Description

Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. MIT students may choose to take one of the two versions of 18.100. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity; it places more emphasis on point-set topology and n-space, whereas Option A is concerned primarily with the real line. Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. MIT students may choose to take one of the two versions of 18.100. Option A chooses less abstract definitions and proofs, and gives applications where possible. Option B is more demanding and for students with more mathematical maturity; it places more emphasis on point-set topology and n-space, whereas Option A is concerned primarily with the real line.

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Reimann integral | Reimann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space | sequences of functions | sequences of functions | series of functions | series of functions | applications | applications | real variable | real variable | metric space | metric space | sets | sets | theorems | theorems | differentiate | differentiate | differentiable | differentiable | converge | converge | uniform | uniform | 18.100 | 18.100

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The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear. The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.

Subjects

compressible fluid dynamics | compressible fluid dynamics | fluid dynamics | fluid dynamics | external flows | external flows | internal flows | internal flows | quasi-on-dimensional | quasi-on-dimensional | quasi-1D | quasi-1D | channel flow | channel flow | multi-dimensional flows | multi-dimensional flows | nozzles | nozzles | diffusers | diffusers | inlets | inlets | loss generation | loss generation | interactions | interactions | aerodynamic shapes | aerodynamic shapes | subsonic | subsonic | supersonic | supersonic | transonic | transonic | hypersonic | hypersonic | shock waves | shock waves | vortices | vortices | disturbance behavior | disturbance behavior | unsteady | unsteady | speed of sound | speed of sound | isentropic flows | isentropic flows | non-isentropic flows | non-isentropic flows | potential flows | potential flows | rotational flows | rotational flows | shaft work | shaft work | heat addition | heat addition | mass addition | mass addition | flow states | flow states | flow regime | flow regime | velocity non-uniformities | velocity non-uniformities | density non-uniformities | density non-uniformities | fluid system components | fluid system components | lift | lift | drag | drag | continuum flow | continuum flow | shock strength | shock strength | characteristics | characteristics | governing equations | governing equations | thermodynamic context | thermodynamic context | characteristic parameters | characteristic parameters | quasi-one-dimensional flow | quasi-one-dimensional flow | disturbances | disturbances | unsteady flow | unsteady flow | gas dynamic discontinuities | gas dynamic discontinuities | detonations | detonations | linear two-dimensional flows | linear two-dimensional flows | non-linear two-dimensional flows | non-linear two-dimensional flows

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

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newyorkcity | newyorkcity | ireland | ireland | dublin | dublin | usa | usa | uniforms | uniforms | glasnevin | glasnevin | leinster | leinster | codublin | codublin | bmh | bmh | bookkeeper | bookkeeper | brassbuttons | brassbuttons | 1916rising | 1916rising | nationallibraryofireland | nationallibraryofireland | magazinefort | magazinefort | conynghamroad | conynghamroad | seanheuston | seanheuston | thefianna | thefianna | fiannaeireann | fiannaeireann | irishvolunteers | irishvolunteers | pipersband | pipersband | liammellows | liammellows | concolbert | concolbert | brendankeogh | brendankeogh | fiannaéireann | fiannaéireann | michaellonergan | michaellonergan | findlaterplace | findlaterplace | keoghbrothers | keoghbrothers | keoghcollection | keoghcollection | spring1914 | spring1914 | patrickholohan | patrickholohan | garryholohan | garryholohan | padraigryan | padraigryan | lonergan’s | lonergan’s | fiannaeireannhistory | fiannaeireannhistory | houlihanbrothers | houlihanbrothers | padriagoriain | padriagoriain | newfiannauniform | newfiannauniform | clery’sdepartmentstore | clery’sdepartmentstore | garryholohans | garryholohans | jerseysandkilts | jerseysandkilts | pádraigóriain | pádraigóriain | liamo’maoiliosa | liamo’maoiliosa | kennedysofparnellstreet | kennedysofparnellstreet | ringsendpowerplant | ringsendpowerplant | gearoiduahuallachain | gearoiduahuallachain | dublinportanddocksboardpowerstation | dublinportanddocksboardpowerstation | fourcourtscommand | fourcourtscommand | ashockingmurder | ashockingmurder | mrsplayfair | mrsplayfair | recordestablishedfirstto50kviews | recordestablishedfirstto50kviews | 100ishyearsago | 100ishyearsago

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eye | eye | hat | hat | mouth | mouth | emblem | emblem | hair | hair | soldier | soldier | nose | nose | belt | belt | interesting | interesting | uniform | uniform | sad | sad | serious | serious | military | military | grain | grain | marks | marks | criminal | criminal | crime | crime | button | button | wife | wife | mugshot | mugshot | lip | lip | unusual | unusual | pocket | pocket | theft | theft | policestation | policestation | crease | crease | firstworldwar | firstworldwar | attentive | attentive | arrested | arrested | aprons | aprons | stealing | stealing | prisoner | prisoner | civilian | civilian | homefront | homefront | newcastleupontyne | newcastleupontyne | fascinating | fascinating | digitalimage | digitalimage | blouses | blouses | wallsend | wallsend | northshields | northshields | 35s | 35s | transcription | transcription | hardlabour | hardlabour | remand | remand | socialhistory | socialhistory | militaryuniform | militaryuniform | blackframe | blackframe | courtcase | courtcase | blackandwhitephotograph | blackandwhitephotograph | stolenproperty | stolenproperty | bedquilt | bedquilt | dwellinghouse | dwellinghouse | footwrap | footwrap | monawilson | monawilson | newspaperreport | newspaperreport | newcastlepostoffice | newcastlepostoffice | 190216 | 190216 | flannelettesheet | flannelettesheet | johnpwilson | johnpwilson | northshieldspolicestation | northshieldspolicestation | theshieldsdailynews | theshieldsdailynews | northshieldslocalstudieslibrary | northshieldslocalstudieslibrary | onemonthprisonterm | onemonthprisonterm | criminalfacesofnorthshieldsfirstworldwar | criminalfacesofnorthshieldsfirstworldwar | microfilmcopies | microfilmcopies | detmason | detmason | 21january1916 | 21january1916 | stantonstreetnewcastle | stantonstreetnewcastle | wifedismissed | wifedismissed | neutralnackground | neutralnackground | pleadedguilty | pleadedguilty | 28january1916 | 28january1916 | 83norfolkstreet | 83norfolkstreet | jenniesawyer | jenniesawyer | williamoliverbrown | williamoliverbrown

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statelibraryofqueensland | statelibraryofqueensland | slq | slq | queensland | queensland | school | school | classroom | classroom | desks | desks | schooluniforms | schooluniforms | uniforms | uniforms | exams | exams

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This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration. This course is meant as a first introduction to rigorous mathematics; understanding and writing of proofs will be emphasized. We will cover basic notions in real analysis: point-set topology, metric spaces, sequences and series, continuity, differentiability, and integration.

Subjects

analysis | analysis | sequences | sequences | series | series | continuity | continuity | differentiability | differentiability | Riemann | Riemann | uniformity | uniformity | limit operations | limit operations | proofs | proofs | point-set topology | point-set topology | n-space | n-space | communication | communication | writing | writing

License

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

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Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the pla

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Riemann integral | Riemann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space

License

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

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Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations. Analysis I covers fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and interchange of limit operations.

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Riemann integral | Riemann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space

License

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

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El Derecho internacional privado (= DIPr.) es el sector del ordenamiento jurídico de cada Estado que se ocupa de la regulación jurídica de las "situaciones privadas internacionales" (= "concepción privatista del DIPr."). Esta concepción privatista del DIPr. es una concepción con coherencia científica (=el objeto del DIPr. está compuesto por una serie de relaciones jurídicas de caracteres similares: son relaciones entre particulares y que presentan carácter internacional). Es una concepción completa (= ofrece una respuesta completa a los tres interrogantes básicos que suscitan las situaciones privadas internacionales: ¿qué tribunales estatales conocen de las controversias que suscitan las situaciones privadas internacionales, ¿qué Derecho aplican a las mismas los tribuna El Derecho internacional privado (= DIPr.) es el sector del ordenamiento jurídico de cada Estado que se ocupa de la regulación jurídica de las "situaciones privadas internacionales" (= "concepción privatista del DIPr."). Esta concepción privatista del DIPr. es una concepción con coherencia científica (=el objeto del DIPr. está compuesto por una serie de relaciones jurídicas de caracteres similares: son relaciones entre particulares y que presentan carácter internacional). Es una concepción completa (= ofrece una respuesta completa a los tres interrogantes básicos que suscitan las situaciones privadas internacionales: ¿qué tribunales estatales conocen de las controversias que suscitan las situaciones privadas internacionales, ¿qué Derecho aplican a las mismas los tribuna

Subjects

ón | ón | Derecho uniforme | Derecho uniforme | Derecho Internacional Privado | Derecho Internacional Privado | competencia judicial internacional | competencia judicial internacional | Derecho internacional privado | Derecho internacional privado | mercado interior | mercado interior | conflicto de Leyes | conflicto de Leyes | ía internacional | ía internacional

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http://creativecommons.org/licenses/by-nc-sa/3.0/

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ireland | children | boats | pier | barco | crane | ships | navy | sails | sailors | arrogant | grupo | uniforms | lighters | rathmullan | donegal | ulster | homens | uniforme | bollards | battleships | glassnegative | britishnavy | marinheiro | loughswilly | gaslighting | robertfrench | williamlawrence | nationallibraryofireland | hmskingedwardvii | lawrencecollection | limerickbybeachcomber | hmsarrogant | vision:outdoor=0989 | wobblyeight

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Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations. Analysis I covers fundamentals of mathematical analysis: metric spaces, convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, interchange of limit operations.

Subjects

mathematical analysis | mathematical analysis | convergence of sequences | convergence of sequences | convergence of series | convergence of series | continuity | continuity | differentiability | differentiability | Riemann integral | Riemann integral | sequences and series of functions | sequences and series of functions | uniformity | uniformity | interchange of limit operations | interchange of limit operations | utility of abstract concepts | utility of abstract concepts | construction of proofs | construction of proofs | point-set topology | point-set topology | n-space | n-space

License

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

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This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed. This course covers harmonic theory on complex manifolds, the Hodge decomposition theorem, the Hard Lefschetz theorem, and Vanishing theorems. Some results and tools on deformation and uniformization of complex manifolds are also discussed.

Subjects

Harmonic theory | Harmonic theory | complex manifolds | complex manifolds | Hodge decomposition theorem | Hodge decomposition theorem | Hard Lefschetz theorem | Hard Lefschetz theorem | Vanishing theorems | Vanishing theorems | deformation of complex manifolds | deformation of complex manifolds | uniformization of complex manifolds | uniformization of complex manifolds

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

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

Subjects

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

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Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications. Wavelets are localized basis functions, good for representing short-time events. The coefficients at each scale are filtered and subsampled to give coefficients at the next scale. This is Mallat's pyramid algorithm for multiresolution, connecting wavelets to filter banks. Wavelets and multiscale algorithms for compression and signal/image processing are developed. Subject is project-based for engineering and scientific applications.

Subjects

Discrete-time filters | Discrete-time filters | convolution | convolution | Fourier transform | Fourier transform | owpass and highpass filters | owpass and highpass filters | Sampling rate change operations | Sampling rate change operations | upsampling and downsampling | upsampling and downsampling | ractional sampling | ractional sampling | interpolation | interpolation | Filter Banks | Filter Banks | time domain (Haar example) and frequency domain | time domain (Haar example) and frequency domain | conditions for alias cancellation and no distortion | conditions for alias cancellation and no distortion | perfect reconstruction | perfect reconstruction | halfband filters and possible factorizations | halfband filters and possible factorizations | Modulation and polyphase representations | Modulation and polyphase representations | Noble identities | Noble identities | block Toeplitz matrices and block z-transforms | block Toeplitz matrices and block z-transforms | polyphase examples | polyphase examples | Matlab wavelet toolbox | Matlab wavelet toolbox | Orthogonal filter banks | Orthogonal filter banks | paraunitary matrices | paraunitary matrices | orthogonality condition (Condition O) in the time domain | orthogonality condition (Condition O) in the time domain | modulation domain and polyphase domain | modulation domain and polyphase domain | Maxflat filters | Maxflat filters | Daubechies and Meyer formulas | Daubechies and Meyer formulas | Spectral factorization | Spectral factorization | Multiresolution Analysis (MRA) | Multiresolution Analysis (MRA) | requirements for MRA | requirements for MRA | nested spaces and complementary spaces; scaling functions and wavelets | nested spaces and complementary spaces; scaling functions and wavelets | Refinement equation | Refinement equation | iterative and recursive solution techniques | iterative and recursive solution techniques | infinite product formula | infinite product formula | filter bank approach for computing scaling functions and wavelets | filter bank approach for computing scaling functions and wavelets | Orthogonal wavelet bases | Orthogonal wavelet bases | connection to orthogonal filters | connection to orthogonal filters | orthogonality in the frequency domain | orthogonality in the frequency domain | Biorthogonal wavelet bases | Biorthogonal wavelet bases | Mallat pyramid algorithm | Mallat pyramid algorithm | Accuracy of wavelet approximations (Condition A) | Accuracy of wavelet approximations (Condition A) | vanishing moments | vanishing moments | polynomial cancellation in filter banks | polynomial cancellation in filter banks | Smoothness of wavelet bases | Smoothness of wavelet bases | convergence of the cascade algorithm (Condition E) | convergence of the cascade algorithm (Condition E) | splines | splines | Bases vs. frames | Bases vs. frames | Signal and image processing | Signal and image processing | finite length signals | finite length signals | boundary filters and boundary wavelets | boundary filters and boundary wavelets | wavelet compression algorithms | wavelet compression algorithms | Lifting | Lifting | ladder structure for filter banks | ladder structure for filter banks | factorization of polyphase matrix into lifting steps | factorization of polyphase matrix into lifting steps | lifting form of refinement equationSec | lifting form of refinement equationSec | Wavelets and subdivision | Wavelets and subdivision | nonuniform grids | nonuniform grids | multiresolution for triangular meshes | multiresolution for triangular meshes | representation and compression of surfaces | representation and compression of surfaces | Numerical solution of PDEs | Numerical solution of PDEs | Galerkin approximation | Galerkin approximation | wavelet integrals (projection coefficients | moments and connection coefficients) | wavelet integrals (projection coefficients | moments and connection coefficients) | convergence | convergence | Subdivision wavelets for integral equations | Subdivision wavelets for integral equations | Compression and convergence estimates | Compression and convergence estimates | M-band wavelets | M-band wavelets | DFT filter banks and cosine modulated filter banks | DFT filter banks and cosine modulated filter banks | Multiwavelets | Multiwavelets

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The Creole languages spoken in the Caribbean are linguistic by-products of the historical events triggered by colonization and the slave trade in Africa and the "New World". In a nutshell, these languages are the results of language acquisition in the specific social settings defined by the history of contact between African and European peoples in 17th-/18th-century Caribbean colonies. One of the best known Creole languages, and the one with the largest community of speakers, is Haitian Creole. Its lexicon and various aspects of its grammar are primarily derived from varieties of French as spoken in 17th-/18th-century colonial Haiti. Other aspects of its grammar seem to have emerged under the influence of African languages, mostly from West and Central Africa. And yet other properties s The Creole languages spoken in the Caribbean are linguistic by-products of the historical events triggered by colonization and the slave trade in Africa and the "New World". In a nutshell, these languages are the results of language acquisition in the specific social settings defined by the history of contact between African and European peoples in 17th-/18th-century Caribbean colonies. One of the best known Creole languages, and the one with the largest community of speakers, is Haitian Creole. Its lexicon and various aspects of its grammar are primarily derived from varieties of French as spoken in 17th-/18th-century colonial Haiti. Other aspects of its grammar seem to have emerged under the influence of African languages, mostly from West and Central Africa. And yet other properties s

Subjects

socio-linguistic | socio-linguistic | creole | creole | caribbean | caribbean | spoken language acquisition | spoken language acquisition | identity | identity | africa | africa | europe | europe | seventeenth century | seventeenth century | eighteenth century | eighteenth century | haitian | haitian | colony | colony | colonial | colonial | dialect | dialect | grench | grench | new world | new world | slavery | slavery | lexicon | lexicon | pidgin | pidgin | culture | culture | religion | religion | music | music | literature | literature | ethnicity | ethnicity | text | text | syntax | syntax | morphology | morphology | uniformity | uniformity | ebonics | ebonics | africal-american english | africal-american english | gullah | gullah | west indian | west indian

License

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

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The course begins with the basics of compressible fluid dynamics, including governing equations, thermodynamic context and characteristic parameters. The next large block of lectures covers quasi-one-dimensional flow, followed by a discussion of disturbances and unsteady flows. The second half of the course comprises gas dynamic discontinuities, including shock waves and detonations, and concludes with another large block dealing with two-dimensional flows, both linear and non-linear.

Subjects

compressible fluid dynamics | fluid dynamics | external flows | internal flows | quasi-on-dimensional | quasi-1D | channel flow | multi-dimensional flows | nozzles | diffusers | inlets | loss generation | interactions | aerodynamic shapes | subsonic | supersonic | transonic | hypersonic | shock waves | vortices | disturbance behavior | unsteady | speed of sound | isentropic flows | non-isentropic flows | potential flows | rotational flows | shaft work | heat addition | mass addition | flow states | flow regime | velocity non-uniformities | density non-uniformities | fluid system components | lift | drag | continuum flow | shock strength | characteristics | governing equations | thermodynamic context | characteristic parameters | quasi-one-dimensional flow | disturbances | unsteady flow | gas dynamic discontinuities | detonations | linear two-dimensional flows | non-linear two-dimensional flows

License

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

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The Creole languages spoken in the Caribbean are linguistic by-products of the historical events triggered by colonization and the slave trade in Africa and the "New World". In a nutshell, these languages are the results of language acquisition in the specific social settings defined by the history of contact between African and European peoples in 17th-/18th-century Caribbean colonies. One of the best known Creole languages, and the one with the largest community of speakers, is Haitian Creole. Its lexicon and various aspects of its grammar are primarily derived from varieties of French as spoken in 17th-/18th-century colonial Haiti. Other aspects of its grammar seem to have emerged under the influence of African languages, mostly from West and Central Africa. And yet other properties s The Creole languages spoken in the Caribbean are linguistic by-products of the historical events triggered by colonization and the slave trade in Africa and the "New World". In a nutshell, these languages are the results of language acquisition in the specific social settings defined by the history of contact between African and European peoples in 17th-/18th-century Caribbean colonies. One of the best known Creole languages, and the one with the largest community of speakers, is Haitian Creole. Its lexicon and various aspects of its grammar are primarily derived from varieties of French as spoken in 17th-/18th-century colonial Haiti. Other aspects of its grammar seem to have emerged under the influence of African languages, mostly from West and Central Africa. And yet other properties s

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socio-linguistic | socio-linguistic | creole | creole | caribbean | caribbean | spoken language acquisition | spoken language acquisition | identity | identity | africa | africa | europe | europe | seventeenth century | seventeenth century | eighteenth century | eighteenth century | haitian | haitian | colony | colony | colonial | colonial | dialect | dialect | grench | grench | new world | new world | slavery | slavery | lexicon | lexicon | pidgin | pidgin | culture | culture | religion | religion | music | music | literature | literature | ethnicity | ethnicity | text | text | syntax | syntax | morphology | morphology | uniformity | uniformity | ebonics | ebonics | africal-american english | africal-american english | gullah | gullah | west indian | west indian

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

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Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area. Dr Feinstein has published two case studies on his use of IT in the teaching of mathematics to undergraduates. In 2009, Dr Feinstein was awarded a University of Nottingham Lord Dearing teaching award for his popular and successful innovations in this area. As taught in 2006-2007 and 2007-2008. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include: – norm topology and topological isomorphism; – boundedness of operators; – compactness and finite dimensionality; – extension of functionals; – weak*-compactness; – sequence spaces and duality; – basic properties of Banach algebras. Suitable for: Undergraduate students L As taught in 2006-2007 and 2007-2008. Functional analysis begins with a marriage of linear algebra and metric topology. These work together in a highly effective way to elucidate problems arising from differential equations. Solutions are sought in an infinite dimensional space of functions. This module paves the way by establishing the principal theorems (all due in part to the great Polish mathematician Stefan Banach) and exploring their diverse consequences. Topics to be covered will include: – norm topology and topological isomorphism; – boundedness of operators; – compactness and finite dimensionality; – extension of functionals; – weak*-compactness; – sequence spaces and duality; – basic properties of Banach algebras. Suitable for: Undergraduate students L

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UNow | UNow | ukoer | ukoer | Functional analysis | Normed spaces | Functional analysis | Normed spaces | Banach spaces | Banach spaces | Bounded linear operators | Bounded linear operators | dual spaces | dual spaces | commutative Banach algebras | commutative Banach algebras | complete metric spaces | complete metric spaces | open mapping theorem | open mapping theorem | closed graph theorem | closed graph theorem | uniform boundedness | uniform boundedness

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Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA) Except for third party materials (materials owned by someone other than The University of Nottingham) and where otherwise indicated, the copyright in the content provided in this resource is owned by The University of Nottingham and licensed under a Creative Commons Attribution-NonCommercial-ShareAlike UK 2.0 Licence (BY-NC-SA)

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Photograph, sepia, mounted on card showing head and shoulder portrait of a soldier in WW1 uniform. 'JR EDIS DURHAM' written in brown ink at left hand corner of portrait Regional Faces of the First World War. The photograph is from an album relating to the men, women and children from Tyne and Wear who lived, worked or fought during the First World War. Accompanying this photo is the biographical and supporting information that we have about them, but the full story is not always known. Our collections records are not very detailed in some cases. We need your help to fill in the blanks. Do you have any information to add to what is already here? A name? A location? What more can you find out and tell us about their life? If you have some extra information about this photograph, please add your comments, information and any links, images or text. Part of the ?Wor Life? project. To find out more please visit www.worlife.org.uk

Subjects

firstworldwar | ww1 | worlife | worfacesregionalfacesofthefirstworldwar | wartime | sepiaphotograph | socialhistory | mounted | card | whiteoutline | neutralbackground | blur | grain | mark | handwriting | uniform | crease | head | shoulder | soldier | military | ww1uniform | jredisdurham | brownink | portrait | regionalfacesofthefirstworldwar | tyneandwear | northeastofengland | unitedkingdom | mysterious | unusual | fascinating | interesting | compelling | button | pocket | cleanshaven | distracted | worlifeproject

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Postcard, black and white, of a young man and woman. The woman is seated with man sitting on the arm of chair with his arm around her shoulders. Woman is wearing a coat, beret and scarf. The man is in military uniform with no cap Regional Faces of the First World War. The photograph is from an album relating to the men, women and children from Tyne and Wear who lived, worked or fought during the First World War. Accompanying this photo is the biographical and supporting information that we have about them, but the full story is not always known. Our collections records are not very detailed in some cases. We need your help to fill in the blanks. Do you have any information to add to what is already here? A name? A location? What more can you find out and tell us about their life? If you have some extra information about this photograph, please add your comments, information and any links, images or text. Part of the ?Wor Life? project. To find out more please visit www.worlife.org.uk

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firstworldwar | ww1 | worlife | socialhistory | blackandwhitephotograph | uniform | worfacesregionalfacesofthefirstworldwar | woman | man | portrait | neutralbackground | postcard | chair | seated | shoulders | arm | coat | beret | scarf | militaryuniform | tyneandwear | newcastle | dailylives | mysterious | button | pocket | crease | line | mark | cleanshaven | attentive | hand | finger | ring | knuckle | hair | head | face | mouth | lip | nose | eye | ear | back | chest | leg | cloth | couple | interesting | worldwarone | grain

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Postcard, black and white, of a soldier standing outside a tent dressed in full uniform and holding a gun in his right hand Regional Faces of the First World War. The photograph is from an album relating to the men, women and children from Tyne and Wear who lived, worked or fought during the First World War. Accompanying this photo is the biographical and supporting information that we have about them, but the full story is not always known. Our collections records are not very detailed in some cases. We need your help to fill in the blanks. Do you have any information to add to what is already here? A name? A location? What more can you find out and tell us about their life? If you have some extra information about this photograph, please add your comments, information and any links, images or text. Part of the ?Wor Life? project. To find out more please visit www.worlife.org.uk

Subjects

firstworldwar | ww1 | worlife | tent | crease | worldwarone | wartime | blackandwhitephotograph | digitalimage | archives | military | socialhistory | postcard | soldier | standing | fulluniform | uniform | gun | hand | regionalfacesofthefirstworldwar | worfacesregionalfacesofthefirstworldwar | mysterious | unusual | fascinating | interesting | whiteoutline | grass | daylight | shadow | tree | rope | darkness | belt | buckle | pocket | button | weapon | posing | portrait | tyneandwear | northeastofengland | unitedkingdom | attentive | cleanshaven | peg | army

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Photograph, black and white, full length studio portrait of young couple, woman wearing a dark velvet skirt, jacket and large hat and soldier wearing military uniform Regional Faces of the First World War. The photograph is from an album relating to the men, women and children from Tyne and Wear who lived, worked or fought during the First World War. Accompanying this photo is the biographical and supporting information that we have about them, but the full story is not always known. Our collections records are not very detailed in some cases. We need your help to fill in the blanks. Do you have any information to add to what is already here? A name? A location? What more can you find out and tell us about their life? If you have some extra information about this photograph, please add your comments, information and any links, images or text. Part of the ?Wor Life? project. To find out more please visit www.worlife.org.uk

Subjects

firstworldwar | ww1 | worlife | socialhistory | whiteoutline | blackandwhitephotograph | digitalimage | archives | documentation | worfacesregionalfacesofthefirstworldwar | studio | wall | youngcouple | fulllengthstudioportrait | woman | man | darkvelvetskirt | civilian | soldier | jacket | largehat | military | uniform | regionalfacesofthefirstworldwar | tyneandwear | mysterious | unusla | unusual | compelling | fascinating | interesting | northeastofengland | unitedkingdom | standing | attentive | button | crease | grain | mark | shoes | floor | pattern | pocket | blur | hand | wartime | dailylife | homefront | worldwarone | portrait | glimpse | view | face | partner | female | male | feminine | masculine | shine | blankexpression | shadow | room | interior | backdrop | darkness | light | nose | lace | leg | clothing | memory | story | militaryuniform

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Members of the Royal Victoria School for the Blind Brownie pack, January 1962 (TWAM ref. DT.TUR/2/28235A). Tyne & Wear Archives is proud to present a series of images relating to the Royal Victoria School for the Blind, Newcastle upon Tyne. The set has been produced to celebrate UK Disability History Month 2014. The Royal Victoria School for the Blind (then known as the Royal Victoria Asylum) was established from a fund to mark the coronation of Queen Victoria in 1837 and was originally located at the Spital before moving to premises in Northumberland Street. In the 1890s the name was changed to the Royal Victoria School, and in 1895 the school moved to the former house of Dr Hodgkinson in Benwell Dene. Pupils came from throughout the North of England. As a result of legislation to integrate special groups within the mainstream education system the school closed in 1985. (Copyright) We're happy for you to share these digital images within the spirit of The Commons. Please cite 'Tyne & Wear Archives & Museums' when reusing. Certain restrictions on high quality reproductions and commercial use of the original physical version apply though; if you're unsure please email archives@twmuseums.org.uk

Subjects

children | education | royalvictoriaschoolfortheblind | newcastleupontyne | brownies | girlguiding | crafts | disability | ukdisabilityhistorymonth | blindness | visualimpairment | blackandwhitephotograph | activities | browniepack | january1962 | 2014 | royalvictoriaasylum | coronation | queenvictoria | 1837 | northofengland | pupils | school | formerhouse | drhodgkinson | benwelldene | integrate | specialgroups | mainstreameducationsystem | 1985 | legislation | socialheritage | abstract | unusual | girl | girls | table | britishflag | crease | hair | uniform | tie | dress | belt | uniforms | eyeglasses | eye | touch | feel | plate | shine | scratch | paint | leg | carpet | pattern | floor | wall | shadow | light | mantelpiece | tile | glass | door | frame | structure | doors | concentrating | absorbed | companion | companionship | identification | read | senses | sensation | awareness

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shadow | portrait | eye | industry | face | wall | shirt | standing | mouth | hair | nose | boot | belt | uniform | factory | floor | serious | head | label | board | helmet | tie | moustache | medical | suit | doctor | ear | syringe | strap | ww2 | letter | lip | medicine | products | uniforms | unusual | baggage | colleague | crease | arp | attentive | distracted | newcastleupontyne | digitalimage | wartime | secondworldwar | worldwartwo | rivertyne | manufacturing | industrialheritage | medicalequipment | elswick | blackandwhitephotograph | scotswood | drclarkson | airraidprecautions | neutralbackground | lordarmstrong | vickersarmstrong | elswickworks | williamgeorgearmstrong | medicalofficer | workshopoftheworld | scotswoodworks | vickersarmstrongcollection | medicalbelt | wartimemedicalbelt | 25november1940

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View of Dr Clarkson and a colleague, wearing wartime medical equipment at the Elswick Works, Newcastle upon Tyne, 25 November 1940 (TWAM ref. 1027/neg15299). Dr Clarkson is ?armed? with a wartime medical belt, holding a syringe and medical supplies. Healing was essential but smiling was optional! ?Workshop of the World? is a phrase often used to describe Britain?s manufacturing dominance during the Nineteenth Century. It?s also a very apt description for the Elswick Works and Scotswood Works of Vickers Armstrong and its predecessor companies. These great factories, situated in Newcastle along the banks of the River Tyne, employed hundreds of thousands of men and women and built a huge variety of products for customers around the globe. The Elswick Works was established by William George Armstrong (later Lord Armstrong) in 1847 to manufacture hydraulic cranes. From these relatively humble beginnings the company diversified into many fields including shipbuilding, armaments and locomotives. By 1953 the Elswick Works covered 70 acres and extended over a mile along the River Tyne. This set of images, mostly taken from our Vickers Armstrong collection, includes fascinating views of the factories at Elswick and Scotswood, the products they produced and the people that worked there. By preserving these archives we can ensure that their legacy lives on. (Copyright) We're happy for you to share this digital image within the spirit of The Commons. Please cite 'Tyne & Wear Archives & Museums' when reusing. Certain restrictions on high quality reproductions and commercial use of the original physical version apply though; if you're unsure please email info@twarchives.org.uk.

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elswickworks | newcastleupontyne | factory | industry | vickersarmstrong | secondworldwar | wartime | medicalequipment | medicalbelt | syringe | medicine | medicalofficer | uniforms | serious | arp | airraidprecautions | doctor | ww2 | industrialheritage | blackandwhitephotograph | medical | worldwartwo | 25november1940 | drclarkson | colleague | wartimemedicalbelt | workshopoftheworld | portrait | manufacturing | scotswoodworks | rivertyne | products | williamgeorgearmstrong | lordarmstrong | vickersarmstrongcollection | elswick | scotswood | digitalimage | suit | uniform | helmet | letter | label | belt | crease | shadow | neutralbackground | unusual | floor | wall | board | boot | baggage | strap | tie | shirt | moustache | hair | head | eye | nose | ear | mouth | lip | face | attentive | distracted | standing

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