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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

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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6.041 Probabilistic Systems Analysis and Applied Probability (MIT) 6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference. This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems | probabilistic systems analysis | probabilistic systems analysis | applied probability | applied probability | uncertainty | uncertainty | uncertainty modeling | uncertainty modeling | uncertainty quantification | uncertainty quantification | analysis of uncertainty | analysis of uncertainty | uncertainty analysis | uncertainty analysis | sample space | sample space | random variables | random variables | transform techniques | transform techniques | simple random processes | simple random processes | probability distribution | probability distribution | Markov process | Markov process | limit theorem | limit theorem | statistical inference | statistical inference

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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16.892J Space System Architecture and Design (MIT) 16.892J Space System Architecture and Design (MIT)

Description

Space System Architecture and Design incorporates lectures, readings and discussion on topics in the architecting of space systems. The class reviews existing space system architectures and the classical methods of designing them. Sessions focus on multi-attribute utility theory as a new design paradigm for space systems, when combined with integrated concurrent engineering and efficient searches of large architectural tradespaces. Designing for flexibility and uncertainty is considered, as are policy and product development issues. Space System Architecture and Design incorporates lectures, readings and discussion on topics in the architecting of space systems. The class reviews existing space system architectures and the classical methods of designing them. Sessions focus on multi-attribute utility theory as a new design paradigm for space systems, when combined with integrated concurrent engineering and efficient searches of large architectural tradespaces. Designing for flexibility and uncertainty is considered, as are policy and product development issues.

Subjects

space system | space system | space system architecture | space system architecture | space architecting | space architecting | uncertainties | uncertainties | space policy | space policy | robustness | robustness | flexibility | flexibility | optimality | optimality | tradespace analysis | tradespace analysis | quality function deployment | quality function deployment | multi-attribute utility theory | multi-attribute utility theory | n-squared | n-squared | design structure matrix | design structure matrix | multi-attribution tradespace exploration | multi-attribution tradespace exploration | MATE | MATE | MATE-CON | MATE-CON | satellite | satellite | classes of space system | classes of space system | XTOS | XTOS | spacetug | spacetug | GINA | GINA | pareto fronts | pareto fronts | engineering design process | engineering design process | optimization methods | optimization methods | genetic algorithms | genetic algorithms | simulated annealing | simulated annealing | MMDOSA | MMDOSA | distributed space systems design optimization | distributed space systems design optimization | clarity test | clarity test | taxonomy of uncertainty | taxonomy of uncertainty | treatment of uncertainty | treatment of uncertainty | irreducible uncertainty | irreducible uncertainty | portfolio theory | portfolio theory | portfolio applications | portfolio applications | taxonomy of flexibility | taxonomy of flexibility | on-orbit servicing | on-orbit servicing | US national space policy | US national space policy | space policy heuristics | space policy heuristics | policy architectures | policy architectures | 16.892 | 16.892 | ESD.353 | ESD.353

License

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6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems analysis | applied probability | uncertainty | uncertainty modeling | uncertainty quantification | analysis of uncertainty | uncertainty analysis | sample space | random variables | transform techniques | simple random processes | probability distribution | Markov process | limit theorem | statistical inference

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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6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems analysis | applied probability | uncertainty | uncertainty modeling | uncertainty quantification | analysis of uncertainty | uncertainty analysis | sample space | random variables | transform techniques | simple random processes | probability distribution | Markov process | limit theorem | statistical inference

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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6.041 Probabilistic Systems Analysis and Applied Probability (MIT)

Description

This course is offered both to undergraduates (6.041) and graduates (6.431), but the assignments differ. 6.041/6.431 introduces students to the modeling, quantification, and analysis of uncertainty. Topics covered include: formulation and solution in sample space, random variables, transform techniques, simple random processes and their probability distributions, Markov processes, limit theorems, and elements of statistical inference.

Subjects

probabilistic systems | probabilistic systems analysis | applied probability | uncertainty | uncertainty modeling | uncertainty quantification | analysis of uncertainty | uncertainty analysis | sample space | random variables | transform techniques | simple random processes | probability distribution | Markov process | limit theorem | statistical inference

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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1.017 Computing and Data Analysis for Environmental Applications (MIT) 1.017 Computing and Data Analysis for Environmental Applications (MIT)

Description

This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm This subject is a computer-oriented introduction to probability and data analysis. It is designed to give students the knowledge and practical experience they need to interpret lab and field data. Basic probability concepts are introduced at the outset because they provide a systematic way to describe uncertainty. They form the basis for the analysis of quantitative data in science and engineering. The MATLAB® programming language is used to perform virtual experiments and to analyze real-world data sets, many downloaded from the web. Programming applications include display and assessment of data sets, investigation of hypotheses, and identification of possible casual relationships between variables. This is the first semester that two courses, Computing and Data Analysis for Environm

Subjects

probability | probability | statistics | statistics | events | events | random variables | random variables | univariate distributions | univariate distributions | multivariate distributions | multivariate distributions | uncertainty propagation | uncertainty propagation | Bernoulli trials | Bernoulli trials | Poisson processed | Poisson processed | conditional probability | conditional probability | Bayes rule | Bayes rule | random sampling | random sampling | point estimation | point estimation | interval estimation | interval estimation | hypothesis testing | hypothesis testing | analysis of variance | analysis of variance | linear regression | linear regression | computational analysis | computational analysis | data analysis | data analysis | environmental engineering | environmental engineering | applications | applications | MATLAB | MATLAB | numerical modeling | numerical modeling | probabilistic concepts | probabilistic concepts | statistical methods | statistical methods | field data | field data | laboratory data | laboratory data | numerical techniques | numerical techniques | Monte Carlo simulation | Monte Carlo simulation | variability | variability | sampling | sampling | data sets | data sets | computer | computer | uncertainty | uncertainty | interpretation | interpretation | quantitative data | quantitative data

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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14.121 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 mechanism

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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14.462 Advanced Macroeconomics II (MIT) 14.462 Advanced Macroeconomics II (MIT)

Description

14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information 14.462 is the second semester of the second-year Ph.D. macroeconomics sequence. The course is intended to introduce the students, not only to particular areas of current research, but also to some very useful analytical tools. It covers a selection of topics that varies from year to year. Recent topics include: Growth and Fluctuations Heterogeneity and Incomplete Markets Optimal Fiscal Policy Time Inconsistency Reputation Coordination Games and Macroeconomic Complementarities Information

Subjects

macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research; analytical tools; analysis; endogenous growth; coordintation; incomplete markets; technolgy; distribution; employment; intellectual property rights; bounded rationality; demographics; complementarities; amplification; recursive equilibria; uncertainty; morris; shin; global games; policy; price; aggregation; social learning; dynamic adjustment; business cycle; heterogeneous agents; savings; utility; aiyagari; steady state; krusell; smith; idiosyncratic investment risk | macroeconomics research | macroeconomics research | analytical tools | analytical tools | analysis | analysis | endogenous growth | endogenous growth | coordintation | coordintation | incomplete markets | incomplete markets | technolgy | technolgy | distribution | distribution | employment | employment | intellectual property rights | intellectual property rights | bounded rationality | bounded rationality | demographics | demographics | complementarities | complementarities | amplification | amplification | recursive equilibria | recursive equilibria | uncertainty | uncertainty | morris | morris | shin | shin | global games | global games | policy | policy | price | price | aggregation | aggregation | social learning | social learning | dynamic adjustment | dynamic adjustment | business cycle | business cycle | heterogeneous agents | heterogeneous agents | savings | savings | utility | utility | aiyagari | aiyagari | steady state | steady state | krusell | krusell | smith | smith | idiosyncratic investment risk | idiosyncratic investment risk | growth | growth | fluctuations | fluctuations | heterogeneity | heterogeneity | optimal fiscal policy | optimal fiscal policy | time inconsistency | time inconsistency | reputation | reputation | information | information | coordination games | coordination games

License

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ESD.71 Engineering Systems Analysis for Design (MIT) ESD.71 Engineering Systems Analysis for Design (MIT)

Description

Engineering systems design must have the flexibility to take advantage of new opportunities while avoiding disasters. This subject develops "real options" analysis to create design flexibility and measure its value so that it can be incorporated into system optimization. It builds on essential concepts of system models, decision analysis, and financial concepts. Emphasis is placed on calculating value of real options with special attention given to efficient analysis and practical applications. The material is organized and presented to deal with the contextual reality of technological systems, that substantially distinguishes the analysis of real options in engineering systems from that of financial options. Note This MIT OpenCourseWare site is based on the materials from Profes Engineering systems design must have the flexibility to take advantage of new opportunities while avoiding disasters. This subject develops "real options" analysis to create design flexibility and measure its value so that it can be incorporated into system optimization. It builds on essential concepts of system models, decision analysis, and financial concepts. Emphasis is placed on calculating value of real options with special attention given to efficient analysis and practical applications. The material is organized and presented to deal with the contextual reality of technological systems, that substantially distinguishes the analysis of real options in engineering systems from that of financial options. Note This MIT OpenCourseWare site is based on the materials from Profes

Subjects

real options | real options | flexibility | flexibility | flexible design | flexible design | engineering systems | engineering systems | complex projects | complex projects | evaluation over time | evaluation over time | risk | risk | uncertainty | uncertainty | valuation | valuation | timing | timing | uncertainty modeling | uncertainty modeling | flexibility valuation | flexibility valuation | methods | methods | design analysis | design analysis | lattice analysis | lattice analysis | monte carlo simulation | monte carlo simulation | flexibility identification. | flexibility identification.

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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16.892J Space System Architecture and Design (MIT)

Description

Space System Architecture and Design incorporates lectures, readings and discussion on topics in the architecting of space systems. The class reviews existing space system architectures and the classical methods of designing them. Sessions focus on multi-attribute utility theory as a new design paradigm for space systems, when combined with integrated concurrent engineering and efficient searches of large architectural tradespaces. Designing for flexibility and uncertainty is considered, as are policy and product development issues.

Subjects

space system | space system architecture | space architecting | uncertainties | space policy | robustness | flexibility | optimality | tradespace analysis | quality function deployment | multi-attribute utility theory | n-squared | design structure matrix | multi-attribution tradespace exploration | MATE | MATE-CON | satellite | classes of space system | XTOS | spacetug | GINA | pareto fronts | engineering design process | optimization methods | genetic algorithms | simulated annealing | MMDOSA | distributed space systems design optimization | clarity test | taxonomy of uncertainty | treatment of uncertainty | irreducible uncertainty | portfolio theory | portfolio applications | taxonomy of flexibility | on-orbit servicing | US national space policy | space policy heuristics | policy architectures | 16.892 | ESD.353

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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ESD.83 Doctoral Seminar in Engineering Systems (MIT) ESD.83 Doctoral Seminar in Engineering Systems (MIT)

Description

In establishing the Engineering Systems Division, MIT has embarked on a bold experiment – bringing together diverse areas of expertise into what is designed to be a new field of study. In many respects, the full scale and scope of Engineering Systems as a field is still emerging. This seminar is simultaneously designed to codify what we presently know and to give direction for future development. In establishing the Engineering Systems Division, MIT has embarked on a bold experiment – bringing together diverse areas of expertise into what is designed to be a new field of study. In many respects, the full scale and scope of Engineering Systems as a field is still emerging. This seminar is simultaneously designed to codify what we presently know and to give direction for future development.

Subjects

engineering systems | engineering systems | complexity | complexity | uncertainty | uncertainty | fragility | fragility | robustness | robustness | systems engineering | systems engineering | systems dynamics | systems dynamics | agent modeling | agent modeling | systems simulations | systems simulations | large-scale systems change | large-scale systems change | modeling paradigms | modeling paradigms | cumulative knowledge | cumulative knowledge | empirical data generation | empirical data generation | boundary setting | boundary setting | network models | network models | policy evaluation | policy evaluation

License

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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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16.410 Principles of Autonomy and Decision Making (MIT) 16.410 Principles of Autonomy and Decision Making (MIT)

Description

This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information

Subjects

autonomy | autonomy | decision | decision | decision-making | decision-making | reasoning | reasoning | optimization | optimization | autonomous | autonomous | autonomous systems | autonomous systems | decision support | decision support | algorithms | algorithms | artificial intelligence | artificial intelligence | a.i. | a.i. | operations | operations | operations research | operations research | logic | logic | deduction | deduction | heuristic search | heuristic search | constraint-based search | constraint-based search | model-based reasoning | model-based reasoning | planning | planning | execution | execution | uncertainty | uncertainty | machine learning | machine learning | linear programming | linear programming | dynamic programming | dynamic programming | integer programming | integer programming | network optimization | network optimization | decision analysis | decision analysis | decision theoretic planning | decision theoretic planning | Markov decision process | Markov decision process | scheme | scheme | propositional logic | propositional logic | constraints | constraints | Markov processes | Markov processes | computational performance | computational performance | satisfaction | satisfaction | learning algorithms | learning algorithms | system state | system state | state | state | search treees | search treees | plan spaces | plan spaces | model theory | model theory | decision trees | decision trees | function approximators | function approximators | optimization algorithms | optimization algorithms | limitations | limitations | tradeoffs | tradeoffs | search and reasoning | search and reasoning | game tree search | game tree search | local stochastic search | local stochastic search | stochastic | stochastic | genetic algorithms | genetic algorithms | constraint satisfaction | constraint satisfaction | propositional inference | propositional inference | rule-based systems | rule-based systems | rule-based | rule-based | model-based diagnosis | model-based diagnosis | neural nets | neural nets | reinforcement learning | reinforcement learning | web-based | web-based | search trees | search trees

License

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ESD.84 Engineering Systems Doctoral Seminar (MIT) ESD.84 Engineering Systems Doctoral Seminar (MIT)

Description

Examines core theory and contextual applications of the emerging field of Engineering Systems. The focus is on doctoral-level analysis of scholarship on key concepts such as complexity, uncertainty, fragility, and robustness, as well as a critical look at the historical roots of the field and related areas such as systems engineering, systems dynamics, agent modeling, and systems simulations. Contextual applications range from aerospace to technology implementation to regulatory systems to large-scale systems change. Special attention is given to the interdependence of social and technical dimensions of engineering systems. Examines core theory and contextual applications of the emerging field of Engineering Systems. The focus is on doctoral-level analysis of scholarship on key concepts such as complexity, uncertainty, fragility, and robustness, as well as a critical look at the historical roots of the field and related areas such as systems engineering, systems dynamics, agent modeling, and systems simulations. Contextual applications range from aerospace to technology implementation to regulatory systems to large-scale systems change. Special attention is given to the interdependence of social and technical dimensions of engineering systems.

Subjects

engineering systems | engineering systems | complexity | complexity | fragility | fragility | robustness | robustness | systems engineering | systems engineering | systems dynamics | systems dynamics | agent modeling | agent modeling | systems simulations | systems simulations | large-scale systems change | large-scale systems change | uncertainty | uncertainty

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14.452 Economic Growth (MIT) 14.452 Economic Growth (MIT)

Description

This half semester class presents an introduction to macroeconomic modeling, focusing on the theory of economic growth and some of its applications. It will introduce a number of models of non-stochastic and stochastic macroeconomic equilibrium. It will use these models to shed light both on the process of economic growth at the world level and on sources of income and growth differences across countries. This half semester class presents an introduction to macroeconomic modeling, focusing on the theory of economic growth and some of its applications. It will introduce a number of models of non-stochastic and stochastic macroeconomic equilibrium. It will use these models to shed light both on the process of economic growth at the world level and on sources of income and growth differences across countries.

Subjects

economic growth | economic growth | development | development | modern | modern | world income distribution | world income distribution | Solow growth model | Solow growth model | income differences | income differences | neoclassical growth | neoclassical growth | optimal and competitive allocations | optimal and competitive allocations | welfare theorems | welfare theorems | overlapping generations | overlapping generations | dynamic efficiency | dynamic efficiency | growth under uncertainty | growth under uncertainty | incomplete markets | incomplete markets | neoclassical endogenous growth | neoclassical endogenous growth | capital accumulation | capital accumulation | externalities | externalities | human capital | human capital | endogenous growth | endogenous growth | expanding input varieties | expanding input varieties | Schumpeterian models | Schumpeterian models | endogenous skill-bias technological change | endogenous skill-bias technological change | endogenous labor-augmenting technological change | endogenous labor-augmenting technological change | interdependences | interdependences | technology diffusion | technology diffusion | open economy | open economy | trade | trade

License

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1.010 Uncertainty in Engineering (MIT) 1.010 Uncertainty in Engineering (MIT)

Description

This undergraduate class serves as an introduction to probability and statistics, with emphasis on engineering applications. The first segment discusses events and their probability, Bayes' Theorem, discrete and continuous random variables and vectors, univariate and multivariate distributions, Bernoulli trials and Poisson point processes, and full-distribution uncertainty propagation and conditional analysis. The second segment deals with second-moment representation of uncertainty and second-moment uncertainty propagation and conditional analysis. The final segment covers random sampling, point and interval estimation, hypothesis testing, and linear regression. Many of the concepts covered in class are illustrated with real-world examples from various areas of engineering. This undergraduate class serves as an introduction to probability and statistics, with emphasis on engineering applications. The first segment discusses events and their probability, Bayes' Theorem, discrete and continuous random variables and vectors, univariate and multivariate distributions, Bernoulli trials and Poisson point processes, and full-distribution uncertainty propagation and conditional analysis. The second segment deals with second-moment representation of uncertainty and second-moment uncertainty propagation and conditional analysis. The final segment covers random sampling, point and interval estimation, hypothesis testing, and linear regression. Many of the concepts covered in class are illustrated with real-world examples from various areas of engineering.

Subjects

statistics | statistics | decision analysis | decision analysis | random variables and vectors | random variables and vectors | uncertainty propagation | uncertainty propagation | conditional distributions | conditional distributions | second-moment analysis | second-moment analysis | system reliability | system reliability | Bayesian analysis and risk-based decision | Bayesian analysis and risk-based decision | estimation of distribution parameters | estimation of distribution parameters | hypothesis testing | hypothesis testing | simple and multiple linear regressions | simple and multiple linear regressions | Poisson and Markov processes | Poisson and Markov processes

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ESD.260J Logistics Systems (MIT) ESD.260J Logistics Systems (MIT)

Description

This course is a survey of analytic tools, approaches, and techniques which are useful in the design and operation of logistics systems and integrated supply chains. The material is taught from a managerial perspective, with an emphasis on where and how specific tools can be used to improve the overall performance and reduce the total cost of a supply chain. There is a strong emphasis on the development and use of fundamental models to illustrate the underlying concepts involved in both intra- and inter-company logistics operations. The following topics are covered: demand forecasting tools, inventory control algorithms, transportation operations and management, vehicle routing, scheduling, fleet dispatching algorithms and approaches, optimization of transportation carrier operations, supp This course is a survey of analytic tools, approaches, and techniques which are useful in the design and operation of logistics systems and integrated supply chains. The material is taught from a managerial perspective, with an emphasis on where and how specific tools can be used to improve the overall performance and reduce the total cost of a supply chain. There is a strong emphasis on the development and use of fundamental models to illustrate the underlying concepts involved in both intra- and inter-company logistics operations. The following topics are covered: demand forecasting tools, inventory control algorithms, transportation operations and management, vehicle routing, scheduling, fleet dispatching algorithms and approaches, optimization of transportation carrier operations, supp

Subjects

Logistics systems | Logistics systems | Supply chain management | Supply chain management | Demand planning | Demand planning | Procurement | Procurement | Inventory | Inventory | Transportation planning | Transportation planning | Reverse logistics | Reverse logistics | Flexible contracting | Flexible contracting | Postponement | Postponement | Portfolio management | Portfolio management | Dual sourcing | Dual sourcing | demand forecasting tools | demand forecasting tools | inventory control algorithms | inventory control algorithms | transportation operations | transportation operations | vehicle routing | vehicle routing | scheduling | scheduling | fleet dispatching algorithms | fleet dispatching algorithms | optimization | optimization | transportation carrier operations | transportation carrier operations | supply chain network design | supply chain network design | procurement | procurement | sourcing | sourcing | auctions | auctions | supply contracts | supply contracts | collaboration | collaboration | supply chain uncertainty | supply chain uncertainty | ESD.260 | ESD.260 | 1.260 | 1.260 | 15.770 | 15.770

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2.853 Manufacturing Systems I: Analytical Methods and Flow Models (MIT) 2.853 Manufacturing Systems I: Analytical Methods and Flow Models (MIT)

Description

Provides ways to conceptualize and analyze manufacturing systems and supply chains in terms of material flow, information flow, capacities, and flow times. Fundamental building blocks: inventory and queuing models, forecasting and uncertainty, optimization, process analysis, linear systems and system dynamics. Factory planning: flow planning, bottleneck characterization, buffer and batch-size tactics, seasonal planning, dynamics and learning for various process flow topologies and for various market contexts.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls files found on this course site. Free  Microsoft® Excel viewer software can also be used to view the .xls files.Microsoft® is a registered trademark Provides ways to conceptualize and analyze manufacturing systems and supply chains in terms of material flow, information flow, capacities, and flow times. Fundamental building blocks: inventory and queuing models, forecasting and uncertainty, optimization, process analysis, linear systems and system dynamics. Factory planning: flow planning, bottleneck characterization, buffer and batch-size tactics, seasonal planning, dynamics and learning for various process flow topologies and for various market contexts.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls files found on this course site. Free  Microsoft® Excel viewer software can also be used to view the .xls files.Microsoft® is a registered trademark

Subjects

manufacturing systems | manufacturing systems | supply chains | supply chains | material flow | material flow | information flow | information flow | capacities | capacities | flow times | flow times | Fundamental building blocks | Fundamental building blocks | inventory | inventory | queuing models | queuing models | forecasting | forecasting | uncertainty | uncertainty | optimization | optimization | process analysis | process analysis | linear systems | linear systems | system dynamics | system dynamics | Factory planning | Factory planning | flow planning | flow planning | bottleneck characterization | bottleneck characterization | buffer | buffer | batch-size tactics | batch-size tactics | seasonal planning | seasonal planning | process flow topologies | process flow topologies | market contexts | market contexts

License

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16.410 Principles of Autonomy and Decision Making (MIT) 16.410 Principles of Autonomy and Decision Making (MIT)

Description

This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information This course surveys a variety of reasoning, optimization, and decision-making methodologies for creating highly autonomous systems and decision support aids. The focus is on principles, algorithms, and their applications, taken from the disciplines of artificial intelligence and operations research. Reasoning paradigms include logic and deduction, heuristic and constraint-based search, model-based reasoning, planning and execution, reasoning under uncertainty, and machine learning. Optimization paradigms include linear, integer and dynamic programming. Decision-making paradigms include decision theoretic planning, and Markov decision processes. This course is offered both to undergraduate (16.410) students as a professional area undergraduate subject, in the field of aerospace information

Subjects

autonomy | autonomy | decision | decision | decision-making | decision-making | reasoning | reasoning | optimization | optimization | autonomous | autonomous | autonomous systems | autonomous systems | decision support | decision support | algorithms | algorithms | artificial intelligence | artificial intelligence | a.i. | a.i. | operations | operations | operations research | operations research | logic | logic | deduction | deduction | heuristic search | heuristic search | constraint-based search | constraint-based search | model-based reasoning | model-based reasoning | planning | planning | execution | execution | uncertainty | uncertainty | machine learning | machine learning | linear programming | linear programming | dynamic programming | dynamic programming | integer programming | integer programming | network optimization | network optimization | decision analysis | decision analysis | decision theoretic planning | decision theoretic planning | Markov decision process | Markov decision process | scheme | scheme | propositional logic | propositional logic | constraints | constraints | Markov processes | Markov processes | computational performance | computational performance | satisfaction | satisfaction | learning algorithms | learning algorithms | system state | system state | state | state | search treees | search treees | plan spaces | plan spaces | model theory | model theory | decision trees | decision trees | function approximators | function approximators | optimization algorithms | optimization algorithms | limitations | limitations | tradeoffs | tradeoffs | search and reasoning | search and reasoning | game tree search | game tree search | local stochastic search | local stochastic search | stochastic | stochastic | genetic algorithms | genetic algorithms | constraint satisfaction | constraint satisfaction | propositional inference | propositional inference | rule-based systems | rule-based systems | rule-based | rule-based | model-based diagnosis | model-based diagnosis | neural nets | neural nets | reinforcement learning | reinforcement learning | web-based | web-based | search trees | search trees

License

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BE.104J Chemicals in the Environment: Toxicology and Public Health (MIT) BE.104J Chemicals in the Environment: Toxicology and Public Health (MIT)

Description

This course addresses the challenges of defining a relationship between exposure to environmental chemicals and human disease. Course topics include epidemiological approaches to understanding disease causation; biostatistical methods; evaluation of human exposure to chemicals, and their internal distribution, metabolism, reactions with cellular components, and biological effects; and qualitative and quantitative health risk assessment methods used in the U.S. as bases for regulatory decision-making. Throughout the term, students consider case studies of local and national interest. This course addresses the challenges of defining a relationship between exposure to environmental chemicals and human disease. Course topics include epidemiological approaches to understanding disease causation; biostatistical methods; evaluation of human exposure to chemicals, and their internal distribution, metabolism, reactions with cellular components, and biological effects; and qualitative and quantitative health risk assessment methods used in the U.S. as bases for regulatory decision-making. Throughout the term, students consider case studies of local and national interest.

Subjects

biostatistics | biostatistics | risk | risk | risk analysis | risk analysis | risk factor | risk factor | environmental agent | environmental agent | environetics | environetics | cause and effect | cause and effect | pollution | pollution | statistical analysis | statistical analysis | toxic | toxic | genetics | genetics | disease | disease | health | health | EPA | EPA | metabolism | metabolism | endocrine | endocrine | immunity | immunity | uncertainty | uncertainty | mortality | mortality | death rate | death rate | prediction | prediction

License

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16.412J Cognitive Robotics (MIT) 16.412J Cognitive Robotics (MIT)

Description

Cognitive robotics addresses the emerging field of autonomous systems possessing artificial reasoning skills. Successfully-applied algorithms and autonomy models form the basis for study, and provide students an opportunity to design such a system as part of their class project. Theory and application are linked through discussion of real systems such as the Mars Exploration Rover.Technical RequirementsAny text editor can be used to view the .ascii, .binary, .map, and .pddl files found on this course site. Any number of development tools can be used to compile and run the .c and .h files found on this course site. Cognitive robotics addresses the emerging field of autonomous systems possessing artificial reasoning skills. Successfully-applied algorithms and autonomy models form the basis for study, and provide students an opportunity to design such a system as part of their class project. Theory and application are linked through discussion of real systems such as the Mars Exploration Rover.Technical RequirementsAny text editor can be used to view the .ascii, .binary, .map, and .pddl files found on this course site. Any number of development tools can be used to compile and run the .c and .h files found on this course site.

Subjects

cognitive robotics | cognitive robotics | robotic systems | robotic systems | intelligence algorithms | intelligence algorithms | robustness algorithms | robustness algorithms | intelligence paradigms | intelligence paradigms | robustness paradigms | robustness paradigms | autonomous robots | autonomous robots | mars explorers | mars explorers | cooperative air vehicles | cooperative air vehicles | embedded devices | embedded devices | real-time deduction | real-time deduction | real-time search | real-time search | temporal planning | temporal planning | decision-theoretic planning | decision-theoretic planning | contingency planning | contingency planning | dynamic execution | dynamic execution | dynamics re-planning | dynamics re-planning | reasoning | reasoning | path planning | path planning | reasoning under uncertainty | reasoning under uncertainty | mapping | mapping | localization | localization | cooperative robotics | cooperative robotics | distributed robotics | distributed robotics | mars exploration rover | mars exploration rover | nursebot | nursebot | museum tourguide | museum tourguide | human-interaction systems | human-interaction systems | navigation | navigation | state-aware robots | state-aware robots | fast planning | fast planning | cooperative planning | cooperative planning | vision-based exploration | vision-based exploration | preplanning | preplanning | 16.412 | 16.412 | 6.834 | 6.834

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8.04 Quantum Physics I (MIT) 8.04 Quantum Physics I (MIT)

Description

Experimental basis of Quantum Physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, De Broglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials, and introduction to hydrogenic systems. Experimental basis of Quantum Physics: photoelectric effect, Compton scattering, photons, Franck-Hertz experiment, the Bohr atom, electron diffraction, De Broglie waves, and wave-particle duality of matter and light. Introduction to wave mechanics: Schroedinger's equation, wave functions, wave packets, probability amplitudes, stationary states, the Heisenberg uncertainty principle, and zero-point energies. Solutions to Schroedinger's equation in one dimension: transmission and reflection at a barrier, barrier penetration, potential wells, the simple harmonic oscillator. Schroedinger's equation in three dimensions: central potentials, and introduction to hydrogenic systems.

Subjects

quantum physics: photoelectric effect | quantum physics: photoelectric effect | Compton scattering | Compton scattering | photons | photons | Franck-Hertz experiment | Franck-Hertz experiment | the Bohr atom | the Bohr atom | electron diffraction | electron diffraction | deBroglie waves | deBroglie waves | wave-particle duality of matter and light | wave-particle duality of matter and light | wave mechanics: Schroedinger's equation | wave mechanics: Schroedinger's equation | wave functions | wave functions | wave packets | wave packets | probability amplitudes | probability amplitudes | stationary states | stationary states | the Heisenberg uncertainty principle | the Heisenberg uncertainty principle | zero-point energies | zero-point energies | transmission and reflection at a barrier | transmission and reflection at a barrier | barrier penetration | barrier penetration | potential wells | potential wells | simple harmonic oscillator | simple harmonic oscillator | Schroedinger's equation in three dimensions: central potentials | Schroedinger's equation in three dimensions: central potentials | introduction to hydrogenic systems | introduction to hydrogenic systems | De Broglie waves | De Broglie waves

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14.01SC Principles of Microeconomics (MIT) 14.01SC Principles of Microeconomics (MIT)

Description

Includes audio/video content: AV lectures. 14.01 Principles of Microeconomics is an introductory undergraduate course that teaches the fundamentals of microeconomics. This course introduces microeconomic concepts and analysis, supply and demand analysis, theories of the firm and individual behavior, competition and monopoly, and welfare economics. Students will also be introduced to the use of microeconomic applications to address problems in current economic policy throughout the semester. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmen Includes audio/video content: AV lectures. 14.01 Principles of Microeconomics is an introductory undergraduate course that teaches the fundamentals of microeconomics. This course introduces microeconomic concepts and analysis, supply and demand analysis, theories of the firm and individual behavior, competition and monopoly, and welfare economics. Students will also be introduced to the use of microeconomic applications to address problems in current economic policy throughout the semester. This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmen

Subjects

Microeconomics | Microeconomics | prices | prices | normative economics | normative economics | positive economics | positive economics | microeconomic applications | microeconomic applications | supply | supply | demand | demand | equilibrium | equilibrium | demand shift | demand shift | supply shift | supply shift | government interference | government interference | elasticity | elasticity | revenue | revenue | empirical economics | empirical economics | consumer theory | consumer theory | preference assumptions | preference assumptions | indifference curves | indifference curves | utility functions | utility functions | marginal utility | marginal utility | budget constraints | budget constraints | marginal rate of transformation | marginal rate of transformation | opportunity cost | opportunity cost | constrained utility maximization | constrained utility maximization | corner solutions | corner solutions | Engel curves | Engel curves | income effect | income effect | substitution effect | substitution effect | Giffin good | Giffin good | labor economics | labor economics | child labor | child labor | producer theory | producer theory | variable inputs | variable inputs | fixed inputs | fixed inputs | firm production functions | firm production functions | marginal rate of technical substitution | marginal rate of technical substitution | returns to scale | returns to scale | productivity | productivity | perfect competition | perfect competition | search theory | search theory | residual demand | residual demand | shutdown decisions | shutdown decisions | market equilibrium | market equilibrium | agency problem | agency problem | welfare economics | welfare economics | consumer surplus | consumer surplus | producer surplus | producer surplus | dead weight loss | dead weight loss | monopoly | monopoly | oligopoly | oligopoly | market power | market power | price discrimination | price discrimination | price regulation | price regulation | antitrust policy | antitrust policy | mergers | mergers | cartel | cartel | game theory | game theory | Nash equilibrium | Nash equilibrium | Cournot model | Cournot model | duopoly | duopoly | non-cooperative competition | non-cooperative competition | Bertrand competition | Bertrand competition | factor markets | factor markets | international trade | international trade | uncertainty | uncertainty | capital markets | capital markets | intertemporal choice | intertemporal choice | real interest rate | real interest rate | compounding | compounding | inflation | inflation | investment | investment | discount rate | discount rate | net present value | net present value | income distribution | income distribution | social welfare function | social welfare function | Utilitarianism | Utilitarianism | Raulsian criteria | Raulsian criteria | Nozickian | Nozickian | commodity egalitarianism | commodity egalitarianism | isowelfare curves | isowelfare curves | social insurance | social insurance | social security | social security | moral hazard | moral hazard | taxation | taxation | EITC | EITC | healthcare | healthcare | PPACA | PPACA

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