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18.06CI Linear Algebra - Communications Intensive (MIT) 18.06CI Linear Algebra - Communications Intensive (MIT)

Description

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space. This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.

Subjects

Linear Alegebra | Linear Alegebra | Latex | Latex | LaTeX2e | LaTeX2e | mathematical writing | mathematical writing | linear spaces | linear spaces | basis | basis | dimension | dimension | linear mappings | linear mappings | matrices | matrices | subspaces | subspaces | direct sums | direct sums | reflections | reflections | Euclidean space | Euclidean space | abstract root systems | abstract root systems | simple roots | simple roots | positive roots | positive roots | Cartan matrix | Cartan matrix | Dynkin diagrams | Dynkin diagrams | classification | classification | 18.06 | 18.06

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18.06CI Linear Algebra - Communications Intensive (MIT)

Description

This is a communication intensive supplement to Linear Algebra (18.06). The main emphasis is on the methods of creating rigorous and elegant proofs and presenting them clearly in writing. The course starts with the standard linear algebra syllabus and eventually develops the techniques to approach a more advanced topic: abstract root systems in a Euclidean space.

Subjects

Linear Alegebra | Latex | LaTeX2e | mathematical writing | linear spaces | basis | dimension | linear mappings | matrices | subspaces | direct sums | reflections | Euclidean space | abstract root systems | simple roots | positive roots | Cartan matrix | Dynkin diagrams | classification | 18.06

License

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16.06 Principles of Automatic Control (MIT) 16.06 Principles of Automatic Control (MIT)

Description

This course introduces the design of feedback control systems as applied to a variety of air and spacecraft systems. Topics include the properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, the Root locus method, Nyquist criterion, frequency-domain design, and state space methods. This course introduces the design of feedback control systems as applied to a variety of air and spacecraft systems. Topics include the properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, the Root locus method, Nyquist criterion, frequency-domain design, and state space methods.

Subjects

classical control systems | classical control systems | feedback control systems | feedback control systems | bode plots | bode plots | time-domain and frequency-domain performance measures | time-domain and frequency-domain performance measures | stability | stability | root locus method | root locus method | nyquist criterion | nyquist criterion | frequency-domain design | frequency-domain design | state space methods | state space methods

License

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Gender Studies Seminar: Latina Women's Voices (MIT) Gender Studies Seminar: Latina Women's Voices (MIT)

Description

This course will explore the rich diversity of women's voices and experiences as reflected in writings and films by and about Latina writers, filmmakers, and artists. Through close readings, class discussions and independently researched student presentations related to each text, we will explore not only the unique, individual voice of the writer, but also the cultural, social and political contexts which inform their narratives. We will also examine the roles that gender, familial ties and social and political preoccupations play in shaping the values of the writers and the nature of the characters encountered in the texts and films. This course will explore the rich diversity of women's voices and experiences as reflected in writings and films by and about Latina writers, filmmakers, and artists. Through close readings, class discussions and independently researched student presentations related to each text, we will explore not only the unique, individual voice of the writer, but also the cultural, social and political contexts which inform their narratives. We will also examine the roles that gender, familial ties and social and political preoccupations play in shaping the values of the writers and the nature of the characters encountered in the texts and films.

Subjects

Latina | Latina | women | women | code-switching | code-switching | first generation | first generation | coming-of-age | coming-of-age | Chicana | Chicana | roots | roots | revolution | revolution | politics | politics | poverty | | poverty | | social criticism | social criticism | kinship | kinship | biography | biography | magic realism | magic realism | mythical historicism | mythical historicism

License

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18.781 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 fractions

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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18.330 Introduction to Numerical Analysis (MIT) 18.330 Introduction to Numerical Analysis (MIT)

Description

This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra. This course analyzed the basic techniques for the efficient numerical solution of problems in science and engineering. Topics spanned root finding, interpolation, approximation of functions, integration, differential equations, direct and iterative methods in linear algebra.

Subjects

series expansions | series expansions | root finding | root finding | interpolation | interpolation | Fourier transform | Fourier transform | approximation functions | approximation functions | least-squares approximation | least-squares approximation | principal component analysis | principal component analysis

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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6.302 Feedback Systems (MIT) 6.302 Feedback Systems (MIT)

Description

This course provides an introduction to the design of feedback systems. Topics covered include: properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, root locus method, Nyquist criterion, frequency-domain design, compensation techniques, application to a wide variety of physical systems, internal and external compensation of operational amplifiers, modeling and compensation of power converter systems, and phase lock loops. This course provides an introduction to the design of feedback systems. Topics covered include: properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, root locus method, Nyquist criterion, frequency-domain design, compensation techniques, application to a wide variety of physical systems, internal and external compensation of operational amplifiers, modeling and compensation of power converter systems, and phase lock loops.

Subjects

feedback system | feedback system | time-domain performance | time-domain performance | frequency-domain performance. stability | frequency-domain performance. stability | root locus method | root locus method | Nyquist criterion | Nyquist criterion | frequency-domain design | frequency-domain design | compensation techniques | compensation techniques | internal compensation | internal compensation | external compensation | external compensation | operational amplifiers | operational amplifiers | power coverter systems | power coverter systems | phase lock loops | phase lock loops

License

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course,which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

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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Squares, roots and powers Squares, roots and powers

Description

From paving your patio to measuring the ingredients for your latest recipe, squares, roots and powers really are part of everyday life. This free course reviews the basics of all three and also describes scientific notation, which is a convenient way of writing or displaying large numbers. First published on Mon, 25 Apr 2016 as Squares, roots and powers. To find out more visit The Open University's Openlearn website. Creative-Commons 2016 From paving your patio to measuring the ingredients for your latest recipe, squares, roots and powers really are part of everyday life. This free course reviews the basics of all three and also describes scientific notation, which is a convenient way of writing or displaying large numbers. First published on Mon, 25 Apr 2016 as Squares, roots and powers. To find out more visit The Open University's Openlearn website. Creative-Commons 2016

Subjects

Mathematics Education | Mathematics Education | roots | roots

License

Except for third party materials and otherwise stated (see http://www.open.ac.uk/conditions terms and conditions), this content is made available under a http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ Creative Commons Attribution-NonCommercial-ShareAlike 2.0 Licence Licensed under a Creative Commons Attribution - NonCommercial-ShareAlike 2.0 Licence - see http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ - Original copyright The Open University

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Icicles

Description

This set, taken from the Spence Family collection at Tyne & Wear Archives offers an intimate view in to a Family enjoying the festive season during this time of change and the invention of Christmas. Reference: DX 1295-1-1-58 At the beginning of the 19th Century, Christmas was hardly celebrated. However, during the Victorian Era Christmas as we know it today was invented, and our modest medieval traditions of evergreens and food were transformed. Much if this change was due to Queen Victoria and her marriage to the German-born Prince Albert. Albert introduced many aspects of Christmas as we know it, most notably the first Christmas tree in the royal family?s home. This was a tradition Albert brought to his family from his own childhood in Germany, but also to every other family in Britain. As a result the Victorians also transformed the idea of Christmas so that it became centred around the family, and our modern day traditions are deeply rooted in those of Victorian Society. (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

festive | victorian | snow | family | tradition | cold | leisure | joy | socialhistory | sepiaphotograph | avictorianchristmas | 19thcentury | icicles | spencerfamilycollection | tyneweararchives | festivity | winter | ice | water | season | holiday | change | invention | christmas | celebration | victorianera | medievaltraditions | evergreens | food | queenvictoria | germanborn | princealbert | introduction | christmastree | royalty | traditional | childhood | germany | britishfamilies | modernday | rooted | victoriansociety | digitalimage | wall | brick | grain | sky | pipe | window | frame | glass | reflection | tree | branch | blur | roof | gutter | moss | timber | mark | intimateview | changes | transformation | bliss | root | bark | seasons

License

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18.098 Street-Fighting Mathematics (MIT) 18.098 Street-Fighting Mathematics (MIT)

Description

This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month. This course teaches the art of guessing results and solving problems without doing a proof or an exact calculation. Techniques include extreme-cases reasoning, dimensional analysis, successive approximation, discretization, generalization, and pictorial analysis. Applications include mental calculation, solid geometry, musical intervals, logarithms, integration, infinite series, solitaire, and differential equations. (No epsilons or deltas are harmed by taking this course.) This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

Subjects

extreme-cases reasoning | extreme-cases reasoning | dimensional analysis | dimensional analysis | discretization | discretization | drag | drag | fluid mechanics | fluid mechanics | pendulum | pendulum | pictorial proofs | pictorial proofs | analogy | analogy | operators | operators | summation | summation | square roots | square roots | logarithms | logarithms | musical intervals | musical intervals | taking out the big part | taking out the big part | integration | integration | differentiation | differentiation

License

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18.S34 Problem Solving Seminar (MIT) 18.S34 Problem Solving Seminar (MIT)

Description

This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates. This course, which is geared toward Freshmen, is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. Students in this course are expected to compete in a nationwide mathematics contest for undergraduates.

Subjects

Pigeonhole Principle | Pigeonhole Principle | probability | probability | congruences and divisibility | congruences and divisibility | recurrences | recurrences | limits | limits | greatest integer function | greatest integer function | inequalities | inequalities | Putnam practice | Putnam practice | hidden independence | hidden independence | roots of polynomials | roots of polynomials

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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What! Never Tasted Hires' Root Beer? You've Missed A Treat. We Keep it Here. What! Never Tasted Hires' Root Beer? You've Missed A Treat. We Keep it Here.

Description

Subjects

tradecards | tradecards | advertising | advertising | advertisements | advertisements | beverages | beverages | softdrinks | softdrinks | rootbeer | rootbeer

License

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2.29 Numerical Marine Hydrodynamics (13.024) (MIT) 2.29 Numerical Marine Hydrodynamics (13.024) (MIT)

Description

Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department Includes audio/video content: AV faculty introductions. This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions. This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.024. In 2005, ocean engineering subjects became part of Course 2 (Department

Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects

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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2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

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E. Root (LOC) E. Root (LOC)

Description

Subjects

libraryofcongress | libraryofcongress | elihuroot | elihuroot | columbiauniversity | columbiauniversity

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18.335J Numerical Methods of Applied Mathematics I (MIT) 18.335J Numerical Methods of Applied Mathematics I (MIT)

Description

IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. Quadrature.Technical RequirementsFile decompression software, such as Winzip or StuffIt, is required to open the .tar files found on this course site. The .tar files contain additional files which require software as well. MATLAB® software is required to run the .m files.Postscript viewer software, such as Ghostscript/Ghostview, can be used to view the .ps files.Ghostscript/Ghostview, Adobe Photoshop, and Adobe Illustrator are among the software tools that can be used to view the .ep IEEE-standard, iterative and direct linear system solution methods, eigendecomposition and model-order reduction, fast Fourier transforms, multigrid, wavelets and other multiresolution methods, matrix sparsification. Nonlinear root finding (Newton's method). Numerical interpolation and extrapolation. Quadrature.Technical RequirementsFile decompression software, such as Winzip or StuffIt, is required to open the .tar files found on this course site. The .tar files contain additional files which require software as well. MATLAB® software is required to run the .m files.Postscript viewer software, such as Ghostscript/Ghostview, can be used to view the .ps files.Ghostscript/Ghostview, Adobe Photoshop, and Adobe Illustrator are among the software tools that can be used to view the .ep

Subjects

IEEE-standard | IEEE-standard | iterative and direct linear system solution methods | iterative and direct linear system solution methods | eigendecomposition and model-order reduction | eigendecomposition and model-order reduction | fast Fourier transforms | fast Fourier transforms | multigrid | multigrid | wavelets | wavelets | other multiresolution methods | other multiresolution methods | matrix sparsification | matrix sparsification | Nonlinear root finding (Newton's method) | Nonlinear root finding (Newton's method) | Numerical interpolation | Numerical interpolation | Numerical extrapolation | Numerical extrapolation | Quadrature | Quadrature | 18.335 | 18.335 | 6.337 | 6.337

License

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6.302 Feedback Systems (MIT) 6.302 Feedback Systems (MIT)

Description

This course provides an introduction to the design of feedback systems. Topics covered include: properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, root locus method, Nyquist criterion, frequency-domain design, compensation techniques, application to a wide variety of physical systems, internal and external compensation of operational amplifiers, modeling and compensation of power converter systems, and phase lock loops. This course provides an introduction to the design of feedback systems. Topics covered include: properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability, root locus method, Nyquist criterion, frequency-domain design, compensation techniques, application to a wide variety of physical systems, internal and external compensation of operational amplifiers, modeling and compensation of power converter systems, and phase lock loops.

Subjects

feedback system | feedback system | time-domain performance | time-domain performance | frequency-domain performance. stability | frequency-domain performance. stability | root locus method | root locus method | Nyquist criterion | Nyquist criterion | frequency-domain design | frequency-domain design | compensation techniques | compensation techniques | internal compensation | internal compensation | external compensation | external compensation | operational amplifiers | operational amplifiers | power coverter systems | power coverter systems | phase lock loops | phase lock loops

License

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2.14 Analysis and Design of Feedback Control Systems (MIT) 2.14 Analysis and Design of Feedback Control Systems (MIT)

Description

This course develops the fundamentals of feedback control using linear transfer function system models. Topics covered include analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and use of z-plane design. Students will complete an extended design case study. Students taking the graduate version (2.140) will attend the recitation sessions and complete additional assignments. This course develops the fundamentals of feedback control using linear transfer function system models. Topics covered include analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and use of z-plane design. Students will complete an extended design case study. Students taking the graduate version (2.140) will attend the recitation sessions and complete additional assignments.

Subjects

feedback loops | feedback loops | control systems | control systems | compensation | compensation | Bode plots | Bode plots | Nyquist plots | Nyquist plots | state space | state space | frequency domain | frequency domain | time domain | time domain | transfer functions | transfer functions | Laplace transform | Laplace transform | root locus | root locus | op-amps | op-amps | gears | gears | motors | motors | actuators | actuators | nonlinear systems | nonlinear systems | stability theory | stability theory | dynamic feedback | dynamic feedback | mechanical engineering problem archive | mechanical engineering problem archive

License

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2.14 Analysis and Design of Feedback Control Systems (MIT) 2.14 Analysis and Design of Feedback Control Systems (MIT)

Description

This course develops the fundamentals of feedback control using linear transfer function system models. It covers analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and the use of z-plane design. Assignments include extended design case studies and capstone group projects. Graduate students are expected to complete additional assignments. This course develops the fundamentals of feedback control using linear transfer function system models. It covers analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and the use of z-plane design. Assignments include extended design case studies and capstone group projects. Graduate students are expected to complete additional assignments.

Subjects

feedback loops | feedback loops | compensation | compensation | Bode plots | Bode plots | Nyquist plots | Nyquist plots | state space | state space | frequency domain | frequency domain | time domain | time domain | transfer functions | transfer functions | Laplace transform | Laplace transform | root locus | root locus | op-amps | op-amps | gears | gears | motors | motors | actuators | actuators | nonlinear systems | nonlinear systems | stability theory | stability theory | control systems | control systems | dynamic feedback | dynamic feedback | mechanical engineering problem archive | mechanical engineering problem archive

License

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2.04A Systems and Controls (MIT) 2.04A Systems and Controls (MIT)

Description

This course provides an introduction to linear systems, transfer functions, and Laplace transforms. It covers stability and feedback, and provides basic design tools for specifications of transient response. It also briefly covers frequency-domain techniques.   This course provides an introduction to linear systems, transfer functions, and Laplace transforms. It covers stability and feedback, and provides basic design tools for specifications of transient response. It also briefly covers frequency-domain techniques.  

Subjects

systems | systems | controls | controls | ordinary differential equations | ordinary differential equations | ODEs | ODEs | differential equations | differential equations | Laplace | Laplace | transfer function | transfer function | flywheel | flywheel | circuits | circuits | impedance | impedance | feedback | feedback | root locus | root locus | linear systems | linear systems | Laplace transforms | Laplace transforms | stability | stability | frequency-domain | frequency-domain | skyscaper | skyscaper

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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16.06 Principles of Automatic Control (MIT) 16.06 Principles of Automatic Control (MIT)

Description

The course deals with introduction to design of feedback control systems, properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability. It also covers root locus method, nyquist criterion, frequency-domain design, and state space methods. The course deals with introduction to design of feedback control systems, properties and advantages of feedback systems, time-domain and frequency-domain performance measures, stability and degree of stability. It also covers root locus method, nyquist criterion, frequency-domain design, and state space methods.

Subjects

feedback control systems | feedback control systems | time-domain and frequency-domain performance measures | time-domain and frequency-domain performance measures | stability | stability | root locus method | root locus method | nyquist criterion | nyquist criterion | frequency-domain design | frequency-domain design | state space methods | state space methods | time-domain performance measures | time-domain performance measures | frequency-domain performance measures | frequency-domain performance measures | aircraft systems | aircraft systems | spacecraft systems | spacecraft systems | control system analysis | control system analysis | time-domain system design | time-domain system design

License

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11.310J Media Technology and City Design and Development (MIT) 11.310J Media Technology and City Design and Development (MIT)

Description

This workshop explores the potential of media technology and the Internet to enhance communication and transform city design and community development in inner-city neighborhoods. The class introduces a variety of methods for describing or representing a place and its residents, for simulating actions and changes, for presenting visions of the future, and for engaging multiple actors in the process of envisioning change and guiding action. Students will engage two neighborhoods: the Mill Creek neighborhood of West Philadelphia, PA, and the Brightwood/Northend neighborhood of Springfield, MA. Students will meet real people working on real projects, put theory into practice, and reflect on insights gained in the process. Our hope is that student work will contribute to new initiatives i This workshop explores the potential of media technology and the Internet to enhance communication and transform city design and community development in inner-city neighborhoods. The class introduces a variety of methods for describing or representing a place and its residents, for simulating actions and changes, for presenting visions of the future, and for engaging multiple actors in the process of envisioning change and guiding action. Students will engage two neighborhoods: the Mill Creek neighborhood of West Philadelphia, PA, and the Brightwood/Northend neighborhood of Springfield, MA. Students will meet real people working on real projects, put theory into practice, and reflect on insights gained in the process. Our hope is that student work will contribute to new initiatives i

Subjects

workshop | workshop | community development in inner-city neighborhoods | community development in inner-city neighborhoods | internet | internet | digital | digital | teaching tool | teaching tool | media | media | urban | urban | design | design | West Philadelphia | West Philadelphia | Mill Creek | Mill Creek | urban environmental design | urban environmental design | information technology | information technology | public education | public education | city design | city design | community development | community development | inner-city neighborhoods | inner-city neighborhoods | design and planning | design and planning | grassroots efforts | grassroots efforts | neighborhood-based design | neighborhood-based design | environmental and community history | environmental and community history | planning | planning | community and watershed | community and watershed | WPLP | WPLP | school and community | school and community | interactive design | interactive design | 11.310 | 11.310 | 4.243 | 4.243

License

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2.29 Numerical Fluid Dynamics (MIT) 2.29 Numerical Fluid Dynamics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs). This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

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11.948 Power of Place: Media Technology, Youth, and City Design and Development (MIT) 11.948 Power of Place: Media Technology, Youth, and City Design and Development (MIT)

Description

This workshop provides an introduction to urban environmental design and explores the potential of information technology and the Internet to transform public education, city design, and community development in inner-city neighborhoods. Integration of comprehensive ("top-down") and grassroots ("bottom-up") approaches to design and planning is a major theme. Students will work in a real neighborhood with real people on a real project, putting theory into practice and reflecting on insights gained in the process. We will study environmental and community history and devise designs for vacant land near a middle school in West Philadelphia within the context of planning for the larger community and watershed. The class website can be found here: Power of Place: Media Technology, You This workshop provides an introduction to urban environmental design and explores the potential of information technology and the Internet to transform public education, city design, and community development in inner-city neighborhoods. Integration of comprehensive ("top-down") and grassroots ("bottom-up") approaches to design and planning is a major theme. Students will work in a real neighborhood with real people on a real project, putting theory into practice and reflecting on insights gained in the process. We will study environmental and community history and devise designs for vacant land near a middle school in West Philadelphia within the context of planning for the larger community and watershed. The class website can be found here: Power of Place: Media Technology, You

Subjects

urban environmental design | urban environmental design | information technology | information technology | public education | public education | city design | city design | community development | community development | inner-city neighborhoods | inner-city neighborhoods | design and planning | design and planning | grassroots efforts | grassroots efforts | neighborhood-based design | neighborhood-based design | West Philadelphia | West Philadelphia | environmental and community history | environmental and community history | planning | planning | community and watershed | community and watershed | WPLP | WPLP | school and community | school and community | interactive design | interactive design | watershed | watershed | schools | schools

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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