | compensated law of demand | Slutsky substitution | Slutsky substitution | price changes and welfare | price changes and welfare | compensating variation | compensating variation | and welfare from new goods | and welfare from new goods | price indexes | price indexes | bias in the U.S. consumer price index | bias in the U.S. consumer price index | integrability | integrability | demand aggregation | demand aggregation | aggregate demand and welfare | aggregate demand and welfare | Frisch demands | Frisch demands | and demand estimation | and demand estimation | increasing differences | increasing differences | producer theory applications | producer theory applications | the LeCh?telier principle | the LeCh?telier principle | Topkis? theorem | Topkis? theorem | Milgrom-Shannon monotonicity theorem | Milgrom-Shannon monotonicity theorem | monopoly pricing | monopoly pricing | monopoly and product quality | monopoly and product quality | nonlinear pricing | nonlinear pricing | and price discrimination | and price discrimination | simple models of externalities | simple models of externalities | government intervention | government intervention | Coase theorem | Coase theorem | Myerson-Sattherthwaite proposition | Myerson-Sattherthwaite proposition | missing markets | missing markets | price vs. quantity regulations | price vs. quantity regulations | Weitzman?s analysis | Weitzman?s analysis | uncertainty | uncertainty | common property externalities | common property externalities | optimization | optimization | equilibrium number of boats | equilibrium number of boats | welfare theorems | welfare theorems | uniqueness and determinacy | uniqueness and determinacy | price-taking assumption | price-taking assumption | Edgeworth box | Edgeworth box | welfare properties | welfare properties | Pareto efficiency | Pareto efficiency | Walrasian equilibrium with transfers | Walrasian equilibrium with transfers | Arrow-Debreu economy | Arrow-Debreu economy | separating hyperplanes | separating hyperplanes | Minkowski?s theorem | Minkowski?s theorem | Existence of Walrasian equilibrium | Existence of Walrasian equilibrium | Kakutani?s fixed point theorem | Kakutani?s fixed point theorem | Debreu-Gale-Kuhn-Nikaido lemma | Debreu-Gale-Kuhn-Nikaido lemma | additional properties of general equilibrium | additional properties of general equilibrium | Microfoundations | Microfoundations | core | core | core convergence | core convergence | general equilibrium with time and uncertainty | general equilibrium with time and uncertainty | Jensen?s inequality | Jensen?s inequality | and security market economy | and security market economy | arbitrage pricing theory | arbitrage pricing theory | and risk-neutral probabilities | and risk-neutral probabilities | Housing markets | Housing markets | competitive equilibrium | competitive equilibrium | one-sided matching house allocation problem | one-sided matching house allocation problem | serial dictatorship | serial dictatorship | two-sided matching | two-sided matching | marriage markets | marriage markets | existence of stable matchings | existence of stable matchings | incentives | incentives | housing markets core mechanism | housing markets core mechanismLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata8.06 Quantum Physics III (MIT) 8.06 Quantum Physics III (MIT)

Description

This course is a continuation of 8.05, Quantum Physics II. Content includes:Natural UnitsCharged particles in a magnetic fieldTime-independent perturbation theoryVariational and semi-classical methodsQuantum ComputingThe adiabatic approximation and Berry’s phaseScatteringTime-dependent perturbation theory This course is a continuation of 8.05, Quantum Physics II. Content includes:Natural UnitsCharged particles in a magnetic fieldTime-independent perturbation theoryVariational and semi-classical methodsQuantum ComputingThe adiabatic approximation and Berry’s phaseScatteringTime-dependent perturbation theorySubjects

natural units | natural units | scales of microscopic phenomena | scales of microscopic phenomena | Time-independent approximation methods: degenerate and non-degenerate perturbation theory | Time-independent approximation methods: degenerate and non-degenerate perturbation theory | variational method | variational method | Born-Oppenheimer approximation | Born-Oppenheimer approximation | spin-orbit and relativistic corrections | spin-orbit and relativistic corrections | Zeeman and Stark effects | Zeeman and Stark effects | Charged particles in a magnetic field | Charged particles in a magnetic field | Landau levels | Landau levels | integer quantum hall effect | integer quantum hall effect | Scattering | Scattering | partial waves | partial waves | Born approximation | Born approximation | Time-dependent perturbation theory | Time-dependent perturbation theory | quantum physics | quantum physicsLicense

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

Human genome sequencing has revolutionized our understanding of disease susceptibility, drug metabolism and human ancestry. This course will explore how these advances have been made possible by revolutionary new sequencing methodologies that have decreased costs and increased throughput of genome analysis, making it possible to examine genetic correlates for a variety of biological processes and disorders. The course will combine discussions of primary scientific research papers with hands-on data analysis and small group presentations. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a Human genome sequencing has revolutionized our understanding of disease susceptibility, drug metabolism and human ancestry. This course will explore how these advances have been made possible by revolutionary new sequencing methodologies that have decreased costs and increased throughput of genome analysis, making it possible to examine genetic correlates for a variety of biological processes and disorders. The course will combine discussions of primary scientific research papers with hands-on data analysis and small group presentations. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in aSubjects

genome sequencing | genome sequencing | genome analysis | genome analysis | disease susceptibility | disease susceptibility | drug metabolism | drug metabolism | human ancestry | human ancestry | mitochondrial DNA | mitochondrial DNA | tyrosine kinase inhibitors | tyrosine kinase inhibitors | BCR-ABL gene fusion | BCR-ABL gene fusion | PCSK9 inhibitors | PCSK9 inhibitors | hypercholesterolemia | hypercholesterolemia | genetic testing | genetic testing | next generation sequencing | next generation sequencing | Single-nucleotide polymorphisms (SNPs) | Single-nucleotide polymorphisms (SNPs) | copy number variations (CNVs) | copy number variations (CNVs) | genome-wide association studies (GWAS) | genome-wide association studies (GWAS) | Chronic myelogenous leukemia (CML) | Chronic myelogenous leukemia (CML) | mosaics | mosaics | chimeras | chimeras | bioinformatics | bioinformaticsLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-7.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

The goal of this course is to prepare you to engage in experimental investigations of questions related to linguistic theory, focusing on phonetics and phonology. The goal of this course is to prepare you to engage in experimental investigations of questions related to linguistic theory, focusing on phonetics and phonology.Subjects

audition | audition | digital signal processing | digital signal processing | acoustics of vowels | acoustics of vowels | adaptive dispersion | adaptive dispersion | spectral analysis | spectral analysis | licensing by cue | licensing by cue | intonation | intonation | meaning of intonation | meaning of intonation | lexicon | lexicon | cntext | cntext | speech perception | speech perception | phonetics | phonetics | phonology | phonology | accent variation | accent variation | laboratory phonology | laboratory phonology | source-filter theory | source-filter theory | A/D conversion | A/D conversion | acoustics | acousticsLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-24.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata8.06 Quantum Physics III (MIT) 8.06 Quantum Physics III (MIT)

Description

Together, this course and its predecessor, 8.05: Quantum Physics II, cover quantum physics with applications drawn from modern physics. Topics in this course include units, time-independent approximation methods, the structure of one- and two-electron atoms, charged particles in a magnetic field, scattering, and time-dependent perturbation theory. In this second term, students are required to research and write a paper on a topic related to the content of 8.05 and 8.06. Together, this course and its predecessor, 8.05: Quantum Physics II, cover quantum physics with applications drawn from modern physics. Topics in this course include units, time-independent approximation methods, the structure of one- and two-electron atoms, charged particles in a magnetic field, scattering, and time-dependent perturbation theory. In this second term, students are required to research and write a paper on a topic related to the content of 8.05 and 8.06.Subjects

natural units | natural units | scales of microscopic phenomena | scales of microscopic phenomena | Time-independent approximation methods: degenerate and non-degenerate perturbation theory | Time-independent approximation methods: degenerate and non-degenerate perturbation theory | variational method | variational method | Born-Oppenheimer approximation | Born-Oppenheimer approximation | spin-orbit and relativistic corrections | spin-orbit and relativistic corrections | Zeeman and Stark effects | Zeeman and Stark effects | Charged particles in a magnetic field | Charged particles in a magnetic field | Landau levels | Landau levels | integer quantum hall effect | integer quantum hall effect | Scattering | Scattering | partial waves | partial waves | Born approximation | Born approximation | Time-dependent perturbation theory | Time-dependent perturbation theoryLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata5.73 Introductory Quantum Mechanics I (MIT) 5.73 Introductory Quantum Mechanics I (MIT)

Description

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

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

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

http://ocw.mit.edu/rss/all/mit-allcourses-5.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata8.321 Quantum Theory I (MIT) 8.321 Quantum Theory I (MIT)

Description

8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement. 8.321 is the first semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: Hilbert spaces, observables, uncertainty relations, eigenvalue problems and methods for solution thereof, time-evolution in the Schrodinger, Heisenberg, and interaction pictures, connections between classical and quantum mechanics, path integrals, quantum mechanics in EM fields, angular momentum, time-independent perturbation theory, density operators, and quantum measurement.Subjects

eigenstates | eigenstates | uncertainty relation | uncertainty relation | observables | observables | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamicsLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata8.322 Quantum Theory II (MIT) 8.322 Quantum Theory II (MIT)

Description

8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation. 8.322 is the second semester of a two-semester subject on quantum theory, stressing principles. Topics covered include: time-dependent perturbation theory and applications to radiation, quantization of EM radiation field, adiabatic theorem and Berry's phase, symmetries in QM, many-particle systems, scattering theory, relativistic quantum mechanics, and Dirac equation.Subjects

uncertainty relation | uncertainty relation | observables | observables | eigenstates | eigenstates | eigenvalues | eigenvalues | probabilities of the results of measurement | probabilities of the results of measurement | transformation theory | transformation theory | equations of motion | equations of motion | constants of motion | constants of motion | Symmetry in quantum mechanics | Symmetry in quantum mechanics | representations of symmetry groups | representations of symmetry groups | Variational and perturbation approximations | Variational and perturbation approximations | Systems of identical particles and applications | Systems of identical particles and applications | Time-dependent perturbation theory | Time-dependent perturbation theory | Scattering theory: phase shifts | Scattering theory: phase shifts | Born approximation | Born approximation | The quantum theory of radiation | The quantum theory of radiation | Second quantization and many-body theory | Second quantization and many-body theory | Relativistic quantum mechanics of one electron | Relativistic quantum mechanics of one electron | probability | probability | measurement | measurement | motion equations | motion equations | motion constants | motion constants | symmetry groups | symmetry groups | quantum mechanics | quantum mechanics | variational approximations | variational approximations | perturbation approximations | perturbation approximations | identical particles | identical particles | time-dependent perturbation theory | time-dependent perturbation theory | scattering theory | scattering theory | phase shifts | phase shifts | quantum theory of radiation | quantum theory of radiation | second quantization | second quantization | many-body theory | many-body theory | relativistic quantum mechanics | relativistic quantum mechanics | one electron | one electron | quantization | quantization | EM radiation field | EM radiation field | electromagnetic radiation field | electromagnetic radiation field | adiabatic theorem | adiabatic theorem | Berry?s phase | Berry?s phase | many-particle systems | many-particle systems | Dirac equation | Dirac equation | Hilbert spaces | Hilbert spaces | time evolution | time evolution | Schrodinger picture | Schrodinger picture | Heisenberg picture | Heisenberg picture | interaction picture | interaction picture | classical mechanics | classical mechanics | path integrals | path integrals | EM fields | EM fields | electromagnetic fields | electromagnetic fields | angular momentum | angular momentum | density operators | density operators | quantum measurement | quantum measurement | quantum statistics | quantum statistics | quantum dynamics | quantum dynamicsLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history. This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history.Subjects

climate | climate | climate change | climate change | proxies | proxies | ice cores | ice cores | primordial atmosphere | primordial atmosphere | ozone chemistry | ozone chemistry | carbon and oxygen cycles | carbon and oxygen cycles | heat and water budgets | heat and water budgets | aerosols | aerosols | water vapor | water vapor | clouds | clouds | ocean circulation | ocean circulation | orbital variations | orbital variations | volcanism | volcanism | plate tectonics | plate tectonics | solar system | solar system | solar variability | solar variability | climate model | climate model | energy balance | energy balanceLicense

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

6.728 covers concepts in elementary quantum mechanics and statistical physics. The course introduces applied quantum physics and  emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others. 6.728 covers concepts in elementary quantum mechanics and statistical physics. The course introduces applied quantum physics and  emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.Subjects

applied quantum physics | applied quantum physics | quantum physics | quantum physics | statistical physics | statistical physics | quantum mechanics | quantum mechanics | Schrodinger | Schrodinger | tunneling | tunneling | harmonic oscillator | harmonic oscillator | hydrogen atom | hydrogen atom | variational methods | variational methods | Fermi-Dirac | Fermi-Dirac | Bose-Einstein | Bose-Einstein | Boltzmann | Boltzmann | distribution function | distribution function | electron microscope | electron microscope | scanning tunneling microscope | scanning tunneling microscope | thermonic emitter | thermonic emitter | atomic force microscope | atomic force microscopeLicense

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata12.520 Geodynamics (MIT) 12.520 Geodynamics (MIT)

Description

This course deals with mechanics of deformation of the crust and mantle, with emphasis on the importance of different rheological descriptions: brittle, elastic, linear and nonlinear fluids, and viscoelastic. This course deals with mechanics of deformation of the crust and mantle, with emphasis on the importance of different rheological descriptions: brittle, elastic, linear and nonlinear fluids, and viscoelastic.Subjects

Geodynamics | Geodynamics | mechanics of deformation | mechanics of deformation | crust | crust | mantle | mantle | rheological descriptions | rheological descriptions | brittle | brittle | elastic | elastic | linear | linear | nonlinear fluids | nonlinear fluids | viscoelastic | viscoelastic | surface tractions | surface tractions | tectonic stress | tectonic stress | quantity expression | quantity expression | stress variations | stress variations | sandbox tectonics | sandbox tectonics | displacement gradients | displacement gradients | strains | strains | rotations | rotations | finite strain | finite strain | motivation | motivation | dislocation | dislocation | plates | plates | topography | topography | rock rheology | rock rheology | accretionary wedge | accretionary wedge | linear fluids | linear fluids | elastic models | elastic models | newtonian fluids | newtonian fluids | stream function | stream function | Rayleigh-Taylor instability | Rayleigh-Taylor instability | diapirism | diapirism | diapirs | diapirs | plumes | plumes | corner flow | corner flow | power law creep | power law creep | viscoelasticity | viscoelasticity | porous media | porous media | Elsasser model | Elsasser model | time dependent porous flow | time dependent porous flowLicense

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

This seminar applies a systems perspective to understand health care delivery today, its stakeholders and problems as well as opportunities. Students are introduced to the 'systems perspective' that has been used successfully in other industries, and will address the introduction of new processes, technologies and strategies to improve overall health outcomes. Students are assigned to teams to work on a semester‐long group project, in collaboration with staff of a nearby Boston hospital. This seminar applies a systems perspective to understand health care delivery today, its stakeholders and problems as well as opportunities. Students are introduced to the 'systems perspective' that has been used successfully in other industries, and will address the introduction of new processes, technologies and strategies to improve overall health outcomes. Students are assigned to teams to work on a semester‐long group project, in collaboration with staff of a nearby Boston hospital.Subjects

HST.926 | HST.926 | health systems | health systems | quality improvement | quality improvement | safety | safety | health care delivery | health care delivery | payment by results | payment by results | health care and information technology | health care and information technology | process change | process change | uncertainty in clinical decision | uncertainty in clinical decision | variation in clinical decision | variation in clinical decision | performance measures in health care | performance measures in health careLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-ESD.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

6.728 is offered under the department's "Devices, Circuits, and Systems" concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others. 6.728 is offered under the department's "Devices, Circuits, and Systems" concentration. The course covers concepts in elementary quantum mechanics and statistical physics, introduces applied quantum physics, and emphasizes an experimental basis for quantum mechanics. Concepts covered include: Schrodinger's equation applied to the free particle, tunneling, the harmonic oscillator, and hydrogen atom, variational methods, Fermi-Dirac, Bose-Einstein, and Boltzmann distribution functions, and simple models for metals, semiconductors, and devices such as electron microscopes, scanning tunneling microscope, thermonic emitters, atomic force microscope, and others.Subjects

applied quantum physics | applied quantum physics | quantum physics | quantum physics | statistical physics | statistical physics | quantum mechanics | quantum mechanics | Schrodinger | Schrodinger | tunneling | tunneling | harmonic oscillator | harmonic oscillator | hydrogen atom | hydrogen atom | variational methods | variational methods | Fermi-Dirac | Fermi-Dirac | Bose-Einstein | Bose-Einstein | Boltzmann | Boltzmann | distribution function | distribution function | electron microscope | electron microscope | scanning tunneling microscope | scanning tunneling microscope | thermonic emitter | thermonic emitter | atomic force microscope | atomic force microscopeLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-6.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ov 12.620J covers the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. The course uses computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration.The following topics are covered: the Lagrangian formulation, action, variational principles, and equations of motion, Hamilton's principle, conserved quantities, rigid bodies and tops, Hamiltonian formulation and canonical equations, surfaces of section, chaos, canonical transformations and generating functions, Liouville's theorem and Poincaré integral invariants, Poincaré-Birkhoff and KAM theorems, invariant curves and cantori, nonlinear resonances, resonance ovSubjects

classical mechanics | classical mechanics | phase space | phase space | computation | computation | Lagrangian formulation | Lagrangian formulation | action | action | variational principles | variational principles | equations of motion | equations of motion | Hamilton's principle | Hamilton's principle | conserved quantities | conserved quantities | rigid bodies and tops | rigid bodies and tops | Hamiltonian formulation | Hamiltonian formulation | canonical equations | canonical equations | surfaces of section | surfaces of section | chaos | chaos | canonical transformations | canonical transformations | generating functions | generating functions | Liouville's theorem | Liouville's theorem | Poincar? integral invariants | Poincar? integral invariants | Poincar?-Birkhoff | Poincar?-Birkhoff | KAM theorem | KAM theorem | invariant curves | invariant curves | cantori | cantori | nonlinear resonances | nonlinear resonances | resonance overlap | resonance overlap | transition to chaos | transition to chaos | chaotic motion | chaotic motion | 12.620 | 12.620 | 6.946 | 6.946 | 8.351 | 8.351License

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

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

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata12.301 Climate Physics and Chemistry (MIT) 12.301 Climate Physics and Chemistry (MIT)

Description

This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history; methods for detecting climate change, including proxies, ice cores, instrumental records, and time series analysis; physical and chemical processes in climate, including primordial atmosphere, ozone chemistry, carbon and oxygen cycles, and heat and water budgets; internal feedback mechanisms, including ice, aerosols, water vapor, clouds, and ocean circulation; climate forcing, including orbital variations, volcanism, plate tectonics, and solar variability; climate models and mechanisms of variability, including energy balance, coupled models, and global ocean and atmosphere models; and outstanding problems. This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history; methods for detecting climate change, including proxies, ice cores, instrumental records, and time series analysis; physical and chemical processes in climate, including primordial atmosphere, ozone chemistry, carbon and oxygen cycles, and heat and water budgets; internal feedback mechanisms, including ice, aerosols, water vapor, clouds, and ocean circulation; climate forcing, including orbital variations, volcanism, plate tectonics, and solar variability; climate models and mechanisms of variability, including energy balance, coupled models, and global ocean and atmosphere models; and outstanding problems.Subjects

climate | climate | climate change | climate change | proxies | proxies | ice cores | ice cores | primordial atmosphere | primordial atmosphere | ozone chemistry | ozone chemistry | carbon and oxygen cycles | carbon and oxygen cycles | heat and water budgets | heat and water budgets | aerosols | aerosols | water vapor | water vapor | clouds | clouds | ocean circulation | ocean circulation | orbital variations | orbital variations | volcanism | volcanism | plate tectonics | plate tectonics | solar system | solar system | solar variability | solar variability | climate model | climate model | energy balance | energy balanceLicense

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata6.780 Semiconductor Manufacturing (MIT) 6.780 Semiconductor Manufacturing (MIT)

Description

6.780 covers statistical modeling and the control of semiconductor fabrication processes and plants. Topics covered include: design of experiments, response surface modeling, and process optimization; defect and parametric yield modeling; process/device/circuit yield optimization; monitoring, diagnosis, and feedback control of equipment and processes; and analysis and scheduling of semiconductor manufacturing operations. 6.780 covers statistical modeling and the control of semiconductor fabrication processes and plants. Topics covered include: design of experiments, response surface modeling, and process optimization; defect and parametric yield modeling; process/device/circuit yield optimization; monitoring, diagnosis, and feedback control of equipment and processes; and analysis and scheduling of semiconductor manufacturing operations.Subjects

Semiconductor manufacturing | Semiconductor manufacturing | statistics | statistics | distributions | distributions | estimation | estimation | hypothesis testing | hypothesis testing | statistical process control | statistical process control | control chart | control chart | control chart design | control chart design | design of experiments | design of experiments | empirical equipment | empirical equipment | process modeling | process modeling | experimental design | experimental design | yield models | yield models | spatial variation | spatial variation | spatial models | spatial models | design for manufacturability | design for manufacturability | equipment monitoring | equipment monitoring | equipment diagnosis | equipment diagnosis | equipment control | equipment control | run by run | run by run | multistage process control | multistage process control | scheduling | scheduling | planning | planning | factory modeling | factory modeling | factory infrastructure | factory infrastructure | environmental | environmental | health and safety | health and safety | computer integrated manufacturing | computer integrated manufacturing | factory operation | factory operation | factory design | factory design | advanced process control | advanced process control | yield learning | yield learningLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-6.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataDescription

We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overl We will study the fundamental principles of classical mechanics, with a modern emphasis on the qualitative structure of phase space. We will use computational ideas to formulate the principles of mechanics precisely. Expression in a computational framework encourages clear thinking and active exploration. We will consider the following topics: the Lagrangian formulation; action, variational principles, and equations of motion; Hamilton's principle; conserved quantities; rigid bodies and tops; Hamiltonian formulation and canonical equations; surfaces of section; chaos; canonical transformations and generating functions; Liouville's theorem and Poincaré integral invariants; Poincaré-Birkhoff and KAM theorems; invariant curves and cantori; nonlinear resonances; resonance overlSubjects

classical mechanics | classical mechanics | computational classical mechanics | computational classical mechanics | structure and interpretation of classical mechanics | structure and interpretation of classical mechanics | phase space | phase space | lagrangian | lagrangian | action | action | variational principles | variational principles | equation of motion | equation of motion | hamilton principle | hamilton principle | rigid bodies | rigid bodies | Hamiltonian | Hamiltonian | canonical equations | canonical equations | surfaces of section | surfaces of section | canonical transformations | canonical transformations | liouville | liouville | Poincare | Poincare | birkhoff | birkhoff | kam theorem | kam theorem | invariant curves | invariant curves | resonance | resonance | chaos | chaosLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-12.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata12.842 Climate Physics and Chemistry (MIT) 12.842 Climate Physics and Chemistry (MIT)

Description

This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history. It is offered to both undergraduate and graduate students with different requirements. This course introduces students to climate studies, including beginnings of the solar system, time scales, and climate in human history. It is offered to both undergraduate and graduate students with different requirements.Subjects

climate | climate | climate change | climate change | proxies | proxies | ice cores | ice cores | primordial atmosphere | primordial atmosphere | ozone chemistry | ozone chemistry | carbon and oxygen cycles | carbon and oxygen cycles | heat and water budgets | heat and water budgets | aerosols | aerosols | water vapor | water vapor | clouds | clouds | ocean circulation | ocean circulation | orbital variations | orbital variations | volcanism | volcanism | plate tectonics | plate tectonics | solar system | solar system | solar variability | solar variability | climate model | climate model | energy balance | energy balanceLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-12.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata3.987 Human Origins and Evolution (MIT)

Description

This course examines the dynamic interrelations among physical and behavioral traits of humans, environment, and culture to provide an integrated framework for studying human biological evolution and modern diversity. Topics include issues in morphological evolution and adaptation; fossil and cultural evidence for human evolution from earliest times through the Pleistocene; evolution of tool use and social behavior; modern human variation and concepts of race. The class also studies stone artifacts and fossil specimens.Subjects

cultural evolution | pre-hominid | hominid | Pleistocene adaptations | morphological variation | race | agriculture | urbanization | paleontology | archaeology | Oligocene | Miocene | Homo | Homo erectus | Homo heidelbergensis | Homo neanderthalensis | Homo sapiens | fossil | cultural evolution | pre-hominid | hominid | Pleistocene adaptations | morphological variation | race | agriculture | urbanization | paleontology | archaeology | Oligocene | Miocene | Homo | Homo erectus | Homo heidelbergensis | Homo neanderthalensis | Homo sapiens | fossilLicense

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

https://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadataInvestigating the German language Investigating the German language

Description

This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Spring Semester 2010. This 10 credit module will look at some of the ways in which German has been developing in recent years. In particular, we will look at variation and change in sentence structure; ways in which new modes of communication (such as texting, chat rooms and other forms of internet communication) are influencing language use; and the use of particles (little words like doch, mal, schon, etc.). By the end of the module, you will have carried out a small research project that allows you to compare Germans’ actual language use with what the dictionaries, grammar-books and other reference works say. Suitable for study at undergraduate level 2. Dr Nicola McLelland, School of Mode This is a module framework. It can be viewed online or downloaded as a zip file. As taught in Spring Semester 2010. This 10 credit module will look at some of the ways in which German has been developing in recent years. In particular, we will look at variation and change in sentence structure; ways in which new modes of communication (such as texting, chat rooms and other forms of internet communication) are influencing language use; and the use of particles (little words like doch, mal, schon, etc.). By the end of the module, you will have carried out a small research project that allows you to compare Germans’ actual language use with what the dictionaries, grammar-books and other reference works say. Suitable for study at undergraduate level 2. Dr Nicola McLelland, School of ModeSubjects

UNow | UNow | variation in German sentence structure | variation in German sentence structure | new modes of communication | new modes of communication | German language | German language | German sentance structure | German sentance structure | use of partcicles | use of partcicles | German grammar | German grammar | ukoer | ukoerLicense

Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA) Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA)Site sourced from

http://unow.nottingham.ac.uk/rss.ashxAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata8.06 Quantum Physics III (MIT) 8.06 Quantum Physics III (MIT)

Description

8.06 is the third course in the three-sequence physics undergraduate Quantum Mechanics curriculum. By the end of this course, you will be able to interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods. This course will introduce some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of Hydrogen, lasers, and particle scattering. 8.06 is the third course in the three-sequence physics undergraduate Quantum Mechanics curriculum. By the end of this course, you will be able to interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods. This course will introduce some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of Hydrogen, lasers, and particle scattering.Subjects

natural units | natural units | scales of microscopic phenomena | scales of microscopic phenomena | Time-independent approximation methods: degenerate and non-degenerate perturbation theory | Time-independent approximation methods: degenerate and non-degenerate perturbation theory | variational method | variational method | Born-Oppenheimer approximation | Born-Oppenheimer approximation | spin-orbit and relativistic corrections | spin-orbit and relativistic corrections | Zeeman and Stark effects | Zeeman and Stark effects | Charged particles in a magnetic field | Charged particles in a magnetic field | Landau levels | Landau levels | integer quantum hall effect | integer quantum hall effect | Scattering | Scattering | partial waves | partial waves | Born approximation | Born approximation | Time-dependent perturbation theory | Time-dependent perturbation theoryLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses.xmlAttribution

Click to get HTML | Click to get attribution | Click to get URLAll metadata

See all metadata