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18.353J Nonlinear Dynamics I: Chaos (MIT) 18.353J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in engineering and science. This course provides an introduction to nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in engineering and science.Subjects

nonlinear dynamics | nonlinear dynamics | chaos | chaos | dissipative systems | dissipative systems | free oscillators | free oscillators | forced oscillators | forced oscillators | nonlinear phenomena | nonlinear phenomena | bifurcation theory | bifurcation theoryLicense

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Includes audio/video content: AV lectures. 8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students i Includes audio/video content: AV lectures. 8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students iSubjects

vibrations | vibrations | waves | waves | mass on a spring | mass on a spring | LC circuit | LC circuit | simple harmonic motion | simple harmonic motion | harmonic oscillators | harmonic oscillators | damping | damping | coupled oscillators | coupled oscillators | traveling waves | traveling waves | standing waves | standing waves | electromagnetic waves | electromagnetic waves | interference | interference | radiating electromagnetic waves | radiating electromagnetic waves | Quality Factor Q | Quality Factor QLicense

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

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See all metadata16.07 Dynamics (MIT) 16.07 Dynamics (MIT)

Description

Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.Subjects

Curvilinear motion | Curvilinear motion | carteian coordinates | carteian coordinates | dynamics | dynamics | equations of motion | equations of motion | intrinsic coordinates | intrinsic coordinates | coordinate systems | coordinate systems | work | work | energy | energy | conservative forces | conservative forces | potential energy | potential energy | linear impulse | linear impulse | mommentum | mommentum | angular impulse | angular impulse | relative motion | relative motion | rotating axes | rotating axes | translating axes | translating axes | Newton's second law | Newton's second law | inertial forces | inertial forces | accelerometers | accelerometers | Newtonian relativity | Newtonian relativity | gravitational attraction | gravitational attraction | 2D rigid body kinematics | 2D rigid body kinematics | conservation laws for systems of particles | conservation laws for systems of particles | 2D rigid body dynamics | 2D rigid body dynamics | pendulums | pendulums | 3D rigid body kinematics | 3D rigid body kinematics | 3d rigid body dynamics | 3d rigid body dynamics | inertia tensor | inertia tensor | gyroscopic motion | gyroscopic motion | torque-free motion | torque-free motion | spin stabilization | spin stabilization | variable mass systems | variable mass systems | rocket equation | rocket equation | central foce motion | central foce motion | Keppler's laws | Keppler's laws | orbits | orbits | orbit transfer | orbit transfer | vibration | vibration | spring mass systems | spring mass systems | forced vibration | forced vibration | isolation | isolation | coupled oscillators | coupled oscillators | normal modes | normal modes | wave propagation | wave propagation | cartesian coordinates | cartesian coordinates | momentum | momentum | central force motion | central force motionLicense

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

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This 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, RiSubjects

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 cycleLicense

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

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See all metadata12.006J Nonlinear Dynamics I: Chaos (MIT) 12.006J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering. This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.Subjects

Forced and parametric oscillators | Forced and parametric oscillators | Phase space | Phase space | Periodic | quasiperiodic | and aperiodic flows | Periodic | quasiperiodic | and aperiodic flows | Sensitivity to initial conditions and strange attractors | Sensitivity to initial conditions and strange attractors | Lorenz attractor | Lorenz attractor | Period doubling | intermittency | and quasiperiodicity | Period doubling | intermittency | and quasiperiodicity | Scaling and universality | Scaling and universality | Analysis of experimental data: Fourier transforms | Analysis of experimental data: Fourier transforms | Poincar? sections | Poincar? sections | fractal dimension | fractal dimension | Lyaponov exponents | Lyaponov exponentsLicense

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

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The goal of this course is to illustrate the spectroscopy of small molecules in the gas phase: quantum mechanical effective Hamiltonian models for rotational, vibrational, and electronic structure; transition selection rules and relative intensities; diagnostic patterns and experimental methods for the assignment of non-textbook spectra; breakdown of the Born-Oppenheimer approximation (spectroscopic perturbations); the stationary phase approximation; nondegenerate and quasidegenerate perturbation theory (van Vleck transformation); qualitative molecular orbital theory (Walsh diagrams); the notation of atomic and molecular spectroscopy. The goal of this course is to illustrate the spectroscopy of small molecules in the gas phase: quantum mechanical effective Hamiltonian models for rotational, vibrational, and electronic structure; transition selection rules and relative intensities; diagnostic patterns and experimental methods for the assignment of non-textbook spectra; breakdown of the Born-Oppenheimer approximation (spectroscopic perturbations); the stationary phase approximation; nondegenerate and quasidegenerate perturbation theory (van Vleck transformation); qualitative molecular orbital theory (Walsh diagrams); the notation of atomic and molecular spectroscopy.Subjects

spectroscopy | spectroscopy | harmonic oscillators | harmonic oscillators | matrix | matrix | hamiltonian | hamiltonian | heisenberg | heisenberg | vibrating rotor | vibrating rotor | Born-Oppenheimer | Born-Oppenheimer | diatomics | diatomics | laser schemes | laser schemes | angular momentum | angular momentum | hund's cases | hund's cases | energy levels | energy levels | second-order effects | second-order effects | perturbations | perturbations | Wigner-Eckart | Wigner-Eckart | Rydberg-Klein-Rees | Rydberg-Klein-Rees | rigid rotor | rigid rotor | asymmetric rotor | asymmetric rotor | vibronic coupling | vibronic coupling | wavepackets | wavepacketsLicense

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

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This 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 cycleLicense

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

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See all metadata5.61 Physical Chemistry (MIT) 5.61 Physical Chemistry (MIT)

Description

This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems — the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy. Acknowledgements The material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW wa This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems — the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, spectroscopy. Acknowledgements The material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW waSubjects

physical chemistry | physical chemistry | quantum mechanics | quantum mechanics | quantum chemistry | quantum chemistry | particles and waves | particles and waves | wave mechanics | wave mechanics | atomic structure | atomic structure | valence orbital | valence orbital | molecular orbital theory | molecular orbital theory | molecular structure | molecular structure | photochemistry | photochemistry | tunneling | tunneling | spherical harmonics | spherical harmonics | rigid rotor | rigid rotor | perturbation theory | perturbation theory | oscillators | oscillators | hartree-fock | hartree-fock | LCAO | LCAOLicense

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

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See all metadata6.776 High Speed Communication Circuits (MIT) 6.776 High Speed Communication Circuits (MIT)

Description

6.776 covers circuit level design issues of high speed communication systems, with primary focus being placed on wireless and broadband data link applications. Specific circuit topics include transmission lines, high speed and low noise amplifiers, VCO's, mixers, power amps, high speed digital circuits, and frequency synthesizers. In addition to learning analysis skills for the above items, students will gain a significant amount of experience in simulating RF circuits in SPICE and also building RF circuits within a lab project. 6.776 covers circuit level design issues of high speed communication systems, with primary focus being placed on wireless and broadband data link applications. Specific circuit topics include transmission lines, high speed and low noise amplifiers, VCO's, mixers, power amps, high speed digital circuits, and frequency synthesizers. In addition to learning analysis skills for the above items, students will gain a significant amount of experience in simulating RF circuits in SPICE and also building RF circuits within a lab project.Subjects

integrated circuit design | integrated circuit design | communication systems | communication systems | wireless | wireless | broadband | broadband | data links | data links | circuit blocks | circuit blocks | communication transceivers | communication transceivers | phase-locked loops | phase-locked loops | PLL | PLL | narrowband | narrowband | low-noise | low-noise | amplifiers | amplifiers | mixers | mixers | voltage-controlled oscillators | voltage-controlled oscillators | power amplifiers | power amplifiers | high speed frequency dividers | high speed frequency dividers | passive component design | passive component design | on-chip inductors | on-chip inductors | capacitors | capacitors | transmission line modeling | transmission line modeling | S-parameters | S-parameters | Smith Chart | Smith ChartLicense

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

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In this seminar, we will discuss some of the main themes that have arisen in the field of systems biology, including the concepts of robustness, stochastic cell-to-cell variability, and the evolution of molecular interactions within complex networks. 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 highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching. In this seminar, we will discuss some of the main themes that have arisen in the field of systems biology, including the concepts of robustness, stochastic cell-to-cell variability, and the evolution of molecular interactions within complex networks. 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 highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.Subjects

systems biology | systems biology | synthetic networks | synthetic networks | noise | noise | gene expression | gene expression | oscillators | oscillators | PCR | PCR | stochastic | stochastic | robustness | robustness | biological networks | biological networks | chemotaxis | chemotaxis | circadian | circadianLicense

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

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See all metadata8.591J Systems Biology (MIT) 8.591J Systems Biology (MIT)

Description

This course introduces the mathematical modeling techniques needed to address key questions in modern biology. An overview of modeling techniques in molecular biology and genetics, cell biology and developmental biology is covered. Key experiments that validate mathematical models are also discussed, as well as molecular, cellular, and developmental systems biology, bacterial chemotaxis, genetic oscillators, control theory and genetic networks, and gradient sensing systems. Additional specific topics include: constructing and modeling of genetic networks, lambda phage as a genetic switch, synthetic genetic switches, circadian rhythms, reaction diffusion equations, local activation and global inhibition models, center finding networks, general pattern formation models, modeling cell-cell co This course introduces the mathematical modeling techniques needed to address key questions in modern biology. An overview of modeling techniques in molecular biology and genetics, cell biology and developmental biology is covered. Key experiments that validate mathematical models are also discussed, as well as molecular, cellular, and developmental systems biology, bacterial chemotaxis, genetic oscillators, control theory and genetic networks, and gradient sensing systems. Additional specific topics include: constructing and modeling of genetic networks, lambda phage as a genetic switch, synthetic genetic switches, circadian rhythms, reaction diffusion equations, local activation and global inhibition models, center finding networks, general pattern formation models, modeling cell-cell coSubjects

molecular systems biology | molecular systems biology | constructing and modeling of genetic networks | constructing and modeling of genetic networks | control theory and genetic networks | control theory and genetic networks | ambda phage as a genetic switch | ambda phage as a genetic switch | synthetic genetic switches | synthetic genetic switches | bacterial chemotaxis | bacterial chemotaxis | genetic oscillators | genetic oscillators | circadian rhythms | circadian rhythms | cellular systems biology | cellular systems biology | reaction diffusion equations | reaction diffusion equations | local activation and global inhibition models | local activation and global inhibition models | gradient sensing systems | gradient sensing systems | center finding networks | center finding networks | developmental systems biology | developmental systems biology | general pattern formation models | general pattern formation models | modeling cell-cell communication | modeling cell-cell communication | quorum sensing | quorum sensing | models for Drosophilia development | models for Drosophilia development | 8.591 | 8.591 | 7.81 | 7.81License

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

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See all metadata12.006J Nonlinear Dynamics I: Chaos (MIT) 12.006J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering. This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.Subjects

Forced and parametric oscillators | Forced and parametric oscillators | Phase space | Phase space | Periodic | quasiperiodic | and aperiodic flows | Periodic | quasiperiodic | and aperiodic flows | Sensitivity to initial conditions and strange attractors | Sensitivity to initial conditions and strange attractors | Lorenz attractor | Lorenz attractor | Period doubling | intermittency | and quasiperiodicity | Period doubling | intermittency | and quasiperiodicity | Scaling and universality | Scaling and universality | Analysis of experimental data: Fourier transforms | Analysis of experimental data: Fourier transforms | Poincar? sections | Poincar? sections | fractal dimension | fractal dimension | Lyaponov exponents | Lyaponov exponentsLicense

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

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See all metadata5.61 Physical Chemistry (MIT) 5.61 Physical Chemistry (MIT)

Description

This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems—the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, and spectroscopy. Acknowledgements The material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCW This course presents an introduction to quantum mechanics. It begins with an examination of the historical development of quantum theory, properties of particles and waves, wave mechanics and applications to simple systems—the particle in a box, the harmonic oscillator, the rigid rotor and the hydrogen atom. The lectures continue with a discussion of atomic structure and the Periodic Table. The final lectures cover applications to chemical bonding including valence bond and molecular orbital theory, molecular structure, and spectroscopy. Acknowledgements The material for 5.61 has evolved over a period of many years, and, accordingly, several faculty members have contributed to the development of the course contents. The original version of the lecture notes that are available on OCWSubjects

quantum mechanics | quantum mechanics | quantum chemistry | quantum chemistry | particles and waves | particles and waves | wave mechanics | wave mechanics | atomic structure | atomic structure | valence orbital | valence orbital | molecular orbital theory | molecular orbital theory | molecular structure | molecular structure | photochemistry | photochemistry | tunneling | tunneling | spherical harmonics | spherical harmonics | rigid rotor | rigid rotor | perturbation theory | perturbation theory | oscillators | oscillators | spectroscopy | spectroscopy | NMR | NMR | hartree-fock | hartree-fock | LCAO | LCAOLicense

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

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See all metadata8.591J Systems Biology (MIT) 8.591J Systems Biology (MIT)

Description

Includes audio/video content: AV lectures. This course provides an introduction to cellular and population-level systems biology with an emphasis on synthetic biology, modeling of genetic networks, cell-cell interactions, and evolutionary dynamics. Cellular systems include genetic switches and oscillators, network motifs, genetic network evolution, and cellular decision-making. Population-level systems include models of pattern formation, cell-cell communication, and evolutionary systems biology. Includes audio/video content: AV lectures. This course provides an introduction to cellular and population-level systems biology with an emphasis on synthetic biology, modeling of genetic networks, cell-cell interactions, and evolutionary dynamics. Cellular systems include genetic switches and oscillators, network motifs, genetic network evolution, and cellular decision-making. Population-level systems include models of pattern formation, cell-cell communication, and evolutionary systems biology.Subjects

molecular systems biology | molecular systems biology | genetic networks | genetic networks | control theory | control theory | synthetic genetic switches | synthetic genetic switches | bacterial chemotaxis | bacterial chemotaxis | genetic oscillators | genetic oscillators | circadian rhythms | circadian rhythms | cellular systems biology | cellular systems biology | reaction diffusion equations | reaction diffusion equations | local activation | local activation | global inhibition models | global inhibition models | gradient sensing systems | gradient sensing systems | center finding networks | center finding networks | general pattern formation models | general pattern formation models | cell-cell communication | cell-cell communication | quorum sensing | quorum sensingLicense

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

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See all metadata18.353J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in engineering and science.Subjects

nonlinear dynamics | chaos | dissipative systems | free oscillators | forced oscillators | nonlinear phenomena | bifurcation 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 https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataRES.8-005 Vibrations and Waves Problem Solving (MIT)

Description

8.03 Physics III: Vibrations and Waves is the third course in the core physics curriculum at MIT, following 8.01 Physics I: Classical Mechanics and 8.02 Physics II: Electricity and Magnetism. Topics include mechanical vibrations and waves, electromagnetic waves, and optics. These Problem Solving Help Videos provide step-by-step solutions to sample problems. Also included is information about how Physics III is typically taught on the MIT campus. Instructor Insights are shared by Professor Wit Busza who has taught Physics III and its associated recitation sessions many times. Professor Busza's insights focus on his approach to problem solving, strategies for supporting students as they solve problems, and common sources of confusion for students in the process of problem solving. Note: TheSubjects

vibrations | waves | mass on a spring | LC circuit | simple harmonic motion | harmonic oscillators | damping | coupled oscillators | traveling waves | standing waves | electromagnetic waves | interference | radiating electromagnetic waves | Quality Factor QLicense

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

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See all metadata12.006J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.Subjects

Forced and parametric oscillators | Phase space | Periodic | quasiperiodic | and aperiodic flows | Sensitivity to initial conditions and strange attractors | Lorenz attractor | Period doubling | intermittency | and quasiperiodicity | Scaling and universality | Analysis of experimental data: Fourier transforms | Poincar? sections | fractal dimension | Lyaponov exponentsLicense

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

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

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

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See all metadata6.776 High Speed Communication Circuits (MIT)

Description

6.776 covers circuit level design issues of high speed communication systems, with primary focus being placed on wireless and broadband data link applications. Specific circuit topics include transmission lines, high speed and low noise amplifiers, VCO's, mixers, power amps, high speed digital circuits, and frequency synthesizers. In addition to learning analysis skills for the above items, students will gain a significant amount of experience in simulating RF circuits in SPICE and also building RF circuits within a lab project.Subjects

integrated circuit design | communication systems | wireless | broadband | data links | circuit blocks | communication transceivers | phase-locked loops | PLL | narrowband | low-noise | amplifiers | mixers | voltage-controlled oscillators | power amplifiers | high speed frequency dividers | passive component design | on-chip inductors | capacitors | transmission line modeling | S-parameters | Smith ChartLicense

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

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See all metadataIntroduction to Electromagnetism

Description

In this course, the student will first learn about waves and oscillations in extended objects using classical mechanics. The course will then examine the sources and laws that govern static electricity and magnetism. A brief look at electrical measurements and circuits will help establish how electromagnetic effects are observed, measured, and applied. These topics lead to an examination of how Maxwell’s equations unify electric and magnetic effects and how the solutions to Maxwell’s equations describe electromagnetic radiation, which will serve as the basis for understanding all electromagnetic radiation -- from very low frequency radiation emitted by power transmission lines to the most powerful astrophysical gamma rays. The course also investigates optics and launches a brief overviSubjects

electromagnetism | wave mechanics | oscillators | resonance | electrostatics | gauss | magnetism | induction | circuitsmaxwell | optics | relativity | lorentz | minkowski | Physical sciences | F000License

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See all metadata12.006J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.Subjects

Forced and parametric oscillators | Phase space | Periodic | quasiperiodic | and aperiodic flows | Sensitivity to initial conditions and strange attractors | Lorenz attractor | Period doubling | intermittency | and quasiperiodicity | Scaling and universality | Analysis of experimental data: Fourier transforms | Poincar? sections | fractal dimension | Lyaponov exponentsLicense

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

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Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.Subjects

Curvilinear motion | carteian coordinates | dynamics | equations of motion | intrinsic coordinates | coordinate systems | work | energy | conservative forces | potential energy | linear impulse | mommentum | angular impulse | relative motion | rotating axes | translating axes | Newton's second law | inertial forces | accelerometers | Newtonian relativity | gravitational attraction | 2D rigid body kinematics | conservation laws for systems of particles | 2D rigid body dynamics | pendulums | 3D rigid body kinematics | 3d rigid body dynamics | inertia tensor | gyroscopic motion | torque-free motion | spin stabilization | variable mass systems | rocket equation | central foce motion | Keppler's laws | orbits | orbit transfer | vibration | spring mass systems | forced vibration | isolation | coupled oscillators | normal modes | wave propagation | cartesian coordinates | momentum | central force motionLicense

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

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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, RiSubjects

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

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

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See all metadata12.006J Nonlinear Dynamics I: Chaos (MIT)

Description

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.Subjects

Forced and parametric oscillators | Phase space | Periodic | quasiperiodic | and aperiodic flows | Sensitivity to initial conditions and strange attractors | Lorenz attractor | Period doubling | intermittency | and quasiperiodicity | Scaling and universality | Analysis of experimental data: Fourier transforms | Poincar? sections | fractal dimension | Lyaponov exponentsLicense

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

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See all metadata7.342 Systems Biology: Stochastic Processes and Biological Robustness (MIT)

Description

In this seminar, we will discuss some of the main themes that have arisen in the field of systems biology, including the concepts of robustness, stochastic cell-to-cell variability, and the evolution of molecular interactions within complex networks. 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 highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.Subjects

systems biology | synthetic networks | noise | gene expression | oscillators | PCR | stochastic | robustness | biological networks | chemotaxis | circadianLicense

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

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