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18.405J Advanced Complexity Theory (MIT) 18.405J Advanced Complexity Theory (MIT)

Description

The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved. The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved.Subjects

Basic time and space classes | Basic time and space classes | polynomial-time hierarchy | polynomial-time hierarchy | Randomized classes: RP | BPP | RL | and their relation to PH | Randomized classes: RP | BPP | RL | and their relation to PH | Counting classes: #P | Counting classes: #P | Non-uniform classes | Non-uniform classes | Oracles | relativization | Oracles | relativization | Interactive proof systems | Interactive proof systems | Pseudo-random generators | Pseudo-random generators | randomness | randomness | Some circuit lower bounds--monotone and AC0. | Some circuit lower bounds--monotone and AC0. | oracles | oracles | relativization | relativization | randomized classes | randomized classes | RP | RP | BPP | BPP | RL | RL | PH | PH | circuit lower bonds | circuit lower bonds | monotone | monotone | AC0 | AC0 | basic time classes | basic time classes | basic space classes | basic space classes | 18.405 | 18.405 | 6.841 | 6.841License

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See all metadata18.405J Advanced Complexity Theory (MIT) 18.405J Advanced Complexity Theory (MIT)

Description

The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved. The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved.Subjects

Basic time and space classes | Basic time and space classes | polynomial-time hierarchy | polynomial-time hierarchy | Randomized classes: RP | BPP | RL | and their relation to PH | Randomized classes: RP | BPP | RL | and their relation to PH | Counting classes: #P | Counting classes: #P | Non-uniform classes | Non-uniform classes | Oracles | relativization | Oracles | relativization | Interactive proof systems | Interactive proof systems | Pseudo-random generators | Pseudo-random generators | randomness | randomness | Some circuit lower bounds--monotone and AC0. | Some circuit lower bounds--monotone and AC0. | oracles | oracles | relativization | relativization | randomized classes | randomized classes | RP | RP | BPP | BPP | RL | RL | PH | PH | circuit lower bonds | circuit lower bonds | monotone | monotone | AC0 | AC0 | basic time classes | basic time classes | basic space classes | basic space classes | 18.405 | 18.405 | 6.841 | 6.841License

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

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The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls files The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls filesSubjects

Unified | Unified | Unified Engineering | Unified Engineering | aerospace | aerospace | CDIO | CDIO | C-D-I-O | C-D-I-O | conceive | conceive | design | design | implement | implement | operate | operate | team | team | team-based | team-based | discipline | discipline | materials | materials | structures | structures | materials and structures | materials and structures | computers | computers | programming | programming | computers and programming | computers and programming | fluids | fluids | fluid mechanics | fluid mechanics | thermodynamics | thermodynamics | propulsion | propulsion | signals | signals | systems | systems | signals and systems | signals and systems | systems problems | systems problems | fundamentals | fundamentals | technical communication | technical communication | graphical communication | graphical communication | communication | communication | reading | reading | research | research | experimentation | experimentation | personal response system | personal response system | prs | prs | active learning | active learning | First law | First law | first law of thermodynamics | first law of thermodynamics | thermo-mechanical | thermo-mechanical | energy | energy | energy conversion | energy conversion | aerospace power systems | aerospace power systems | propulsion systems | propulsion systems | aerospace propulsion systems | aerospace propulsion systems | heat | heat | work | work | thermal efficiency | thermal efficiency | forms of energy | forms of energy | energy exchange | energy exchange | processes | processes | heat engines | heat engines | engines | engines | steady-flow energy equation | steady-flow energy equation | energy flow | energy flow | flows | flows | path-dependence | path-dependence | path-independence | path-independence | reversibility | reversibility | irreversibility | irreversibility | state | state | thermodynamic state | thermodynamic state | performance | performance | ideal cycle | ideal cycle | simple heat engine | simple heat engine | cycles | cycles | thermal pressures | thermal pressures | temperatures | temperatures | linear static networks | linear static networks | loop method | loop method | node method | node method | linear dynamic networks | linear dynamic networks | classical methods | classical methods | state methods | state methods | state concepts | state concepts | dynamic systems | dynamic systems | resistive circuits | resistive circuits | sources | sources | voltages | voltages | currents | currents | Thevinin | Thevinin | Norton | Norton | initial value problems | initial value problems | RLC networks | RLC networks | characteristic values | characteristic values | characteristic vectors | characteristic vectors | transfer function | transfer function | ada | ada | ada programming | ada programming | programming language | programming language | software systems | software systems | programming style | programming style | computer architecture | computer architecture | program language evolution | program language evolution | classification | classification | numerical computation | numerical computation | number representation systems | number representation systems | assembly | assembly | SimpleSIM | SimpleSIM | RISC | RISC | CISC | CISC | operating systems | operating systems | single user | single user | multitasking | multitasking | multiprocessing | multiprocessing | domain-specific classification | domain-specific classification | recursive | recursive | execution time | execution time | fluid dynamics | fluid dynamics | physical properties of a fluid | physical properties of a fluid | fluid flow | fluid flow | mach | mach | reynolds | reynolds | conservation | conservation | conservation principles | conservation principles | conservation of mass | conservation of mass | conservation of momentum | conservation of momentum | conservation of energy | conservation of energy | continuity | continuity | inviscid | inviscid | steady flow | steady flow | simple bodies | simple bodies | airfoils | airfoils | wings | wings | channels | channels | aerodynamics | aerodynamics | forces | forces | moments | moments | equilibrium | equilibrium | freebody diagram | freebody diagram | free-body | free-body | free body | free body | planar force systems | planar force systems | equipollent systems | equipollent systems | equipollence | equipollence | support reactions | support reactions | reactions | reactions | static determinance | static determinance | determinate systems | determinate systems | truss analysis | truss analysis | trusses | trusses | method of joints | method of joints | method of sections | method of sections | statically indeterminate | statically indeterminate | three great principles | three great principles | 3 great principles | 3 great principles | indicial notation | indicial notation | rotation of coordinates | rotation of coordinates | coordinate rotation | coordinate rotation | stress | stress | extensional stress | extensional stress | shear stress | shear stress | notation | notation | plane stress | plane stress | stress equilbrium | stress equilbrium | stress transformation | stress transformation | mohr | mohr | mohr's circle | mohr's circle | principal stress | principal stress | principal stresses | principal stresses | extreme shear stress | extreme shear stress | strain | strain | extensional strain | extensional strain | shear strain | shear strain | strain-displacement | strain-displacement | compatibility | compatibility | strain transformation | strain transformation | transformation of strain | transformation of strain | mohr's circle for strain | mohr's circle for strain | principal strain | principal strain | extreme shear strain | extreme shear strain | uniaxial stress-strain | uniaxial stress-strain | material properties | material properties | classes of materials | classes of materials | bulk material properties | bulk material properties | origin of elastic properties | origin of elastic properties | structures of materials | structures of materials | atomic bonding | atomic bonding | packing of atoms | packing of atoms | atomic packing | atomic packing | crystals | crystals | crystal structures | crystal structures | polymers | polymers | estimate of moduli | estimate of moduli | moduli | moduli | composites | composites | composite materials | composite materials | modulus limited design | modulus limited design | material selection | material selection | materials selection | materials selection | measurement of elastic properties | measurement of elastic properties | stress-strain | stress-strain | stress-strain relations | stress-strain relations | anisotropy | anisotropy | orthotropy | orthotropy | measurements | measurements | engineering notation | engineering notation | Hooke | Hooke | Hooke's law | Hooke's law | general hooke's law | general hooke's law | equations of elasticity | equations of elasticity | boundary conditions | boundary conditions | multi-disciplinary | multi-disciplinary | models | models | engineering systems | engineering systems | experiments | experiments | investigations | investigations | experimental error | experimental error | design evaluation | design evaluation | evaluation | evaluation | trade studies | trade studies | effects of engineering | effects of engineering | social context | social context | engineering drawings | engineering drawings | 16.01 | 16.01 | 16.02 | 16.02 | 16.03 | 16.03 | 16.04 | 16.04License

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

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This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program.This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in repres This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program.This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in represSubjects

planning | planning | communication | communication | digital | digital | media | media | communications | communications | visualization | visualization | the role of digital technologies | the role of digital technologies | mobilizing communities | mobilizing communities | Athena | Athena | Element K | Element K | the ESRI virtual campus | the ESRI virtual campus | Computer Resources Laboratory (CRL) | Computer Resources Laboratory (CRL) | Campus Wide Information Systems Support (CWIS) | Campus Wide Information Systems Support (CWIS) | the GIS Laboratory | the GIS Laboratory | Rotch Library | Rotch Library | software tools | software tools | Adobe Photoshop | Adobe Photoshop | Illustrator | Illustrator | ESRI's ArcView | ESRI's ArcView | Microsoft's Access | Microsoft's Access | Macromedia's Dreamweaver | Macromedia's DreamweaverLicense

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

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Includes audio/video content: AV selected lectures, AV faculty introductions, AV special element video. The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines. Includes audio/video content: AV selected lectures, AV faculty introductions, AV special element video. The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Subjects

Unified | Unified | Unified Engineering | Unified Engineering | aerospace | aerospace | CDIO | CDIO | C-D-I-O | C-D-I-O | conceive | conceive | design | design | implement | implement | operate | operate | team | team | team-based | team-based | discipline | discipline | materials | materials | structures | structures | materials and structures | materials and structures | computers | computers | programming | programming | computers and programming | computers and programming | fluids | fluids | fluid mechanics | fluid mechanics | thermodynamics | thermodynamics | propulsion | propulsion | signals | signals | systems | systems | signals and systems | signals and systems | systems problems | systems problems | fundamentals | fundamentals | technical communication | technical communication | graphical communication | graphical communication | communication | communication | reading | reading | research | research | experimentation | experimentation | personal response system | personal response system | prs | prs | active learning | active learning | First law | First law | first law of thermodynamics | first law of thermodynamics | thermo-mechanical | thermo-mechanical | energy | energy | energy conversion | energy conversion | aerospace power systems | aerospace power systems | propulsion systems | propulsion systems | aerospace propulsion systems | aerospace propulsion systems | heat | heat | work | work | thermal efficiency | thermal efficiency | forms of energy | forms of energy | energy exchange | energy exchange | processes | processes | heat engines | heat engines | engines | engines | steady-flow energy equation | steady-flow energy equation | energy flow | energy flow | flows | flows | path-dependence | path-dependence | path-independence | path-independence | reversibility | reversibility | irreversibility | irreversibility | state | state | thermodynamic state | thermodynamic state | performance | performance | ideal cycle | ideal cycle | simple heat engine | simple heat engine | cycles | cycles | thermal pressures | thermal pressures | temperatures | temperatures | linear static networks | linear static networks | loop method | loop method | node method | node method | linear dynamic networks | linear dynamic networks | classical methods | classical methods | state methods | state methods | state concepts | state concepts | dynamic systems | dynamic systems | resistive circuits | resistive circuits | sources | sources | voltages | voltages | currents | currents | Thevinin | Thevinin | Norton | Norton | initial value problems | initial value problems | RLC networks | RLC networks | characteristic values | characteristic values | characteristic vectors | characteristic vectors | transfer function | transfer function | ada | ada | ada programming | ada programming | programming language | programming language | software systems | software systems | programming style | programming style | computer architecture | computer architecture | program language evolution | program language evolution | classification | classification | numerical computation | numerical computation | number representation systems | number representation systems | assembly | assembly | SimpleSIM | SimpleSIM | RISC | RISC | CISC | CISC | operating systems | operating systems | single user | single user | multitasking | multitasking | multiprocessing | multiprocessing | domain-specific classification | domain-specific classification | recursive | recursive | execution time | execution time | fluid dynamics | fluid dynamics | physical properties of a fluid | physical properties of a fluid | fluid flow | fluid flow | mach | mach | reynolds | reynolds | conservation | conservation | conservation principles | conservation principles | conservation of mass | conservation of mass | conservation of momentum | conservation of momentum | conservation of energy | conservation of energy | continuity | continuity | inviscid | inviscid | steady flow | steady flow | simple bodies | simple bodies | airfoils | airfoils | wings | wings | channels | channels | aerodynamics | aerodynamics | forces | forces | moments | moments | equilibrium | equilibrium | freebody diagram | freebody diagram | free-body | free-body | free body | free body | planar force systems | planar force systems | equipollent systems | equipollent systems | equipollence | equipollence | support reactions | support reactions | reactions | reactions | static determinance | static determinance | determinate systems | determinate systems | truss analysis | truss analysis | trusses | trusses | method of joints | method of joints | method of sections | method of sections | statically indeterminate | statically indeterminate | three great principles | three great principles | 3 great principles | 3 great principles | indicial notation | indicial notation | rotation of coordinates | rotation of coordinates | coordinate rotation | coordinate rotation | stress | stress | extensional stress | extensional stress | shear stress | shear stress | notation | notation | plane stress | plane stress | stress equilbrium | stress equilbrium | stress transformation | stress transformation | mohr | mohr | mohr's circle | mohr's circle | principal stress | principal stress | principal stresses | principal stresses | extreme shear stress | extreme shear stress | strain | strain | extensional strain | extensional strain | shear strain | shear strain | strain-displacement | strain-displacement | compatibility | compatibility | strain transformation | strain transformation | transformation of strain | transformation of strain | mohr's circle for strain | mohr's circle for strain | principal strain | principal strain | extreme shear strain | extreme shear strain | uniaxial stress-strain | uniaxial stress-strain | material properties | material properties | classes of materials | classes of materials | bulk material properties | bulk material properties | origin of elastic properties | origin of elastic properties | structures of materials | structures of materials | atomic bonding | atomic bonding | packing of atoms | packing of atoms | atomic packing | atomic packing | crystals | crystals | crystal structures | crystal structures | polymers | polymers | estimate of moduli | estimate of moduli | moduli | moduli | composites | composites | composite materials | composite materials | modulus limited design | modulus limited design | material selection | material selection | materials selection | materials selection | measurement of elastic properties | measurement of elastic properties | stress-strain | stress-strain | stress-strain relations | stress-strain relations | anisotropy | anisotropy | orthotropy | orthotropy | measurements | measurements | engineering notation | engineering notation | Hooke | Hooke | Hooke's law | Hooke's law | general hooke's law | general hooke's law | equations of elasticity | equations of elasticity | boundary conditions | boundary conditions | multi-disciplinary | multi-disciplinary | models | models | engineering systems | engineering systems | experiments | experiments | investigations | investigations | experimental error | experimental error | design evaluation | design evaluation | evaluation | evaluation | trade studies | trade studies | effects of engineering | effects of engineering | social context | social context | engineering drawings | engineering drawingsLicense

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

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See all metadata8.022 Physics II: Electricity and Magnetism (MIT) 8.022 Physics II: Electricity and Magnetism (MIT)

Description

This course runs parallel to 8.02, but assumes that students have some knowledge of vector calculus. The class introduces Maxwell's equations, in both differential and integral form, along with electrostatic and magnetic vector potential, and the properties of dielectrics and magnetic materials. This class was taught by an undergraduate in the Experimental Study Group (ESG). Student instructors are paired with ESG faculty members, who advise and oversee the students' teaching efforts. This course runs parallel to 8.02, but assumes that students have some knowledge of vector calculus. The class introduces Maxwell's equations, in both differential and integral form, along with electrostatic and magnetic vector potential, and the properties of dielectrics and magnetic materials. This class was taught by an undergraduate in the Experimental Study Group (ESG). Student instructors are paired with ESG faculty members, who advise and oversee the students' teaching efforts.Subjects

Electricity | Electricity | Magnetism | Magnetism | Maxwell's equations | Maxwell's equations | electrostatic potential | electrostatic potential | vector potential | vector potential | dielectrics | dielectrics | Coulomb's Law | Coulomb's Law | Electric Field | Electric Field | Electric Flux | Electric Flux | Gauss's Law | Gauss's Law | Electric Potential Gradient | Electric Potential Gradient | Poisson Equations | Poisson Equations | Laplace Equations | Laplace Equations | Curl | Curl | Conductors | Conductors | Capacitance | Capacitance | Resistance | Resistance | Kirchhoff's Rules | Kirchhoff's Rules | EMF | EMF | RC Circuits | RC Circuits | Th?venin Equivalence | Th?venin Equivalence | Magnetic Force | Magnetic Force | Magnetic Field | Magnetic Field | Ampere's Law | Ampere's Law | Special Relativity | Special Relativity | Spacetime | Spacetime | Biot-Savart Law | Biot-Savart Law | Faraday's Law | Faraday's Law | Lenz's Law | Lenz's Law | RL Circuits | RL Circuits | AC Circuits | AC Circuits | Electromagnetic Radiation | Electromagnetic Radiation | Poynting Vector | Poynting VectorLicense

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

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See all metadata8.022 Physics II: Electricity and Magnetism (MIT) 8.022 Physics II: Electricity and Magnetism (MIT)

Description

Course 8.022 is one of several second-term freshman physics courses offered at MIT. It is geared towards students who are looking for a thorough and challenging introduction to electricity and magnetism. Topics covered include: Electric and magnetic field and potential; introduction to special relativity; Maxwell's equations, in both differential and integral form; and properties of dielectrics and magnetic materials. In addition to the theoretical subject matter, several experiments in electricity and magnetism are performed by the students in the laboratory. Acknowledgments Prof. Sciolla would like to acknowledge the contributions of MIT Professors Scott Hughes and Peter Fisher to the development of this course. She would also like to acknowledge that these course materials include cont Course 8.022 is one of several second-term freshman physics courses offered at MIT. It is geared towards students who are looking for a thorough and challenging introduction to electricity and magnetism. Topics covered include: Electric and magnetic field and potential; introduction to special relativity; Maxwell's equations, in both differential and integral form; and properties of dielectrics and magnetic materials. In addition to the theoretical subject matter, several experiments in electricity and magnetism are performed by the students in the laboratory. Acknowledgments Prof. Sciolla would like to acknowledge the contributions of MIT Professors Scott Hughes and Peter Fisher to the development of this course. She would also like to acknowledge that these course materials include contSubjects

Electricity | Electricity | Magnetism | Magnetism | Maxwell's equations | Maxwell's equations | electrostatic potential | electrostatic potential | vector potential | vector potential | dielectrics | dielectrics | Coulomb's Law | Coulomb's Law | Electric Field | Electric Field | Electric Flux | Electric Flux | Gauss's Law | Gauss's Law | Electric Potential Gradient | Electric Potential Gradient | Poisson Equations | Poisson Equations | Laplace Equations | Laplace Equations | Curl | Curl | Conductors | Conductors | Capacitance | Capacitance | Resistance | Resistance | Kirchhoff's Rules | Kirchhoff's Rules | EMF | EMF | RC Circuits | RC Circuits | Th?venin Equivalence | Th?venin Equivalence | Magnetic Force | Magnetic Force | Magnetic Field | Magnetic Field | Ampere's Law | Ampere's Law | Special Relativity | Special Relativity | Spacetime | Spacetime | Biot-Savart Law | Biot-Savart Law | Faraday's Law | Faraday's Law | Lenz's Law | Lenz's Law | RL Circuits | RL Circuits | AC Circuits | AC Circuits | Electromagnetic Radiation | Electromagnetic Radiation | Poynting Vector | Poynting Vector | Magnetism | Maxwell's equations; | Magnetism | Maxwell's equations;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.htmSite sourced from

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This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program. This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in repre This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program. This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in repreSubjects

planning | planning | communication | communication | digital | digital | media | media | communications | communications | visualization | visualization | the role of digital technologies | the role of digital technologies | mobilizing communities | mobilizing communities | Athena | Athena | Element K | Element K | the ESRI virtual campus | the ESRI virtual campus | Computer Resources Laboratory (CRL) | Computer Resources Laboratory (CRL) | Campus Wide Information Systems Support (CWIS) | Campus Wide Information Systems Support (CWIS) | the GIS Laboratory | the GIS Laboratory | Rotch Library | Rotch Library | software tools | software tools | Adobe Photoshop | Adobe Photoshop | Illustrator | Illustrator | ESRI's ArcView | ESRI's ArcView | Microsoft's Access | Microsoft's Access | Macromedia's Dreamweaver | Macromedia's DreamweaverLicense

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

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See all metadata18.405J Advanced Complexity Theory (MIT)

Description

The topics for this course cover various aspects of complexity theory, such as the basic time and space classes, the polynomial-time hierarchy and the randomized classes . This is a pure theory class, so no applications were involved.Subjects

Basic time and space classes | polynomial-time hierarchy | Randomized classes: RP | BPP | RL | and their relation to PH | Counting classes: #P | Non-uniform classes | Oracles | relativization | Interactive proof systems | Pseudo-random generators | randomness | Some circuit lower bounds--monotone and AC0. | oracles | relativization | randomized classes | RP | BPP | RL | PH | circuit lower bonds | monotone | AC0 | basic time classes | basic space classes | 18.405 | 6.841License

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

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See all metadata11.204 Planning, Communications, and Digital Media (MIT)

Description

This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program. This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in repreSubjects

planning | communication | digital | media | communications | visualization | the role of digital technologies | mobilizing communities | Athena | Element K | the ESRI virtual campus | Computer Resources Laboratory (CRL) | Campus Wide Information Systems Support (CWIS) | the GIS Laboratory | Rotch Library | software tools | Adobe Photoshop | Illustrator | ESRI's ArcView | Microsoft's Access | Macromedia's DreamweaverLicense

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

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See all metadata8.022 Physics II: Electricity and Magnetism (MIT)

Description

This course runs parallel to 8.02, but assumes that students have some knowledge of vector calculus. The class introduces Maxwell's equations, in both differential and integral form, along with electrostatic and magnetic vector potential, and the properties of dielectrics and magnetic materials. This class was taught by an undergraduate in the Experimental Study Group (ESG). Student instructors are paired with ESG faculty members, who advise and oversee the students' teaching efforts.Subjects

Electricity | Magnetism | Maxwell's equations | electrostatic potential | vector potential | dielectrics | Coulomb's Law | Electric Field | Electric Flux | Gauss's Law | Electric Potential Gradient | Poisson Equations | Laplace Equations | Curl | Conductors | Capacitance | Resistance | Kirchhoff's Rules | EMF | RC Circuits | Th?venin Equivalence | Magnetic Force | Magnetic Field | Ampere's Law | Special Relativity | Spacetime | Biot-Savart Law | Faraday's Law | Lenz's Law | RL Circuits | AC Circuits | Electromagnetic Radiation | Poynting VectorLicense

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

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

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See all metadataDescription

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Subjects

Unified | Unified Engineering | aerospace | CDIO | C-D-I-O | conceive | design | implement | operate | team | team-based | discipline | materials | structures | materials and structures | computers | programming | computers and programming | fluids | fluid mechanics | thermodynamics | propulsion | signals | systems | signals and systems | systems problems | fundamentals | technical communication | graphical communication | communication | reading | research | experimentation | personal response system | prs | active learning | First law | first law of thermodynamics | thermo-mechanical | energy | energy conversion | aerospace power systems | propulsion systems | aerospace propulsion systems | heat | work | thermal efficiency | forms of energy | energy exchange | processes | heat engines | engines | steady-flow energy equation | energy flow | flows | path-dependence | path-independence | reversibility | irreversibility | state | thermodynamic state | performance | ideal cycle | simple heat engine | cycles | thermal pressures | temperatures | linear static networks | loop method | node method | linear dynamic networks | classical methods | state methods | state concepts | dynamic systems | resistive circuits | sources | voltages | currents | Thevinin | Norton | initial value problems | RLC networks | characteristic values | characteristic vectors | transfer function | ada | ada programming | programming language | software systems | programming style | computer architecture | program language evolution | classification | numerical computation | number representation systems | assembly | SimpleSIM | RISC | CISC | operating systems | single user | multitasking | multiprocessing | domain-specific classification | recursive | execution time | fluid dynamics | physical properties of a fluid | fluid flow | mach | reynolds | conservation | conservation principles | conservation of mass | conservation of momentum | conservation of energy | continuity | inviscid | steady flow | simple bodies | airfoils | wings | channels | aerodynamics | forces | moments | equilibrium | freebody diagram | free-body | free body | planar force systems | equipollent systems | equipollence | support reactions | reactions | static determinance | determinate systems | truss analysis | trusses | method of joints | method of sections | statically indeterminate | three great principles | 3 great principles | indicial notation | rotation of coordinates | coordinate rotation | stress | extensional stress | shear stress | notation | plane stress | stress equilbrium | stress transformation | mohr | mohr's circle | principal stress | principal stresses | extreme shear stress | strain | extensional strain | shear strain | strain-displacement | compatibility | strain transformation | transformation of strain | mohr's circle for strain | principal strain | extreme shear strain | uniaxial stress-strain | material properties | classes of materials | bulk material properties | origin of elastic properties | structures of materials | atomic bonding | packing of atoms | atomic packing | crystals | crystal structures | polymers | estimate of moduli | moduli | composites | composite materials | modulus limited design | material selection | materials selection | measurement of elastic properties | stress-strain | stress-strain relations | anisotropy | orthotropy | measurements | engineering notation | Hooke | Hooke's law | general hooke's law | equations of elasticity | boundary conditions | multi-disciplinary | models | engineering systems | experiments | investigations | experimental error | design evaluation | evaluation | trade studies | effects of engineering | social context | engineering drawingsLicense

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

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See all metadata11.204 Planning, Communications, and Digital Media (MIT)

Description

This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program. This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in repreSubjects

planning | communication | digital | media | communications | visualization | the role of digital technologies | mobilizing communities | Athena | Element K | the ESRI virtual campus | Computer Resources Laboratory (CRL) | Campus Wide Information Systems Support (CWIS) | the GIS Laboratory | Rotch Library | software tools | Adobe Photoshop | Illustrator | ESRI's ArcView | Microsoft's Access | Macromedia's DreamweaverLicense

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

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

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

See all metadataDescription

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Technical RequirementsMicrosoft® Excel software is recommended for viewing the .xls filesSubjects

Unified | Unified Engineering | aerospace | CDIO | C-D-I-O | conceive | design | implement | operate | team | team-based | discipline | materials | structures | materials and structures | computers | programming | computers and programming | fluids | fluid mechanics | thermodynamics | propulsion | signals | systems | signals and systems | systems problems | fundamentals | technical communication | graphical communication | communication | reading | research | experimentation | personal response system | prs | active learning | First law | first law of thermodynamics | thermo-mechanical | energy | energy conversion | aerospace power systems | propulsion systems | aerospace propulsion systems | heat | work | thermal efficiency | forms of energy | energy exchange | processes | heat engines | engines | steady-flow energy equation | energy flow | flows | path-dependence | path-independence | reversibility | irreversibility | state | thermodynamic state | performance | ideal cycle | simple heat engine | cycles | thermal pressures | temperatures | linear static networks | loop method | node method | linear dynamic networks | classical methods | state methods | state concepts | dynamic systems | resistive circuits | sources | voltages | currents | Thevinin | Norton | initial value problems | RLC networks | characteristic values | characteristic vectors | transfer function | ada | ada programming | programming language | software systems | programming style | computer architecture | program language evolution | classification | numerical computation | number representation systems | assembly | SimpleSIM | RISC | CISC | operating systems | single user | multitasking | multiprocessing | domain-specific classification | recursive | execution time | fluid dynamics | physical properties of a fluid | fluid flow | mach | reynolds | conservation | conservation principles | conservation of mass | conservation of momentum | conservation of energy | continuity | inviscid | steady flow | simple bodies | airfoils | wings | channels | aerodynamics | forces | moments | equilibrium | freebody diagram | free-body | free body | planar force systems | equipollent systems | equipollence | support reactions | reactions | static determinance | determinate systems | truss analysis | trusses | method of joints | method of sections | statically indeterminate | three great principles | 3 great principles | indicial notation | rotation of coordinates | coordinate rotation | stress | extensional stress | shear stress | notation | plane stress | stress equilbrium | stress transformation | mohr | mohr's circle | principal stress | principal stresses | extreme shear stress | strain | extensional strain | shear strain | strain-displacement | compatibility | strain transformation | transformation of strain | mohr's circle for strain | principal strain | extreme shear strain | uniaxial stress-strain | material properties | classes of materials | bulk material properties | origin of elastic properties | structures of materials | atomic bonding | packing of atoms | atomic packing | crystals | crystal structures | polymers | estimate of moduli | moduli | composites | composite materials | modulus limited design | material selection | materials selection | measurement of elastic properties | stress-strain | stress-strain relations | anisotropy | orthotropy | measurements | engineering notation | Hooke | Hooke's law | general hooke's law | equations of elasticity | boundary conditions | multi-disciplinary | models | engineering systems | experiments | investigations | experimental error | design evaluation | evaluation | trade studies | effects of engineering | social context | engineering drawings | 16.01 | 16.02 | 16.03 | 16.04License

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

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

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

See all metadata11.204 Planning, Communications, and Digital Media (MIT)

Description

This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program.This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in represSubjects

planning | communication | digital | media | communications | visualization | the role of digital technologies | mobilizing communities | Athena | Element K | the ESRI virtual campus | Computer Resources Laboratory (CRL) | Campus Wide Information Systems Support (CWIS) | the GIS Laboratory | Rotch Library | software tools | Adobe Photoshop | Illustrator | ESRI's ArcView | Microsoft's Access | Macromedia's DreamweaverLicense

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

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

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

See all metadata8.022 Physics II: Electricity and Magnetism (MIT)

Description

This course runs parallel to 8.02, but assumes that students have some knowledge of vector calculus. The class introduces Maxwell's equations, in both differential and integral form, along with electrostatic and magnetic vector potential, and the properties of dielectrics and magnetic materials. This class was taught by an undergraduate in the Experimental Study Group (ESG). Student instructors are paired with ESG faculty members, who advise and oversee the students' teaching efforts.Subjects

Electricity | Magnetism | Maxwell's equations | electrostatic potential | vector potential | dielectrics | Coulomb's Law | Electric Field | Electric Flux | Gauss's Law | Electric Potential Gradient | Poisson Equations | Laplace Equations | Curl | Conductors | Capacitance | Resistance | Kirchhoff's Rules | EMF | RC Circuits | Th?venin Equivalence | Magnetic Force | Magnetic Field | Ampere's Law | Special Relativity | Spacetime | Biot-Savart Law | Faraday's Law | Lenz's Law | RL Circuits | AC Circuits | Electromagnetic Radiation | Poynting VectorLicense

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

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See all metadata8.022 Physics II: Electricity and Magnetism (MIT)

Description

Course 8.022 is one of several second-term freshman physics courses offered at MIT. It is geared towards students who are looking for a thorough and challenging introduction to electricity and magnetism. Topics covered include: Electric and magnetic field and potential; introduction to special relativity; Maxwell's equations, in both differential and integral form; and properties of dielectrics and magnetic materials. In addition to the theoretical subject matter, several experiments in electricity and magnetism are performed by the students in the laboratory. Acknowledgments Prof. Sciolla would like to acknowledge the contributions of MIT Professors Scott Hughes and Peter Fisher to the development of this course. She would also like to acknowledge that these course materials include contSubjects

Electricity | Magnetism | Maxwell's equations | electrostatic potential | vector potential | dielectrics | Coulomb's Law | Electric Field | Electric Flux | Gauss's Law | Electric Potential Gradient | Poisson Equations | Laplace Equations | Curl | Conductors | Capacitance | Resistance | Kirchhoff's Rules | EMF | RC Circuits | Th?venin Equivalence | Magnetic Force | Magnetic Field | Ampere's Law | Special Relativity | Spacetime | Biot-Savart Law | Faraday's Law | Lenz's Law | RL Circuits | AC Circuits | Electromagnetic Radiation | Poynting Vector | Magnetism | Maxwell's equations;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.htmSite sourced from

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

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

See all metadataDescription

The basic objective of Unified Engineering is to give a solid understanding of the fundamental disciplines of aerospace engineering, as well as their interrelationships and applications. These disciplines are Materials and Structures (M); Computers and Programming (C); Fluid Mechanics (F); Thermodynamics (T); Propulsion (P); and Signals and Systems (S). In choosing to teach these subjects in a unified manner, the instructors seek to explain the common intellectual threads in these disciplines, as well as their combined application to solve engineering Systems Problems (SP). Throughout the year, the instructors emphasize the connections among the disciplines.Subjects

Unified | Unified Engineering | aerospace | CDIO | C-D-I-O | conceive | design | implement | operate | team | team-based | discipline | materials | structures | materials and structures | computers | programming | computers and programming | fluids | fluid mechanics | thermodynamics | propulsion | signals | systems | signals and systems | systems problems | fundamentals | technical communication | graphical communication | communication | reading | research | experimentation | personal response system | prs | active learning | First law | first law of thermodynamics | thermo-mechanical | energy | energy conversion | aerospace power systems | propulsion systems | aerospace propulsion systems | heat | work | thermal efficiency | forms of energy | energy exchange | processes | heat engines | engines | steady-flow energy equation | energy flow | flows | path-dependence | path-independence | reversibility | irreversibility | state | thermodynamic state | performance | ideal cycle | simple heat engine | cycles | thermal pressures | temperatures | linear static networks | loop method | node method | linear dynamic networks | classical methods | state methods | state concepts | dynamic systems | resistive circuits | sources | voltages | currents | Thevinin | Norton | initial value problems | RLC networks | characteristic values | characteristic vectors | transfer function | ada | ada programming | programming language | software systems | programming style | computer architecture | program language evolution | classification | numerical computation | number representation systems | assembly | SimpleSIM | RISC | CISC | operating systems | single user | multitasking | multiprocessing | domain-specific classification | recursive | execution time | fluid dynamics | physical properties of a fluid | fluid flow | mach | reynolds | conservation | conservation principles | conservation of mass | conservation of momentum | conservation of energy | continuity | inviscid | steady flow | simple bodies | airfoils | wings | channels | aerodynamics | forces | moments | equilibrium | freebody diagram | free-body | free body | planar force systems | equipollent systems | equipollence | support reactions | reactions | static determinance | determinate systems | truss analysis | trusses | method of joints | method of sections | statically indeterminate | three great principles | 3 great principles | indicial notation | rotation of coordinates | coordinate rotation | stress | extensional stress | shear stress | notation | plane stress | stress equilbrium | stress transformation | mohr | mohr's circle | principal stress | principal stresses | extreme shear stress | strain | extensional strain | shear strain | strain-displacement | compatibility | strain transformation | transformation of strain | mohr's circle for strain | principal strain | extreme shear strain | uniaxial stress-strain | material properties | classes of materials | bulk material properties | origin of elastic properties | structures of materials | atomic bonding | packing of atoms | atomic packing | crystals | crystal structures | polymers | estimate of moduli | moduli | composites | composite materials | modulus limited design | material selection | materials selection | measurement of elastic properties | stress-strain | stress-strain relations | anisotropy | orthotropy | measurements | engineering notation | Hooke | Hooke's law | general hooke's law | equations of elasticity | boundary conditions | multi-disciplinary | models | engineering systems | experiments | investigations | experimental error | design evaluation | evaluation | trade studies | effects of engineering | social context | engineering drawingsLicense

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

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

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

See all metadata11.204 Planning, Communications, and Digital Media (MIT)

Description

This course focuses on methods of digital visualization and communication and their application to planning issues. Lectures will introduce a variety of methods for describing or representing a place and its residents, for simulating changes, for presenting visions of the future, and for engaging multiple actors in the process of guiding action. Through a series of laboratory exercises, students will apply these methods in the construction of a web-based portfolio. The portfolio is not only the final project for the course, but will serve as a container for other course work throughout the MCP program. This course aims to introduce students to (1) such persistent and recurring themes as place, race, power and the environment that face planners, (2) the role of digital technologies in repreSubjects

planning | communication | digital | media | communications | visualization | the role of digital technologies | mobilizing communities | Athena | Element K | the ESRI virtual campus | Computer Resources Laboratory (CRL) | Campus Wide Information Systems Support (CWIS) | the GIS Laboratory | Rotch Library | software tools | Adobe Photoshop | Illustrator | ESRI's ArcView | Microsoft's Access | Macromedia's DreamweaverLicense

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

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

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

See all metadata