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18.950 Differential Geometry (MIT) 18.950 Differential Geometry (MIT)

Description

This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied. This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied.Subjects

Metrics | Metrics | Lie bracket | Lie bracket | connections | connections | geodesics | geodesics | tensors | tensors | intrinsic and extrinsic curvature | intrinsic and extrinsic curvature | defined manifolds using coordinate charts | defined manifolds using coordinate charts | Curves and surfaces in three dimensions | Curves and surfaces in three dimensions | Gauss-Bonnet theorem for surfaces | Gauss-Bonnet theorem for surfaces | general relativity | general relativityLicense

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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6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc. 6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc.Subjects

electromagnetic | electromagnetic | electromagnetic field | electromagnetic field | forces | forces | motion | motion | electric | electric | magnetic | magnetic | quasistatic | quasistatic | Maxwell's equations | Maxwell's equations | dielectric | dielectric | conduction | conduction | magnetization | magnetization | boundary value problems | boundary value problems | force densities | force densities | stress tensors | stress tensors | polarization | polarization | thermodynamics | thermodynamics | equations of motion | equations of motion | energy conservation | energy conservation | synchronous | synchronous | induction | induction | commutator machines | commutator machines | sensors | sensors | transducers | transducers | microelectromechanical systems | microelectromechanical systems | electromechanical waves | electromechanical waves | charge transport phenomena | charge transport phenomenaLicense

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 faculty introductions. This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, and Includes audio/video content: AV faculty introductions. This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, andSubjects

electromagnetic | electromagnetic | electromagnetic field | electromagnetic field | forces | forces | motion | motion | electric | electric | magnetic | magnetic | quasistatic | quasistatic | Maxwell's equations | Maxwell's equations | dielectric | dielectric | conduction | conduction | magnetization | magnetization | boundary value problems | boundary value problems | force densities | force densities | stress tensors | stress tensors | polarization | polarization | thermodynamics | thermodynamics | equations of motion | equations of motion | energy conservation | energy conservation | synchronous | synchronous | induction | induction | commutator machines | commutator machines | sensors | sensors | transducers | transducers | microelectromechanical systems | microelectromechanical systems | electromechanical waves | electromechanical waves | charge transport phenomena | charge transport phenomenaLicense

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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6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams. 6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams.Subjects

electromagnetic | electromagnetic | electromagnetic field | electromagnetic field | forces | forces | motion | motion | electric | electric | magnetic | magnetic | quasistatic | quasistatic | Maxwell's equations | Maxwell's equations | dielectric | dielectric | conduction | conduction | magnetization | magnetization | boundary value problems | boundary value problems | force densities | force densities | stress tensors | stress tensors | polarization | polarization | thermodynamics | thermodynamics | equations of motion | equations of motion | energy conservation | energy conservation | synchronous | synchronous | induction | induction | commutator machines | commutator machines | sensors | sensors | transducers | transducers | microelectromechanical systems | microelectromechanical systems | electromechanical waves | electromechanical waves | charge transport phenomena | charge transport phenomenaLicense

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 metadata8.962 General Relativity (MIT) 8.962 General Relativity (MIT)

Description

8.962 is MIT's graduate course in general relativity, which covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology. 8.962 is MIT's graduate course in general relativity, which covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.Subjects

Spacetime | Spacetime | tensors | tensors | special relativity | special relativity | differential geometry | differential geometry | Einstein's equation | Einstein's equation | gravitation | gravitation | cosmological constant | cosmological constant | Hilbert action | Hilbert action | general relativity | general relativity | gravitational waves | gravitational waves | gravitational lensing | gravitational lensing | cosmology | cosmology | Schwarzschild solution | Schwarzschild solution | black holes | black holesLicense

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

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See all metadata6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams.Subjects

electromagnetic | electromagnetic field | forces | motion | electric | magnetic | quasistatic | Maxwell's equations | dielectric | conduction | magnetization | boundary value problems | force densities | stress tensors | polarization | thermodynamics | equations of motion | energy conservation | synchronous | induction | commutator machines | sensors | transducers | microelectromechanical systems | electromechanical waves | charge transport phenomenaLicense

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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Authors: Professor Peter Dunsby COURSE OUTLINE General Physics 1. Mathematical Tools 2. Linear Algebra and Tensors Relativity 1. General Relativity 2. Mathematics Clicked 464 times. Last clicked 11/19/2014 - 14:42. Teaching & Learning Context: This website contains lecture notes on Special and General Relativity, with a mathematical approach. The first part is exclusively dedicated to Special Relativity and its mathematical treatment using Tensors. The last four subjects go through General Relativity, explaining its principles, the effects of gravity and how to apply Tensors to the study of curvaturSubjects

Mathematics and Applied Mathematics | Science | Downloadable Documents | Text/HTML Webpages | Lecture Notes | English | Post-secondary | linear algebra | mathematics | relativity | special relativity | tensorsLicense

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See all metadata18.950 Differential Geometry (MIT)

Description

This course is an introduction to differential geometry of curves and surfaces in three dimensional Euclidean space. First and second fundamental forms, Gaussian and mean curvature, parallel transport, geodesics, Gauss-Bonnet theorem, complete surfaces, minimal surfaces and Bernstein's theorem are among the main topics studied.Subjects

Metrics | Lie bracket | connections | geodesics | tensors | intrinsic and extrinsic curvature | defined manifolds using coordinate charts | Curves and surfaces in three dimensions | Gauss-Bonnet theorem for surfaces | general relativityLicense

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

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See all metadata6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena.Technical RequirementsRealOne™ Player software is required to run the .rm files found on this course site.RealOne™ is a trademark or a registered trademark of RealNetworks, Inc.Subjects

electromagnetic | electromagnetic field | forces | motion | electric | magnetic | quasistatic | Maxwell's equations | dielectric | conduction | magnetization | boundary value problems | force densities | stress tensors | polarization | thermodynamics | equations of motion | energy conservation | synchronous | induction | commutator machines | sensors | transducers | microelectromechanical systems | electromechanical waves | charge transport phenomenaLicense

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 metadata8.962 General Relativity (MIT)

Description

8.962 is MIT's graduate course in general relativity, which covers the basic principles of Einstein's general theory of relativity, differential geometry, experimental tests of general relativity, black holes, and cosmology.Subjects

Spacetime | tensors | special relativity | differential geometry | Einstein's equation | gravitation | cosmological constant | Hilbert action | general relativity | gravitational waves | gravitational lensing | cosmology | Schwarzschild solution | black holesLicense

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

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See all metadata6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

This course examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgments The instructor would like to thank Thomas Larsen and Matthew Pegler for transcribing into LaTeX the homework problems, homework solutions, and exam solutions.Subjects

electromagnetic | electromagnetic field | forces | motion | electric | magnetic | quasistatic | Maxwell's equations | dielectric | conduction | magnetization | boundary value problems | force densities | stress tensors | polarization | thermodynamics | equations of motion | energy conservation | synchronous | induction | commutator machines | sensors | transducers | microelectromechanical systems | electromechanical waves | charge transport phenomenaLicense

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

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See all metadata6.641 Electromagnetic Fields, Forces, and Motion (MIT)

Description

6.641 examines electric and magnetic quasistatic forms of Maxwell's equations applied to dielectric, conduction, and magnetization boundary value problems. Topics covered include: electromagnetic forces, force densities, and stress tensors, including magnetization and polarization; thermodynamics of electromagnetic fields, equations of motion, and energy conservation; applications to synchronous, induction, and commutator machines; sensors and transducers; microelectromechanical systems; propagation and stability of electromechanical waves; and charge transport phenomena. Acknowledgement The instructor would like to thank Thomas Larsen for transcribing into LaTeX selected homework problems, homework solutions, and exams.Subjects

electromagnetic | electromagnetic field | forces | motion | electric | magnetic | quasistatic | Maxwell's equations | dielectric | conduction | magnetization | boundary value problems | force densities | stress tensors | polarization | thermodynamics | equations of motion | energy conservation | synchronous | induction | commutator machines | sensors | transducers | microelectromechanical systems | electromechanical waves | charge transport phenomenaLicense

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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