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Description

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor C This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor CSubjects

energetics | energetics | visualization | visualization | graph | graph | plot | plot | chart | chart | materials science | materials science | DMSE | DMSE | structure | structure | symmetry | symmetry | mechanics | mechanics | physicss | physicss | solids and soft materials | solids and soft materials | linear algebra | linear algebra | orthonormal basis | orthonormal basis | eigenvalue | eigenvalue | eigenvector | eigenvector | quadratic form | quadratic form | tensor operation | tensor operation | symmetry operation | symmetry operation | calculus | calculus | complex analysis | complex analysis | differential equations | differential equations | ODE | ODE | solution | solution | vector | vector | matrix | matrix | determinant | determinant | theory of distributions | theory of distributions | fourier analysis | fourier analysis | random walk | random walk | Mathematica | Mathematica | simulation | simulationLicense

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

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See all metadata6.003 Signals and Systems (MIT) 6.003 Signals and Systems (MIT)

Description

This course covers fundamentals of signal and system analysis, with applications drawn from filtering, audio and image processing, communications, and automatic control. Topics include convolution, Fourier series and transforms, sampling and discrete-time processing of continuous-time signals, modulation, Laplace and Z-transforms, and feedback systems. This course covers fundamentals of signal and system analysis, with applications drawn from filtering, audio and image processing, communications, and automatic control. Topics include convolution, Fourier series and transforms, sampling and discrete-time processing of continuous-time signals, modulation, Laplace and Z-transforms, and feedback systems.Subjects

signal and system analysis | signal and system analysis | filtering | filtering | audio | audio | audio processing | audio processing | image processing | image processing | communications | communications | automatic control | automatic control | convolution | convolution | Fourier series | Fourier series | fourier transforms | fourier transforms | sampling | sampling | discrete-time processing | discrete-time processing | modulation | modulation | Laplace transforms | Laplace transforms | Z-transforms | Z-transforms | feedback systems | feedback systemsLicense

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

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See all metadataFourier Telescope Fourier Telescope

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See all metadataIntroduction to Partial Differential Equations

Description

Partial differential equations (PDEs) describe the relationships among the derivatives of an unknown function with respect to different independent variables, such as time and position. Experiment and observation provide information about the connections between rates of change of an important quantity, such as heat, with respect to different variables. This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mathematics 222)Subjects

partial differential equations | sets | functions | derivatives | heat | diffusion | linear | fourier series | bounded domains | functional analysis | solution methods | impulse-response | fourier transform | unbounded domain | Computer science | I100License

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

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

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

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See all metadata18.034 Honors Differential Equations (MIT) 18.034 Honors Differential Equations (MIT)

Description

This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems. This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.Subjects

First order equations | First order equations | Separation | Separation | initial value problems | initial value problems | Systems | Systems | linear equations | linear equations | independence of solutions | independence of solutions | undetermined coefficients | undetermined coefficients | Singular points | Singular points | periodic orbits for planar systems | periodic orbits for planar systems | first order ode's | first order ode's | second order ode's | second order ode's | fourier series | fourier series | laplace transform | laplace transform | linear systems | linear systems | nonlinear systems | nonlinear systems | constant coefficients | constant coefficientsLicense

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

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The applications of pattern recognition techniques to problems of machine vision is the main focus for this course. Topics covered include, an overview of problems of machine vision and pattern classification, image formation and processing, feature extraction from images, biological object recognition, bayesian decision theory, and clustering. The applications of pattern recognition techniques to problems of machine vision is the main focus for this course. Topics covered include, an overview of problems of machine vision and pattern classification, image formation and processing, feature extraction from images, biological object recognition, bayesian decision theory, and clustering.Subjects

comonent analysis | comonent analysis | PCA | PCA | ICA | ICA | fourier analysis | fourier analysis | vision | vision | machine vision | machine vision | pattern matching | pattern matching | pattern analysis | pattern analysis | pattern recognition | pattern recognition | scene analysis | scene analysis | tracking | tracking | feature extraction | feature extraction | color | color | color space | color space | clustering | clustering | bayesian decisions | bayesian decisions | gesture recognition | gesture recognition | action recognition | action recognition | image processing | image processing | image formation | image formation | density estimation | density estimation | classification | classification | morphable models | morphable models | component analysis | component analysisLicense

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

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This course presents the fundamentals of digital signal processing with particular emphasis on problems in biomedical research and clinical medicine. It covers principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. The focus of the course is a series of labs that provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. The labs are done in MATLAB® during weekly lab sessions that take place in an electronic classroom. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs. This course presents the fundamentals of digital signal processing with particular emphasis on problems in biomedical research and clinical medicine. It covers principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. The focus of the course is a series of labs that provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. The labs are done in MATLAB® during weekly lab sessions that take place in an electronic classroom. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs.Subjects

HST.582 | HST.582 | 6.555 | 6.555 | 16.456 | 16.456 | signal processing | signal processing | medicine | medicine | biological signal | biological signal | diagnosis | diagnosis | diagnostic tool | diagnostic tool | physiology | physiology | cardiology | cardiology | speech recognition | speech recognition | speech processing | speech processing | imaging | imaging | medical imaging | medical imaging | MRI | MRI | ultrasound | ultrasound | ECG | ECG | electrocardiogram | electrocardiogram | fourier | fourier | FFT | FFT | applications of probabilitym | applications of probabilitym | noise | noise | MATLAB | MATLAB | digital filter | digital filter | DSP | DSPLicense

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

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See all metadataRES.6-007 Signals and Systems (MIT) RES.6-007 Signals and Systems (MIT)

Description

Includes audio/video content: AV lectures. This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace. Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products. The course presents and integrates the basic concepts for both continuous-time and discrete-time signals and systems. Signal and system representations are developed for both time and frequency domains. These representations are related through the Fourier tran Includes audio/video content: AV lectures. This course was developed in 1987 by the MIT Center for Advanced Engineering Studies. It was designed as a distance-education course for engineers and scientists in the workplace. Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products. The course presents and integrates the basic concepts for both continuous-time and discrete-time signals and systems. Signal and system representations are developed for both time and frequency domains. These representations are related through the Fourier tranSubjects

signal processing | signal processing | digital signals | digital signals | digital systems | digital systems | analog signal processing | analog signal processing | analog systems | analog systems | fourier transform | fourier transform | discrete-time equations | discrete-time equations | continuous-time equations | continuous-time equations | sampling | samplingLicense

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

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This unit shows how partial differential equations can be used to model phenomena such as waves and heat transfer. The prerequisite requirements to gain full advantage from this unit are an understanding of ordinary differential equations and basic familiarity with partial differential equations.Subjects

mathematics and statistics | differential | equations | fourier | mathematics | maths_modelling | modelling | Education | X000License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Site sourced from

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This unit is concerned with the technique of expressing a periodic function as a sum of terms, where each term is a constant, a sine function or a cosine function. There is a strong analogy with the technique of expressing a (non-periodic) function as a Taylor series, which is a sum of terms that are powers of the independent variable(s); in both cases, working with just the first few terms generally gives a useful approximation. This unit assumes the following background knowledge: the definition of the period; forced oscillations and resonance; integration by parts.Subjects

mathematics and statistics | fourier | mathematics | maths_modelling | oscillation | periodic_function | Education | X000License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/Site sourced from

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See all metadataTwo dimensional heat conduction (UH-Case 1)

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.Subjects

ukoer | engscoer | cc-by | university of hertfordshire | he | higher education | engineering | hertfordshireunioer | conduction | conduction equation | fouriers equation | heat transfer | oer | uni herts | uniofhertfordshire | steady state | two dimensional | thermal | isotherm | heat flux | engineering educational video | mark russell | blended learning unit | blu | Engineering | H000License

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See all metadataTwo dimensional heat conduction (UH-Case 2)

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.Subjects

ukoer | engscoer | cc-by | university of hertfordshire | he | higher education | engineering | hertfordshireunioer | conduction | conduction equation | fouriers equation | heat transfer | oer | uni herts | uniofhertfordshire | steady state | two dimensional | thermal | isotherm | heat flux | engineering educational video | mark russell | blended learning unit | blu | Engineering | H000License

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See all metadataTwo dimensional heat conduction (UH-Case 3)

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.Subjects

ukoer | engscoer | cc-by | university of hertfordshire | he | higher education | engineering | hertfordshireunioer | conduction | conduction equation | fouriers equation | heat transfer | oer | uni herts | uniofhertfordshire | steady state | two dimensional | thermal | isotherm | heat flux | engineering educational video | mark russell | blended learning unit | blu | Engineering | H000License

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See all metadataTwo dimensional heat conduction (UH-Case 4)

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.Subjects

ukoer | engscoer | cc-by | university of hertfordshire | he | higher education | engineering | hertfordshireunioer | conduction | conduction equation | fouriers equation | heat transfer | oer | uni herts | uniofhertfordshire | steady state | two dimensional | thermal | isotherm | heat flux | engineering educational video | mark russell | blended learning unit | blu | Engineering | H000License

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See all metadataTwo dimensional heat conduction (UH-Case 5)

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.Subjects

ukoer | engscoer | cc-by | university of hertfordshire | he | higher education | engineering | hertfordshireunioer | conduction | conduction equation | fouriers equation | heat transfer | oer | uni herts | uniofhertfordshire | steady state | two dimensional | thermal | isotherm | heat flux | engineering educational video | mark russell | blended learning unit | blu | Engineering | H000License

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See all metadata3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor CSubjects

energetics | visualization | graph | plot | chart | materials science | DMSE | structure | symmetry | mechanics | physicss | solids and soft materials | linear algebra | orthonormal basis | eigenvalue | eigenvector | quadratic form | tensor operation | symmetry operation | calculus | complex analysis | differential equations | ODE | solution | vector | matrix | determinant | theory of distributions | fourier analysis | random walk | Mathematica | simulationLicense

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

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See all metadataTwo dimensional heat conduction (UH-Case 6)

Description

This open educational resource was released through the Higher Education Academy Engineering Subject Centre Open Engineering Resources Pilot project. The project was funded by HEFCE and the JISC/HE Academy UKOER programme.Subjects

ukoer | engscoer | cc-by | university of hertfordshire | he | higher education | engineering | hertfordshireunioer | conduction | conduction equation | fouriers equation | heat transfer | oer | uni herts | uniofhertfordshire | steady state | two dimensional | thermal | isotherm | heat flux | engineering educational video | mark russell | blended learning unit | blu | Engineering | H000License

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Wales undergraduate level and as a CPD training resourceSubjects

ukoer | sfsoer | oer | open educational resources | metadata | analytical science | cpd training resource | analytical chemistry | measurement science | analytical process model | skills for analytical science | skills for analytical chemistry | analytical sample preparation | separation and concentration of analytes | units of measurement | volumetric techniques | gravimetric techniques | calibration methods | standard-addition | method of internal-standards | statistical analysis of data | measurement uncertainty | chromatographic methods | thin layer chromatography | gc | gas chromatography | hplc | high-performance liquid chromatography | capillary electrophoresis | potentiometry | ion-selective electrodes | amperometry | coulometry | plated film thickness | electromagnetic spectrum | electronic transitions | vibrational energy | comparison of spectroscopic techniques | fluorescence spectroscopy | mid infra-red spectroscopy | near infra-red spectroscopy | aas | atomic absorption spectroscopy | atomic emission spectroscopy | inductively coupled plasme emission spectroscopy | icpms | icpes | atomic fluorescence spectroscopy | comparison of elemental analysis techniques | principles of mass spectroscopy | electron impact mass spectroscopy | chemical ionisation mass spectroscopy | quadrupole mass spectroscopy | time-of-flight mass analysers | ion-trap mass analysers | off-line sampling systems | at-line sampling systems | on-line sampling systems | in-line sampling systems | performance characteristics of analytical techniques | flow injection analysis | fia | process gc | process ir | process ms | process uv/visible | quality management | quality assurance | qa | vam principles | quality control | qc | analytical method validation | analytical method performance characteristics | sampling of solids | liquids and gases | measurement of ph | karl fischer titration | uv/visible spectroscopy | beer's law | beer-lambert law | deviations from beer's law | mid ir spectroscopy | near ir spectroscopy | raman spectroscopy | fourier transform spectroscopies | x-ray methods | x-ray fluorescence spectroscopy | gc-ms | lc-ms | Physical sciences | F000License

Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales Attribution-Noncommercial-No Derivative Works 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-nd/2.0/uk/ http://creativecommons.org/licenses/by-nc-nd/2.0/uk/Site sourced from

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See all metadataNumerical Methods for Engineers

Description

This course examines how numerical methods are used by engineers to translate the language of mathematics and physics into information that may be used to make engineering decisions. Often, this translation is implemented so that calculations may be done by machines (computers). This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mechanical Engineering 205)Subjects

algebra | binary | numerical differentiation | newton-raphson | interpolation | regression | optimization | integration | fourier series | Engineering | H000License

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See all metadataNumerical Methods for Engineers

Description

This course examines how numerical methods are used by engineers to translate the language of mathematics and physics into information that may be used to make engineering decisions. Often, this translation is implemented so that calculations may be done by machines (computers). This free course may be completed online at any time. See course site for detailed overview and learning outcomes. (Mechanical Engineering 205)Subjects

algebra | binary | numerical differentiation | newton-raphson | interpolation | regression | optimization | integration | fourier series | Engineering | H000License

Attribution 2.0 UK: England & Wales Attribution 2.0 UK: England & Wales http://creativecommons.org/licenses/by/2.0/uk/ http://creativecommons.org/licenses/by/2.0/uk/Site sourced from

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See all metadata9.913 Pattern Recognition for Machine Vision (MIT)

Description

The applications of pattern recognition techniques to problems of machine vision is the main focus for this course. Topics covered include, an overview of problems of machine vision and pattern classification, image formation and processing, feature extraction from images, biological object recognition, bayesian decision theory, and clustering.Subjects

comonent analysis | PCA | ICA | fourier analysis | vision | machine vision | pattern matching | pattern analysis | pattern recognition | scene analysis | tracking | feature extraction | color | color space | clustering | bayesian decisions | gesture recognition | action recognition | image processing | image formation | density estimation | classification | morphable models | component analysisLicense

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

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See all metadataHST.582J Biomedical Signal and Image Processing (MIT)

Description

This course presents the fundamentals of digital signal processing with particular emphasis on problems in biomedical research and clinical medicine. It covers principles and algorithms for processing both deterministic and random signals. Topics include data acquisition, imaging, filtering, coding, feature extraction, and modeling. The focus of the course is a series of labs that provide practical experience in processing physiological data, with examples from cardiology, speech processing, and medical imaging. The labs are done in MATLAB® during weekly lab sessions that take place in an electronic classroom. Lectures cover signal processing topics relevant to the lab exercises, as well as background on the biological signals processed in the labs.Subjects

HST.582 | 6.555 | 16.456 | signal processing | medicine | biological signal | diagnosis | diagnostic tool | physiology | cardiology | speech recognition | speech processing | imaging | medical imaging | MRI | ultrasound | ECG | electrocardiogram | fourier | FFT | applications of probabilitym | noise | MATLAB | digital filter | DSPLicense

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

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See all metadata18.034 Honors Differential Equations (MIT)

Description

This course covers the same material as 18.03 with more emphasis on theory. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.Subjects

First order equations | Separation | initial value problems | Systems | linear equations | independence of solutions | undetermined coefficients | Singular points | periodic orbits for planar systems | first order ode's | second order ode's | fourier series | laplace transform | linear systems | nonlinear systems | constant coefficientsLicense

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

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See all metadata6.003 Signals and Systems (MIT)

Description

This course covers fundamentals of signal and system analysis, with applications drawn from filtering, audio and image processing, communications, and automatic control. Topics include convolution, Fourier series and transforms, sampling and discrete-time processing of continuous-time signals, modulation, Laplace and Z-transforms, and feedback systems.Subjects

signal and system analysis | filtering | audio | audio processing | image processing | communications | automatic control | convolution | Fourier series | fourier transforms | sampling | discrete-time processing | modulation | Laplace transforms | Z-transforms | feedback systemsLicense

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