Searching for vectors : 82 results found | RSS Feed for this search

8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay. Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.Subjects

Einstein's postulates | Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects and paradoxes | relativistic effects and paradoxes | Minkowski diagrams | Minkowski diagrams | invariants and four-vectors | invariants and four-vectors | momentum | energy and mass | momentum | energy and mass | particle collisions | particle collisions | Relativity and electricity | Relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | General Relativity | General Relativity | principle of equivalence | principle of equivalence | the Schwarzchild metric | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | gravitational red shift | particle trajectories | particle trajectories | light trajectories | light trajectories | invariants | invariants | four-vectors | four-vectors | momentum | momentum | energy | energy | mass | mass | relativistic effects | relativistic effects | paradoxes | paradoxes | electricity | electricity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Schwarzchild metric | Schwarzchild metric | geodesics | geodesics | Shaprio delay | Shaprio delay | relativistic kinematics | relativistic kinematics | relativistic dynamics | relativistic dynamics | electromagnetism | electromagnetism | hubble expansion | hubble expansion | universe | universe | equivalence principle | equivalence principle | curved space time | curved space time | Ether Theory | Ether Theory | constants | constants | speed of light | speed of light | c | c | graph | graph | pythagorem theorem | pythagorem theorem | triangle | triangle | arrows | arrowsLicense

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

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

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

See all metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams | constant coefficients | constant coefficients | complex numbers | complex numbers | exponentials | exponentials | eigenvalues | eigenvalues | eigenvectors | eigenvectorsLicense

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

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

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

See all metadata18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | ODE | modeling physical systems | first-order ODE's | Linear ODE's | second order ODE's | second order ODE's with constant coefficients | Undetermined coefficients | variation of parameters | Sinusoidal signals | exponential signals | oscillations | damping | resonance | Complex numbers and exponentials | Fourier series | periodic solutions | Delta functions | convolution | Laplace transform methods | Matrix systems | first order linear systems | eigenvalues and eigenvectors | Non-linear autonomous systems | critical point analysis | phase plane diagrams | constant coefficients | complex numbers | exponentials | eigenvalues | eigenvectorsLicense

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 metadataDescription

This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. To understand and treat any disease with a genetic basis or predisposition, scientists and clinicians need effective ways of manipulating the levels of genes and gene products. Conventional methods for the genetic modification of many experimental organisms are technically demanding and time consuming. Just over 5 years ago, a new mechanism of gene-silencing, termed RNA interference (RNAi), was discovered. In addition to being a fascinating biological process, RNAi provides a revolutionary technology that has a This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. To understand and treat any disease with a genetic basis or predisposition, scientists and clinicians need effective ways of manipulating the levels of genes and gene products. Conventional methods for the genetic modification of many experimental organisms are technically demanding and time consuming. Just over 5 years ago, a new mechanism of gene-silencing, termed RNA interference (RNAi), was discovered. In addition to being a fascinating biological process, RNAi provides a revolutionary technology that has aSubjects

RNA interference | RNA interference | RNAi | RNAi | RNA | RNA | genetic analysis | genetic analysis | gene therapy | gene therapy | gene products | gene products | gene silencing | gene silencing | gene expression | gene expression | human disease models | human disease models | mRNA | mRNA | genetic interference | genetic interference | short interfering RNA | short interfering RNA | siRNAs | siRNAs | expression vectors | expression vectors | RNA sequences | RNA sequences | nucleotide fragments | nucleotide fragments | microRNA | microRNA | mRNA degradation | mRNA degradation | transgenic mice | transgenic mice | lentivirus | lentivirus | knock-down animals | knock-down animals | tissue specificity | tissue specificityLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-7.xmlAttribution

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

See all metadata8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year. Topics include Einstein's postulates, the Lorentz transformation, relativistic effects and paradoxes, and applications involving electromagnetism and particle physics. This course also provides a brief introduction to some concepts of general relativity, including the principle of equivalence, the Schwartzschild metric and black holes, and the FRW metric and cosmology. This course, which concentrates on special relativity, is normally taken by physics majors in their sophomore year. Topics include Einstein's postulates, the Lorentz transformation, relativistic effects and paradoxes, and applications involving electromagnetism and particle physics. This course also provides a brief introduction to some concepts of general relativity, including the principle of equivalence, the Schwartzschild metric and black holes, and the FRW metric and cosmology.Subjects

relativity | relativity | special relativity | special relativity | Einstein's postulates | Einstein's postulates | simultaneity | simultaneity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects | relativistic effects | Minkowski diagrams | Minkowski diagrams | relativistic invariants | relativistic invariants | four-vectors | four-vectors | relativitistic particle collisions | relativitistic particle collisions | relativity and electricity | relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | general relativity | general relativity | Schwarzchild metric | Schwarzchild metric | gravitational | gravitational | red shift | red shift | light trajectories | light trajectories | geodesics | geodesics | Shapiro delay | Shapiro delayLicense

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

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

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

See all metadataDescription

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

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

See all metadata8.20 Introduction to Special Relativity (MIT) 8.20 Introduction to Special Relativity (MIT)

Description

This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.AcknowledgementsProf. Knuteson wishes to acknowledge that this course was originally designed and taught by Prof. Robert Jaffe. This course introduces the basic ideas and equations of Einstein's Special Theory of Relativity. If you have hoped to understand the physics of Lorentz contraction, time dilation, the "twin paradox", and E=mc2, you're in the right place.AcknowledgementsProf. Knuteson wishes to acknowledge that this course was originally designed and taught by Prof. Robert Jaffe.Subjects

Einstein's Special Theory of Relativity | Einstein's Special Theory of Relativity | Lorentz transformations | Lorentz transformations | length contraction | length contraction | time dilation | time dilation | four vectors | four vectors | Lorentz invariants | Lorentz invariants | relativistic energy and momentum | relativistic energy and momentum | relativistic kinematics | relativistic kinematics | Doppler shift | Doppler shift | space-time diagrams | space-time diagrams | relativity paradoxes | relativity paradoxes | 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

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

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

See all metadataMathematical Methods II Mathematical Methods II

Description

This course consists of a introduction to linear algebra. This course consists of a introduction to linear algebra.Subjects

Bachelor in Statistics and Business | Bachelor in Statistics and Business | Algebra | Algebra | Prerequisites | Prerequisites | Systems of linear equations | Systems of linear equations | Eigenvalues and eigenvectors | Eigenvalues and eigenvectors | General information | General information | Orthogonality and least-square problems | Orthogonality and least-square problems | Singular value decomposition | Singular value decomposition | ística y Empresa | ística y Empresa | Real vector spaces | Real vector spaces | Matrices and determinants | Matrices and determinants | Diagonalization | Diagonalization | 2012 | 2012License

Copyright 2015, UC3M http://creativecommons.org/licenses/by-nc-sa/4.0/Site sourced from

http://ocw.uc3m.es/ocwuniversia/rss_allAttribution

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

See all metadata18.318 Topics in Algebraic Combinatorics (MIT) 18.318 Topics in Algebraic Combinatorics (MIT)

Description

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings. The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.Subjects

algebraic combinatorics | algebraic combinatorics | matrix-tree theorem | matrix-tree theorem | linear algebra | linear algebra | commutative algebra | commutative algebra | exterior algebra | exterior algebra | counting faces of simplicial complexes | counting faces of simplicial complexes | tilings | tilings | Young's lattice | Young's lattice | Shannon capacity | Shannon capacity | Fisher inequality | Fisher inequality | Hadamard matrices | Hadamard matrices | f-vectors | f-vectors | Sperner Property | Sperner Property | -Binomial Coeffcients | -Binomial CoeffcientsLicense

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

http://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 class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site. The class will cover mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from 3.012 to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, fourier analysis and random walks.Technical RequirementsMathematica® software is required to run the .nb files found on this course site.Subjects

energetics | energetics | materials structure and symmetry: applied fields | materials structure and symmetry: applied fields | mechanics and physics of solids and soft materials | mechanics and physics of solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalues | eigenvalues | eigenvectors | eigenvectors | quadratic forms | quadratic forms | tensor operations | tensor operations | symmetry operations | symmetry operations | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walks | random walks | mathematical technicques | mathematical technicques | materials science | materials science | materials engineering | materials engineering | materials structure | materials structure | symmetry | symmetry | applied fields | applied fields | materials response | materials response | solids mechanics | solids mechanics | solids physics | solids physics | soft materials | soft materials | multi-variable calculus | multi-variable calculus | ordinary differential equations | ordinary differential equations | partial differential equations | partial differential equations | applied mathematics | applied mathematics | mathematical techniques | mathematical techniquesLicense

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

http://ocw.mit.edu/rss/all/mit-allarchivedcourses.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 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

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

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

See all metadata1.010 Uncertainty in Engineering (MIT) 1.010 Uncertainty in Engineering (MIT)

Description

This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes' theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life. This course gives an introduction to probability and statistics, with emphasis on engineering applications. Course topics include events and their probability, the total probability and Bayes' theorems, discrete and continuous random variables and vectors, uncertainty propagation and conditional analysis. Second-moment representation of uncertainty, random sampling, estimation of distribution parameters (method of moments, maximum likelihood, Bayesian estimation), and simple and multiple linear regression. Concepts illustrated with examples from various areas of engineering and everyday life.Subjects

fundamentals of probability | fundamentals of probability | random processes | random processes | 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 | Bayes theorem | Bayes theorem | total probability theorem | total probability theorem | 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 processesLicense

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

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

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

See all metadataDescription

This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems. This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.Subjects

fundamentals of probability | fundamentals of probability | random processes | random processes | 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 processesLicense

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

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

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

See all metadataDescription

Dr Arturo Reyes-Sandoval tells us about his research on a vaccine against Plasmodium vivax. Dr Reyes Sandoval aims to develop a novel malaria vaccine against Plasmodium vivax, one of the four malaria parasites that affect humans. P. vivax is found in Africa, Asia, Latin America and the Western Pacific. 40 percent of the world's population is exposed to the disease that is responsible for around 130 to 350 million clinical cases every year. Wales; http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Subjects

recombinant viral vectors | Plasmodium vivax | malaria vaccines | recombinant viral vectors | Plasmodium vivax | malaria vaccinesLicense

http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Site sourced from

http://mediapub.it.ox.ac.uk/feeds/129165/audio.xmlAttribution

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

See all metadata18.S997 Introduction To MATLAB Programming (MIT) 18.S997 Introduction To MATLAB Programming (MIT)

Description

Includes audio/video content: AV lectures. This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular. Includes audio/video content: AV lectures. This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.Subjects

MATLAB | programming | MATLAB | programming | variables | variables | plotting | plotting | scripts | scripts | functions | functions | flow control | flow control | statistics | statistics | data structures | data structures | images | images | vectors | vectors | matrices | matrices | root-finding | root-finding | Newton's Method | Newton's Method | Secant Method | Secant Method | Basins of Attraction | Basins of Attraction | Conway Game of Life | Conway Game of Life | Game of Life | Game of Life | vectorization | vectorization | debugging | debugging | scope | scope | function block | function blockLicense

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

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

See all metadataMAS.622J Pattern Recognition and Analysis (MIT) MAS.622J Pattern Recognition and Analysis (MIT)

Description

This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class. This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class.Subjects

MAS.622 | MAS.622 | 1.126 | 1.126 | pattern recognition | pattern recognition | feature detection | feature detection | classification | classification | probability theory | probability theory | pattern analysis | pattern analysis | conditional probability | conditional probability | bayes rule | bayes rule | random vectors | decision theory | random vectors | decision theory | ROC curves | ROC curves | likelihood ratio test | likelihood ratio test | fisher discriminant | fisher discriminant | template-based recognition | template-based recognition | feature extraction | feature extraction | eigenvector and multilinear analysis | eigenvector and multilinear analysis | linear discriminant | linear discriminant | perceptron learning | perceptron learning | optimization by gradient descent | optimization by gradient descent | support vecotr machines | support vecotr machines | K-nearest-neighbor classification | K-nearest-neighbor classification | parzen estimation | parzen estimation | unsupervised learning | unsupervised learning | clustering | clustering | vector quantization | vector quantization | K-means | K-means | Expectation-Maximization | Expectation-Maximization | Hidden markov models | Hidden markov models | viterbi algorithm | viterbi algorithm | Baum-Welch algorithm | Baum-Welch algorithm | linear dynamical systems | linear dynamical systems | Kalman filtering | Kalman filtering | Bayesian networks | Bayesian networks | decision trees | decision trees | reinforcement learning | reinforcement learning | genetic algorithms | genetic algorithmsLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-MAS.xmlAttribution

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

See all metadata1.010 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 processesLicense

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

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

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

See all metadata7.01SC Fundamentals of Biology (MIT) 7.01SC Fundamentals of Biology (MIT)

Description

Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and recombinant DNA. These principles are necessary to understanding the basic mechanisms of life and anchor the biological knowledge that is required to understand many of the challenges in everyday life, from human health and disease to loss of biodiversity and environmental quality. Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and recombinant DNA. These principles are necessary to understanding the basic mechanisms of life and anchor the biological knowledge that is required to understand many of the challenges in everyday life, from human health and disease to loss of biodiversity and environmental quality.Subjects

amino acids | amino acids | carboxyl group | carboxyl group | amino group | amino group | side chains | side chains | polar | polar | hydrophobic | hydrophobic | primary structure | primary structure | secondary structure | secondary structure | tertiary structure | tertiary structure | quaternary structure | quaternary structure | x-ray crystallography | x-ray crystallography | alpha helix | alpha helix | beta sheet | beta sheet | ionic bond | ionic bond | non-polar bond | non-polar bond | van der Waals interactions | van der Waals interactions | proton gradient | proton gradient | cyclic photophosphorylation | cyclic photophosphorylation | sunlight | sunlight | ATP | ATP | chlorophyll | chlorophyll | chlorophyll a | chlorophyll a | electrons | electrons | hydrogen sulfide | hydrogen sulfide | biosynthesis | biosynthesis | non-cyclic photophosphorylation | non-cyclic photophosphorylation | photosystem II | photosystem II | photosystem I | photosystem I | cyanobacteria | cyanobacteria | chloroplast | chloroplast | stroma | stroma | thylakoid membrane | thylakoid membrane | Genetics | Genetics | Mendel | Mendel | Mendel's Laws | Mendel's Laws | cloning | cloning | restriction enzymes | restriction enzymes | vector | vector | insert DNA | insert DNA | ligase | ligase | library | library | E.Coli | E.Coli | phosphatase | phosphatase | yeast | yeast | transformation | transformation | ARG1 gene | ARG1 gene | ARG1 mutant yeast | ARG1 mutant yeast | yeast wild-type | yeast wild-type | cloning by complementation | cloning by complementation | Human Beta Globin gene | Human Beta Globin gene | protein tetramer | protein tetramer | vectors | vectors | antibodies | antibodies | human promoter | human promoter | splicing | splicing | mRNA | mRNA | cDNA | cDNA | reverse transcriptase | reverse transcriptase | plasmid | plasmid | electrophoresis | electrophoresis | DNA sequencing | DNA sequencing | primer | primer | template | template | capillary tube | capillary tube | laser detector | laser detector | human genome project | human genome project | recombinant DNA | recombinant DNA | clone | clone | primer walking | primer walking | subcloning | subcloning | computer assembly | computer assembly | shotgun sequencing | shotgun sequencing | open reading frame | open reading frame | databases | databases | polymerase chain reaction (PCR) | polymerase chain reaction (PCR) | polymerase | polymerase | nucleotides | nucleotides | Thermus aquaticus | Thermus aquaticus | Taq polymerase | Taq polymerase | thermocycler | thermocycler | resequencing | resequencing | in vitro fertilization | in vitro fertilization | pre-implantation diagnostics | pre-implantation diagnostics | forensics | forensics | genetic engineering | genetic engineering | DNA sequences | DNA sequences | therapeutic proteins | therapeutic proteins | E. coli | E. coli | disease-causing mutations | disease-causing mutations | cleavage of DNA | cleavage of DNA | bacterial transformation | bacterial transformation | recombinant DNA revolution | recombinant DNA revolution | biotechnology industry | biotechnology industry | Robert Swanson | Robert Swanson | toxin gene | toxin gene | pathogenic bacterium | pathogenic bacterium | biomedical research | biomedical research | S. Pyogenes | S. Pyogenes | origin of replication | origin of replicationLicense

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

http://ocw.mit.edu/rss/all/mit-allcourses-7.xmlAttribution

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

See all metadataDescription

Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in freshman- and sophomore-level introductory mathematics courses. Complex Variables, Differential Equations, and Linear Algebra is the third course in the series, consisting of 20 Videos, 3 Study Guides, and a set of Supplementary Notes. Students should have mastered the first two courses in the series (Single Variable Calculus and Multivariable Calculus) before taking this course. The series was first released in 1972, but equally valuable today for students who are learning these topics for the first time.Subjects

Complex Variables | Complex Variables | Differential Equations | Differential Equations | Linear Algebra | Linear Algebra | Complex Numbers | Complex Numbers | Conformal Mappings | Conformal Mappings | Sequences and Series | Sequences and Series | Linear Differential Equations | Linear Differential Equations | Undetermined Coefficients | Undetermined Coefficients | Power Series | Power Series | Laplace Transforms | Laplace Transforms | Vector Spaces | Vector Spaces | Spanning Vectors | Spanning Vectors | Constructing Bases | Constructing Bases | Linear Transformations | Linear Transformations | Determinant | Determinant | Eigenvectors | Eigenvectors | Dot Products | Dot Products | Orthogonal Functions | Orthogonal FunctionsLicense

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

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

See all metadataDescription

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.Subjects

Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | relativistic effects and paradoxes | Minkowski diagrams | invariants and four-vectors | momentum | energy and mass | particle collisions | Relativity and electricity | Coulomb's law | magnetic fields | Newtonian cosmology | General Relativity | principle of equivalence | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle trajectories | light trajectories | invariants | four-vectors | momentum | energy | mass | relativistic effects | paradoxes | electricity | time dilation | length contraction | clock synchronization | Schwarzchild metric | geodesics | Shaprio delay | relativistic kinematics | relativistic dynamics | electromagnetism | hubble expansion | universe | equivalence principle | curved space time | Ether Theory | constants | speed of light | c | graph | pythagorem theorem | triangle | arrowsLicense

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 metadata18.03SC Differential Equations (MIT) 18.03SC Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

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

See all metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Includes audio/video content: AV lectures. Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time.Subjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

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

See all metadataDescription

Includes audio/video content: AV lectures. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos w Includes audio/video content: AV lectures. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos wSubjects

differential equations | differential equations | ODE | MATLAB | ODE | MATLAB | first order equations | first order equations | second order equations | second order equations | matrices | matrices | Laplace transform | Laplace transform | linear algebra | linear algebra | eigenvalues | eigenvalues | eigenvectors | eigenvectors | Fourier series | Fourier series | Runge-Kutta | Runge-Kutta | Tumbling box | Tumbling box | predator-prey equations | predator-prey equations | Lorenz Attractor | Lorenz AttractorLicense

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

http://ocw.mit.edu/rss/all/mit-allavcourses.xmlAttribution

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

See all metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods Matrix systems | Laplace transform methods Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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

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

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

See all metadata8.20 Introduction to Special Relativity (MIT) 8.20 Introduction to Special Relativity (MIT)

Description

Introduces the basic ideas and equations of Einstein's Special Theory of Relativity. Topics include: Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of General Relativity. Introduces the basic ideas and equations of Einstein's Special Theory of Relativity. Topics include: Lorentz transformations, length contraction and time dilation, four vectors, Lorentz invariants, relativistic energy and momentum, relativistic kinematics, Doppler shift, space-time diagrams, relativity paradoxes, and some concepts of General Relativity.Subjects

Einstein's Special Theory of Relativity | Einstein's Special Theory of Relativity | Lorentz transformations | Lorentz transformations | length contraction | length contraction | ime dilation | ime dilation | time dilation | time dilation | four vectors | four vectors | Lorentz invariants | Lorentz invariants | relativistic energy and momentum | relativistic energy and momentum | relativistic kinematics | relativistic kinematics | Doppler shift | Doppler shift | space-time diagrams | space-time diagrams | relativity paradoxes | relativity paradoxes | 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

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

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

See all metadata