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6.231 Dynamic Programming and Stochastic Control (MIT) 6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations. This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Subjects

dynamic programming | dynamic programming | stochastic control | stochastic control | decision making | decision making | uncertainty | uncertainty | sequential decision making | sequential decision making | finite horizon | finite horizon | infinite horizon | infinite horizon | approximation methods | approximation methods | state space | state space | large state space | large state space | optimal control | optimal control | dynamical system | dynamical system | dynamic programming and optimal control | dynamic programming and optimal control | deterministic systems | deterministic systems | shortest path | shortest path | state information | state information | rollout | rollout | stochastic shortest path | stochastic shortest path | approximate dynamic programming | approximate dynamic programming

License

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16.888 Multidisciplinary System Design Optimization (MIT) 16.888 Multidisciplinary System Design Optimization (MIT)

Description

This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers. This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers.

Subjects

optimization | optimization | multidisciplinary design optimization | multidisciplinary design optimization | MDO | MDO | subsystem identification | subsystem identification | interface design | interface design | linear constrained optimization fomulation | linear constrained optimization fomulation | non-linear constrained optimization formulation | non-linear constrained optimization formulation | scalar optimization | scalar optimization | vector optimization | vector optimization | systems engineering | systems engineering | complex systems | complex systems | heuristic search methods | heuristic search methods | tabu search | tabu search | simulated annealing | simulated annealing | genertic algorithms | genertic algorithms | sensitivity | sensitivity | tradeoff analysis | tradeoff analysis | goal programming | goal programming | isoperformance | isoperformance | pareto optimality | pareto optimality | flowchart | flowchart | design vector | design vector | simulation model | simulation model | objective vector | objective vector | input | input | discipline | discipline | output | output | coupling | coupling | multiobjective optimization | multiobjective optimization | optimization algorithms | optimization algorithms | tradespace exploration | tradespace exploration | numerical techniques | numerical techniques | direct methods | direct methods | penalty methods | penalty methods | heuristic techniques | heuristic techniques | SA | SA | GA | GA | approximation methods | approximation methods | sensitivity analysis | sensitivity analysis | isoperformace | isoperformace | output evaluation | output evaluation | MSDO framework | MSDO framework

License

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

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8.06 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 theory

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 theory | quantum physics | quantum physics

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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5.73 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 theory

License

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

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8.06 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 theory

License

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

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8.06 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 theory

License

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

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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.

Subjects

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

License

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

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6.231 Dynamic Programming and Stochastic Control (MIT)

Description

This course covers the basic models and solution techniques for problems of sequential decision making under uncertainty (stochastic control). We will consider optimal control of a dynamical system over both a finite and an infinite number of stages (finite and infinite horizon). We will also discuss some approximation methods for problems involving large state spaces. Applications of dynamic programming in a variety of fields will be covered in recitations.

Subjects

dynamic programming | stochastic control | decision making | uncertainty | sequential decision making | finite horizon | infinite horizon | approximation methods | state space | large state space | optimal control | dynamical system | dynamic programming and optimal control | deterministic systems | shortest path | state information | rollout | stochastic shortest path | approximate dynamic programming

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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16.888 Multidisciplinary System Design Optimization (MIT)

Description

This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers.

Subjects

optimization | multidisciplinary design optimization | MDO | subsystem identification | interface design | linear constrained optimization fomulation | non-linear constrained optimization formulation | scalar optimization | vector optimization | systems engineering | complex systems | heuristic search methods | tabu search | simulated annealing | genertic algorithms | sensitivity | tradeoff analysis | goal programming | isoperformance | pareto optimality | flowchart | design vector | simulation model | objective vector | input | discipline | output | coupling | multiobjective optimization | optimization algorithms | tradespace exploration | numerical techniques | direct methods | penalty methods | heuristic techniques | SA | GA | approximation methods | sensitivity analysis | isoperformace | output evaluation | MSDO framework

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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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

Subjects

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

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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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.

Subjects

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

License

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

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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.

Subjects

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

License

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

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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.

Subjects

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

License

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

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