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6.161 Modern Optics Project Laboratory (MIT) 6.161 Modern Optics Project Laboratory (MIT)

Description

6.161 explores modern optics through lectures, laboratory exercises, and projects. Topics covered include: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, imaging and transforming properties of lenses, spatial filtering, coherent optical processors, holography, optical properties of materials, lasers, nonlinear optics, electro-optic and acousto-optic materials and devices, optical detectors, fiber optics, and optical communication. This course is worth 12 Engineering Design Points. 6.161 explores modern optics through lectures, laboratory exercises, and projects. Topics covered include: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, imaging and transforming properties of lenses, spatial filtering, coherent optical processors, holography, optical properties of materials, lasers, nonlinear optics, electro-optic and acousto-optic materials and devices, optical detectors, fiber optics, and optical communication. This course is worth 12 Engineering Design Points.Subjects

modern optics lab | modern optics lab | modern optics | modern optics | laboratory | laboratory | polarization | polarization | light | light | reflection | reflection | refraction | refraction | coherence | coherence | interference | interference | Fraunhofer diffraction | Fraunhofer diffraction | Fresnel diffraction | Fresnel diffraction | imaging | imaging | transforming | transforming | lenses | lenses | spatial filtering | spatial filtering | coherent optical processors | coherent optical processors | holography | holography | optical properties of materials | optical properties of materials | lasers | lasers | nonlinear optics | nonlinear optics | electro-optic | electro-optic | acousto-optic | acousto-optic | optical detectors | optical detectors | fiber optics | fiber optics | optical communication | optical communicationLicense

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See all metadata6.161 Modern Optics Project Laboratory (MIT) 6.161 Modern Optics Project Laboratory (MIT)

Description

6.161 offers an introduction to laboratory optics, optical principles, and optical devices and systems. This course covers a wide range of topics, including: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, holography, imaging and transforming properties of lenses, spatial filtering, two-lens coherent optical processor, optical properties of materials, lasers, electro-optic, acousto-optic and liquid-crystal light modulators, optical detectors, optical waveguides and fiber-optic communication systems. Students engage in extensive oral and written communication exercises. There are 12 engineering design points associated with this subject. 6.161 offers an introduction to laboratory optics, optical principles, and optical devices and systems. This course covers a wide range of topics, including: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, holography, imaging and transforming properties of lenses, spatial filtering, two-lens coherent optical processor, optical properties of materials, lasers, electro-optic, acousto-optic and liquid-crystal light modulators, optical detectors, optical waveguides and fiber-optic communication systems. Students engage in extensive oral and written communication exercises. There are 12 engineering design points associated with this subject.Subjects

modern optics lab | modern optics lab | modern optics | modern optics | laboratory | laboratory | polarization | polarization | light | light | reflection | reflection | refraction | refraction | coherence | coherence | interference | interference | Fraunhofer diffraction | Fraunhofer diffraction | Fresnel diffraction | Fresnel diffraction | imaging | imaging | transforming | transforming | lenses | lenses | spatial filtering | spatial filtering | coherent optical processors | coherent optical processors | holography | holography | optical properties of materials | optical properties of materials | lasers | lasers | nonlinear optics | nonlinear optics | electro-optic | electro-optic | acousto-optic | acousto-optic | optical detectors | optical detectors | fiber optics | fiber optics | optical communication | optical communicationLicense

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 metadata6.632 Electromagnetic Wave Theory (MIT) 6.632 Electromagnetic Wave Theory (MIT)

Description

6.632 is a graduate subject on electromagnetic wave theory, emphasizing mathematical approaches, problem solving, and physical interpretation. Topics covered include: waves in media, equivalence principle, duality and complementarity, Huygens' principle, Fresnel and Fraunhofer diffraction, dyadic Green's functions, Lorentz transformation, and Maxwell-Minkowski theory. Examples deal with limiting cases of Maxwell's theory and diffraction and scattering of electromagnetic waves. 6.632 is a graduate subject on electromagnetic wave theory, emphasizing mathematical approaches, problem solving, and physical interpretation. Topics covered include: waves in media, equivalence principle, duality and complementarity, Huygens' principle, Fresnel and Fraunhofer diffraction, dyadic Green's functions, Lorentz transformation, and Maxwell-Minkowski theory. Examples deal with limiting cases of Maxwell's theory and diffraction and scattering of electromagnetic waves.Subjects

electromagnetic wave theory | electromagnetic wave theory | waves in media | waves in media | equivalence principle | equivalence principle | duality | duality | complementarity | complementarity | Huygens' principle | Huygens' principle | Fresnel diffraction | Fresnel diffraction | Fraunhofer diffraction | Fraunhofer diffraction | dyadic Green's functions | dyadic Green's functions | Lorentz transformation | Lorentz transformation | Maxwell-Minkowski theory | Maxwell-Minkowski theory | Maxwell | Maxwell | diffraction | diffraction | scattering | scatteringLicense

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 metadata8.03 Physics III (MIT) 8.03 Physics III (MIT)

Description

Mechanical vibrations and waves, simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations and normal modes, vibrations of continuous systems, reflection and refraction, phase and group velocity. Optics, wave solutions to Maxwell's equations, polarization, Snell's law, interference, Huygens's principle, Fraunhofer diffraction, and gratings. Mechanical vibrations and waves, simple harmonic motion, superposition, forced vibrations and resonance, coupled oscillations and normal modes, vibrations of continuous systems, reflection and refraction, phase and group velocity. Optics, wave solutions to Maxwell's equations, polarization, Snell's law, interference, Huygens's principle, Fraunhofer diffraction, and gratings.Subjects

Mechanical vibrations and waves | Mechanical vibrations and waves | simple harmonic motion | simple harmonic motion | superposition | superposition | forced vibrations and resonance | forced vibrations and resonance | coupled oscillations and normal modes | coupled oscillations and normal modes | vibrations of continuous systems | vibrations of continuous systems | reflection and refraction | reflection and refraction | phase and group velocity | phase and group velocity | wave solutions to Maxwell's equations | wave solutions to Maxwell's equations | polarization | polarization | Snell's Law | Snell's Law | interference | interference | Huygens's principle | Huygens's principle | Fraunhofer diffraction | Fraunhofer diffraction | gratings | gratingsLicense

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 metadata12.744 Marine Isotope Chemistry (MIT) 12.744 Marine Isotope Chemistry (MIT)

Description

The objective of this course is to develop an understanding of principles of marine isotope geochemistry, its systematics, and its application to the study of the behavior and history of the oceans within the earth system. The emphasis is on developing the underlying concepts and theory as well as proficiency in working with practical isotope systems. The course is divided into four sections: nuclear systematics, Earth formation and evolution, stable isotopes, and applications to the ocean system. The objective of this course is to develop an understanding of principles of marine isotope geochemistry, its systematics, and its application to the study of the behavior and history of the oceans within the earth system. The emphasis is on developing the underlying concepts and theory as well as proficiency in working with practical isotope systems. The course is divided into four sections: nuclear systematics, Earth formation and evolution, stable isotopes, and applications to the ocean system.Subjects

oceanography | oceanography | chemical oceanography | chemical oceanography | isotope geochemistry | isotope geochemistry | geochemistry | geochemistry | marine science | marine science | isotopes | isotopes | radiocarbon | radiocarbon | radioactive decay | radioactive decay | radiometric dating | radiometric dating | mass spectrometry | mass spectrometry | isotope fractionation | isotope fractionation | fractionation | fractionation | water column | water column | whoi | whoi | woods hole | woods hole | earth science | earth science | atmosphere | atmosphere | ocean | oceanLicense

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See all metadata6.161 Modern Optics Project Laboratory (MIT)

Description

6.161 offers an introduction to laboratory optics, optical principles, and optical devices and systems. This course covers a wide range of topics, including: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, holography, imaging and transforming properties of lenses, spatial filtering, two-lens coherent optical processor, optical properties of materials, lasers, electro-optic, acousto-optic and liquid-crystal light modulators, optical detectors, optical waveguides and fiber-optic communication systems. Students engage in extensive oral and written communication exercises. There are 12 engineering design points associated with this subject.Subjects

modern optics lab | modern optics | laboratory | polarization | light | reflection | refraction | coherence | interference | Fraunhofer diffraction | Fresnel diffraction | imaging | transforming | lenses | spatial filtering | coherent optical processors | holography | optical properties of materials | lasers | nonlinear optics | electro-optic | acousto-optic | optical detectors | fiber optics | optical communicationLicense

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 metadata6.632 Electromagnetic Wave Theory (MIT)

Description

6.632 is a graduate subject on electromagnetic wave theory, emphasizing mathematical approaches, problem solving, and physical interpretation. Topics covered include: waves in media, equivalence principle, duality and complementarity, Huygens' principle, Fresnel and Fraunhofer diffraction, dyadic Green's functions, Lorentz transformation, and Maxwell-Minkowski theory. Examples deal with limiting cases of Maxwell's theory and diffraction and scattering of electromagnetic waves.Subjects

electromagnetic wave theory | waves in media | equivalence principle | duality | complementarity | Huygens' principle | Fresnel diffraction | Fraunhofer diffraction | dyadic Green's functions | Lorentz transformation | Maxwell-Minkowski theory | Maxwell | diffraction | scatteringLicense

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 metadata6.632 Electromagnetic Wave Theory (MIT)

Description

6.632 is a graduate subject on electromagnetic wave theory, emphasizing mathematical approaches, problem solving, and physical interpretation. Topics covered include: waves in media, equivalence principle, duality and complementarity, Huygens' principle, Fresnel and Fraunhofer diffraction, dyadic Green's functions, Lorentz transformation, and Maxwell-Minkowski theory. Examples deal with limiting cases of Maxwell's theory and diffraction and scattering of electromagnetic waves.Subjects

electromagnetic wave theory | waves in media | equivalence principle | duality | complementarity | Huygens' principle | Fresnel diffraction | Fraunhofer diffraction | dyadic Green's functions | Lorentz transformation | Maxwell-Minkowski theory | Maxwell | diffraction | scatteringLicense

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 metadata6.161 Modern Optics Project Laboratory (MIT)

Description

6.161 explores modern optics through lectures, laboratory exercises, and projects. Topics covered include: polarization properties of light, reflection and refraction, coherence and interference, Fraunhofer and Fresnel diffraction, imaging and transforming properties of lenses, spatial filtering, coherent optical processors, holography, optical properties of materials, lasers, nonlinear optics, electro-optic and acousto-optic materials and devices, optical detectors, fiber optics, and optical communication. This course is worth 12 Engineering Design Points.Subjects

modern optics lab | modern optics | laboratory | polarization | light | reflection | refraction | coherence | interference | Fraunhofer diffraction | Fresnel diffraction | imaging | transforming | lenses | spatial filtering | coherent optical processors | holography | optical properties of materials | lasers | nonlinear optics | electro-optic | acousto-optic | optical detectors | fiber optics | optical communicationLicense

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 metadataDescription

This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers. This course covers algebraic approaches to electromagnetism and nano-photonics. Topics include photonic crystals, waveguides, perturbation theory, diffraction, computational methods, applications to integrated optical devices, and fiber-optic systems. Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.Subjects

linear algebra | linear algebra | eigensystems for Maxwell's equations | eigensystems for Maxwell's equations | symmetry groups | symmetry groups | representation theory | representation theory | Bloch's theorem | Bloch's theorem | numerical eigensolver methods | numerical eigensolver methods | time and frequency-domain computation | time and frequency-domain computation | perturbation theory | perturbation theory | coupled-mode theories | coupled-mode theories | waveguide theory | waveguide theory | adiabatic transitions | adiabatic transitions | Optical phenomena | Optical phenomena | photonic crystals | photonic crystals | band gaps | band gaps | anomalous diffraction | anomalous diffraction | mechanisms for optical confinement | mechanisms for optical confinement | optical fibers | optical fibers | integrated optical devices | integrated optical devicesLicense

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 metadata8.04 Quantum Physics I (MIT) 8.04 Quantum Physics I (MIT)

Description

Includes audio/video content: AV lectures. This course covers the experimental basis of quantum physics. It introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.It is the first course in the undergraduate Quantum Physics sequence, followed by 8.05 Quantum Physics II and 8.06 Quantum Physics III. Includes audio/video content: AV lectures. This course covers the experimental basis of quantum physics. It introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.It is the first course in the undergraduate Quantum Physics sequence, followed by 8.05 Quantum Physics II and 8.06 Quantum Physics III.Subjects

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

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

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See all metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail. The course covers group theory and its representations, and focuses on the Sylow theorem, Schur's lemma, and proof of the orthogonality relations. It also analyzes the rings, the factorization processes, and the fields. Topics such as the formal construction of integers and polynomials, homomorphisms and ideals, the Gauss' lemma, quadratic imaginary integers, Gauss primes, and finite and function fields are discussed in detail.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

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 metadata2.717J Optical Engineering (MIT) 2.717J Optical Engineering (MIT)

Description

This course concerns the theory and practice of optical methods in engineering and system design, with an emphasis on diffraction, statistical optics, holography, and imaging. It provides the engineering methodology skills necessary to incorporate optical components in systems serving diverse areas such as precision engineering and metrology, bio-imaging, and computing (sensors, data storage, communication in multi-processor systems). Experimental demonstrations and a design project are included. This course concerns the theory and practice of optical methods in engineering and system design, with an emphasis on diffraction, statistical optics, holography, and imaging. It provides the engineering methodology skills necessary to incorporate optical components in systems serving diverse areas such as precision engineering and metrology, bio-imaging, and computing (sensors, data storage, communication in multi-processor systems). Experimental demonstrations and a design project are included.Subjects

optical methods in engineering and system design | optical methods in engineering and system design | diffraction | statistical optics | holography | and imaging | diffraction | statistical optics | holography | and imaging | Statistical Optics | Inverse Problems (i.e. theory of imaging) | Statistical Optics | Inverse Problems (i.e. theory of imaging) | applications in precision engineering and metrology | bio-imaging | and computing (sensors | data storage | communication in multi-processor systems) | applications in precision engineering and metrology | bio-imaging | and computing (sensors | data storage | communication in multi-processor systems) | Fourier optics | Fourier optics | probability | probability | stochastic processes | stochastic processes | light statistics | light statistics | theory of light coherence | theory of light coherence | van Cittert-Zernicke Theorem | van Cittert-Zernicke Theorem | statistical optics applications | statistical optics applications | inverse problems | inverse problems | information-theoretic views | information-theoretic views | information theory | information theory | 2.717 | 2.717 | MAS.857 | MAS.857License

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 metadata12.108 Structure of Earth Materials (MIT) 12.108 Structure of Earth Materials (MIT)

Description

This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets. This course provides a comprehensive introduction to crystalline structure, crystal chemistry, and bonding in rock-forming minerals. It introduces the theory relating crystal structure and crystal symmetry to physical properties such as refractive index, elastic modulus, and seismic velocity. It surveys the distribution of silicate, oxide, and metallic minerals in the interiors and on the surfaces of planets, and discusses the processes that led to their formation. It also addresses why diamonds are hard and why micas split into thin sheets.Subjects

Crystal Symmetry | Crystal Symmetry | Point Groups | Point Groups | Space Groups | Space Groups | Crystal Chemistry | Crystal Chemistry | Bonding | Bonding | Electron Diffraction | Electron Diffraction | Crystal lattices | Crystal lattices | Tensor Analysis | Tensor Analysis | Optical Properties | Optical Properties | Elastic Properties | Elastic Properties | Magnetic Properties | Magnetic Properties | Stress | Stress | Strain | StrainLicense

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See all metadataDeli celote - ulomki (imenovalci 2 do 6) Fractional parts of the number (denominator 2-6)

Description

Vaje za utrjevanje. Imenovalci od 2 do 6, cela števila do 100, z ostankom. Exercises to drill calculating fractional parts of the number (denominators 2-6).Subjects

znanstvene vede | sciences | matematika | mathematics | celo število | whole number | ulomek | fraction | del celote | fractional partLicense

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Priprava na pisno ocenjevanje znanja iz ulomkov Collection of different exercises that include fractions.Subjects

znanstvene vede | sciences | matematika | mathematics | ulomek | fraction | krajšanje | reducing fraction | računanje | calculatingLicense

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See all metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

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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Imenovalci od 2 do 10, cela števila do 1000, brez ostanka Exercises to drill calculating fractional parts of the number (denominators 2-10).Subjects

znanstvene vede | sciences | matematika | mathematics | ulomek | fraction | celo število | whole number | del celote | fractional partLicense

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See all metadata18.781 Theory of Numbers (MIT) 18.781 Theory of Numbers (MIT)

Description

This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions. This course is an elementary introduction to number theory with no algebraic prerequisites. Topics covered include primes, congruences, quadratic reciprocity, diophantine equations, irrational numbers, continued fractions, and partitions.Subjects

primes | primes | divisibility | divisibility | fundamental theorem of arithmetic | fundamental theorem of arithmetic | gcd | gcd | Euclidean algorithm | Euclidean algorithm | congruences | congruences | Chinese remainder theorem | Chinese remainder theorem | Hensel's lemma | Hensel's lemma | primitive roots | primitive roots | quadratic residues | quadratic residues | reciprocity | reciprocity | arithmetic functions | arithmetic functions | Diophantine equations | Diophantine equations | continued fractions | continued fractionsLicense

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 metadata22.105 Electromagnetic Interactions (MIT) 22.105 Electromagnetic Interactions (MIT)

Description

This course is a graduate level subject on electromagnetic theory with particular emphasis on basics and applications to Nuclear Science and Engineering. The basic topics covered include electrostatics, magnetostatics, and electromagnetic radiation. The applications include transmission lines, waveguides, antennas, scattering, shielding, charged particle collisions, Bremsstrahlung radiation, and Cerenkov radiation. Acknowledgments Professor Freidberg would like to acknowledge the immense contributions made to this course by its previous instructors, Ian Hutchinson and Ron Parker. This course is a graduate level subject on electromagnetic theory with particular emphasis on basics and applications to Nuclear Science and Engineering. The basic topics covered include electrostatics, magnetostatics, and electromagnetic radiation. The applications include transmission lines, waveguides, antennas, scattering, shielding, charged particle collisions, Bremsstrahlung radiation, and Cerenkov radiation. Acknowledgments Professor Freidberg would like to acknowledge the immense contributions made to this course by its previous instructors, Ian Hutchinson and Ron Parker.Subjects

electrostatics | electrostatics | coulomb's law | coulomb's law | gauss's law | gauss's law | potentials | potentials | laplace equations | laplace equations | poisson equations | poisson equations | capacitors | capacitors | resistors | resistors | child-langmuir law | child-langmuir law | magnetostatics | magnetostatics | ampere's law | ampere's law | biot-savart law | biot-savart law | magnets | magnets | inductors | inductors | superconducting magnets | superconducting magnets | single particle motion | single particle motion | lorentz force | lorentz force | quasi-statics | quasi-statics | faraday's law | faraday's law | maxwell equations | maxwell equations | plane waves | plane waves | reflection | reflection | refraction | refraction | klystrons | klystrons | gyrotrons | gyrotrons | lienard-wiechert potentials | lienard-wiechert potentials | thomson scattering | thomson scattering | compton scattering | compton scattering | synchrotron radiation | synchrotron radiation | bremsstrahlung radiation | bremsstrahlung radiation | cerenkov radiation | cerenkov radiationLicense

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

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See all metadata18.702 Algebra II (MIT) 18.702 Algebra II (MIT)

Description

This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory. This undergraduate level course follows Algebra I. Topics include group representations, rings, ideals, fields, polynomial rings, modules, factorization, integers in quadratic number fields, field extensions, and Galois theory.Subjects

Sylow theorems | Sylow theorems | Group Representations | Group Representations | definitions | definitions | unitary representations | unitary representations | characters | characters | Schur's Lemma | Schur's Lemma | Rings: Basic Definitions | Rings: Basic Definitions | homomorphisms | homomorphisms | fractions | fractions | Factorization | Factorization | unique factorization | unique factorization | Gauss' Lemma | Gauss' Lemma | explicit factorization | explicit factorization | maximal ideals | maximal ideals | Quadratic Imaginary Integers | Quadratic Imaginary Integers | Gauss Primes | Gauss Primes | quadratic integers | quadratic integers | ideal factorization | ideal factorization | ideal classes | ideal classes | Linear Algebra over a Ring | Linear Algebra over a Ring | free modules | free modules | integer matrices | integer matrices | generators and relations | generators and relations | structure of abelian groups | structure of abelian groups | Rings: Abstract Constructions | Rings: Abstract Constructions | relations in a ring | relations in a ring | adjoining elements | adjoining elements | Fields: Field Extensions | Fields: Field Extensions | algebraic elements | algebraic elements | degree of field extension | degree of field extension | ruler and compass | ruler and compass | symbolic adjunction | symbolic adjunction | finite fields | finite fields | Fields: Galois Theory | Fields: Galois Theory | the main theorem | the main theorem | cubic equations | cubic equations | symmetric functions | symmetric functions | primitive elements | primitive elements | quartic equations | quartic equations | quintic equations | quintic equationsLicense

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 metadata22.55J Principles of Radiation Interactions (MIT) 22.55J Principles of Radiation Interactions (MIT)

Description

The central theme of this course is the interaction of radiation with biological material. The course is intended to provide a broad understanding of how different types of radiation deposit energy, including the creation and behavior of secondary radiations; of how radiation affects cells and why the different types of radiation have very different biological effects. Topics will include: the effects of radiation on biological systems including DNA damage; in vitro cell survival models; and in vivo mammalian systems. The course covers radiation therapy, radiation syndromes in humans and carcinogenesis. Environmental radiation sources on earth and in space, and aspects of radiation protection are also discussed. Examples from the current literature will be used to supplement lecture materi The central theme of this course is the interaction of radiation with biological material. The course is intended to provide a broad understanding of how different types of radiation deposit energy, including the creation and behavior of secondary radiations; of how radiation affects cells and why the different types of radiation have very different biological effects. Topics will include: the effects of radiation on biological systems including DNA damage; in vitro cell survival models; and in vivo mammalian systems. The course covers radiation therapy, radiation syndromes in humans and carcinogenesis. Environmental radiation sources on earth and in space, and aspects of radiation protection are also discussed. Examples from the current literature will be used to supplement lecture materiSubjects

Interaction of radiation with biological material | Interaction of radiation with biological material | how different types of radiation deposit energy | how different types of radiation deposit energy | secondary radiations | secondary radiations | how radiation affects cells | how radiation affects cells | biological effects | biological effects | effects of radiation on biological systems | effects of radiation on biological systems | DNA damage | DNA damage | in vitro cell survival models | in vitro cell survival models | in vivo mammalian systems | in vivo mammalian systems | radiation therapy | radiation therapy | radiation syndromes in humans | radiation syndromes in humans | carcinogenesis | carcinogenesis | Environmental radiation sources | Environmental radiation sources | radiation protection | radiation protection | cells | cells | tissues | tissues | radiation interactions | radiation interactions | radiation chemistry | radiation chemistry | LET | LET | tracks | tracks | chromosome damags | chromosome damags | in vivo | in vivo | in vitro | in vitro | cell survival curves | cell survival curves | dose response | dose response | RBE | RBE | clustered damage | clustered damage | radiation response | radiation response | tumor kinetics | tumor kinetics | tumor radiobiology | tumor radiobiology | fractionation | fractionation | protons | protons | alpha particles | alpha particles | whole body exposure | whole body exposure | chronic exposure | chronic exposure | space | space | microbeams | microbeams | radon | radon | background radiation | background radiation | 22.55 | 22.55 | HST.560 | HST.560License

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 metadata22.105 Electromagnetic Interactions (MIT) 22.105 Electromagnetic Interactions (MIT)

Description

This course is a graduate level subject on electromagnetic theory with particular emphasis on basics and applications to Nuclear Science and Engineering. The basic topics covered include electrostatics, magnetostatics, and electromagnetic radiation. The applications include transmission lines, waveguides, antennas, scattering, shielding, charged particle collisions, Bremsstrahlung radiation, and Cerenkov radiation. Acknowledgments Professor Freidberg would like to acknowledge the immense contributions made to this course by its previous instructors, Ian Hutchinson and Ron Parker. This course is a graduate level subject on electromagnetic theory with particular emphasis on basics and applications to Nuclear Science and Engineering. The basic topics covered include electrostatics, magnetostatics, and electromagnetic radiation. The applications include transmission lines, waveguides, antennas, scattering, shielding, charged particle collisions, Bremsstrahlung radiation, and Cerenkov radiation. Acknowledgments Professor Freidberg would like to acknowledge the immense contributions made to this course by its previous instructors, Ian Hutchinson and Ron Parker.Subjects

electrostatics | electrostatics | coulomb's law | coulomb's law | gauss's law | gauss's law | potentials | potentials | laplace equations | laplace equations | poisson equations | poisson equations | capacitors | capacitors | resistors | resistors | child-langmuir law | child-langmuir law | magnetostatics | magnetostatics | ampere's law | ampere's law | biot-savart law | biot-savart law | magnets | magnets | inductors | inductors | superconducting magnets | superconducting magnets | single particle motion | single particle motion | lorentz force | lorentz force | quasi-statics | quasi-statics | faraday's law | faraday's law | maxwell equations | maxwell equations | plane waves | plane waves | reflection | reflection | refraction | refraction | klystrons | klystrons | gyrotrons | gyrotrons | lienard-wiechert potentials | lienard-wiechert potentials | thomson scattering | thomson scattering | compton scattering | compton scattering | synchrotron radiation | synchrotron radiation | bremsstrahlung radiation | bremsstrahlung radiation | cerenkov radiation | cerenkov radiationLicense

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 metadata3.014 Materials Laboratory (MIT) 3.014 Materials Laboratory (MIT)

Description

This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degre This course is a required sophomore subject in the Department of Materials Science and Engineering, designed to be taken in conjunction with the core lecture subject 3.012 Fundamentals of Materials Science and Engineering. The laboratory subject combines experiments illustrating the principles of quantum mechanics, thermodynamics and structure with intensive oral and written technical communication practice. Specific topics include: experimental exploration of the connections between energetics, bonding and structure of materials, and application of these principles in instruments for materials characterization; demonstration of the wave-like nature of electrons; hands-on experience with techniques to quantify energy (DSC), bonding (XPS, AES, FTIR, UV/Vis and force spectroscopy), and degreSubjects

electron | electron | electronic properties | electronic properties | magnetism | magnetism | magentic properties | magentic properties | structure | structure | crystal | crystal | lattice | lattice | energy | energy | thermodynamics | thermodynamics | differential scanning calorimetry (DSC) | differential scanning calorimetry (DSC) | x-ray diffraction (XRD) | x-ray diffraction (XRD) | scanning probe microscopy (AFM | scanning probe microscopy (AFM | STM) | STM) | scanning electron microscopy (SEM) | scanning electron microscopy (SEM) | UV/Vis | UV/Vis | Raman spectroscopy | Raman spectroscopy | FTIR spectroscopy | FTIR spectroscopy | x-ray photoelectron spectroscopy (XPS) | x-ray photoelectron spectroscopy (XPS) | vibrating sample magnetometry (VSM) | vibrating sample magnetometry (VSM) | dynamic light scattering (DLS) | dynamic light scattering (DLS) | phonon | phonon | quantum | quantum | quantum mechanics | quantum mechanics | radiation | radiation | battery | battery | fuel cell | fuel cell | ferromagnetism | ferromagnetism | ferromagnetic | ferromagnetic | polymer | polymer | glass | glass | corrosion | corrosionLicense

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 metadata8.231 Physics of Solids I (MIT) 8.231 Physics of Solids I (MIT)

Description

The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetism The topics covered in this course include:Periodic Structure and Symmetry of CrystalsDiffraction, Reciprocal LatticeChemical BondingLattice DynamicsPhononsThermal PropertiesFree Electron GasModel of MetalsBloch Theorem and Band StructureNearly Free Electron ApproximationTight Binding MethodFermi SurfaceSemiconductorsElectronsHolesImpuritiesOptical PropertiesExcitons andMagnetismSubjects

periodic structure and symmetry of crystals | periodic structure and symmetry of crystals | diffraction | diffraction | reciprocal lattice | reciprocal lattice | chemical bonding | chemical bonding | phonons | phonons | thermal properties | thermal properties | free electron gas | free electron gas | model of metals | model of metals | Bloch theorem and band structure | Bloch theorem and band structure | nearly free electron approximation | nearly free electron approximation | tight binding method | tight binding method | Fermi surface | Fermi surface | semiconductors | semiconductors | electrons | electrons | holes | holes | impurities | impurities | optical properties | optical properties | excitons | excitons | magnetism | magnetismLicense

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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