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18.305 Advanced Analytic Methods in Science and Engineering (MIT) 18.305 Advanced Analytic Methods in Science and Engineering (MIT)

Description

Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own. Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.

Subjects

elementary methods complex analysis | elementary methods complex analysis | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | expansions around regular irregular singular points | expansions around regular irregular singular points | asymptotic evaluation integrals | asymptotic evaluation integrals | regular perturbations | regular perturbations | WKB method | WKB method | multiple scale method | multiple scale method | boundary-layer techniques. | boundary-layer techniques. | asymptotic evaluation integrals | regular perturbations | asymptotic evaluation integrals | regular perturbations | boundary-layer techniques | boundary-layer techniques

License

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

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5.80 Small-Molecule Spectroscopy and Dynamics (MIT) 5.80 Small-Molecule Spectroscopy and Dynamics (MIT)

Description

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 | wavepackets

License

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

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

Description

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

Subjects

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

License

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

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Modeling the Space Environment Modeling the Space Environment

Description

Effects of space environment on satellite orbits. Numerical models used to compute orbital perturbations. Effects of space environment on satellite orbits. Numerical models used to compute orbital perturbations.

Subjects

Orbital perturbations | Orbital perturbations | Space environment | Space environment | Astrodynamics | Astrodynamics | Numerical models | Numerical models | Ingeniería aeroespacial | Ingeniería aeroespacial

License

Copyright 2009, by the Contributing Authors http://creativecommons.org/licenses/by-nc-sa/3.0/

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18.305 Advanced Analytic Methods in Science and Engineering (MIT)

Description

Advanced Analytic Methods in Science and Engineering is a comprehensive treatment of the advanced methods of applied mathematics. It was designed to strengthen the mathematical abilities of graduate students and train them to think on their own.

Subjects

elementary methods complex analysis | ordinary differential equations | partial differential equations | expansions around regular irregular singular points | asymptotic evaluation integrals | regular perturbations | WKB method | multiple scale method | boundary-layer techniques. | asymptotic evaluation integrals | regular perturbations | boundary-layer techniques

License

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

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6.243J Dynamics of Nonlinear Systems (MIT)

Description

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

Subjects

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

License

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

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6.243J Dynamics of Nonlinear Systems (MIT)

Description

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

Subjects

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

License

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

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5.80 Small-Molecule Spectroscopy and Dynamics (MIT)

Description

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

License

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

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