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Description

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications. This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.Subjects

Random matrix theory | Random matrix theory | Matrix Jacobians | Matrix Jacobians | Wishart Matrices | Wishart Matrices | Wigner's Semi-Circular laws | Wigner's Semi-Circular laws | Matrix beta ensembles | Matrix beta ensembles | free probability | free probability | spherical coordinates | spherical coordinates | wedging | wedging | Plucker coordinates | Plucker coordinates | matrix factorizations | matrix factorizations | householder transformations | householder transformations | Stiefel manifold | Stiefel manifold | Cauchey-Binet theorem | Cauchey-Binet theorem | Telatar's paper | Telatar's paper | level densities | level densities | orthogonal polynomials | orthogonal polynomials | matrix integrals | matrix integrals | hypergeometric functions | hypergeometric functions | wireless communictions | wireless communictions | eigenvalue density | eigenvalue density | sample covariance matrices | sample covariance matrices | Marcenko-Pastur theorem | Marcenko-Pastur theorem | wireless communications | wireless communicationsLicense

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See all metadata1.050 Solid Mechanics (MIT) 1.050 Solid Mechanics (MIT)

Description

Includes audio/video content: AV faculty introductions. 1.050 is a sophomore-level engineering mechanics course, commonly labelled "Statics and Strength of Materials" or "Solid Mechanics I." This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking. Includes audio/video content: AV faculty introductions. 1.050 is a sophomore-level engineering mechanics course, commonly labelled "Statics and Strength of Materials" or "Solid Mechanics I." This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking.Subjects

solid mechanics | solid mechanics | engineering design | engineering design | open ended exercises | open ended exercises | matrix analysis of structures | matrix analysis of structures | structural mechanics | structural mechanics | static equilibrium | static equilibrium | force resultants | force resultants | support conditions | support conditions | determinate planar structures | determinate planar structures | beams | beams | trusses | trusses | frames | frames | stress | stress | strain | strain | shear | shear | bending | bending | torsion | torsion | matrix methods | matrix methods | elastic stability | elastic stability | design exercises | design exercises | interactive exercises | interactive exercises | systems thinking | systems thinkingLicense

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 metadata7.06 Cell Biology (MIT) 7.06 Cell Biology (MIT)

Description

This course deals with the biology of cells of higher organisms: The structure, function, and biosynthesis of cellular membranes and organelles; cell growth and oncogenic transformation; transport, receptors, and cell signaling; the cytoskeleton, the extracellular matrix, and cell movements; chromatin structure and RNA synthesis. This course deals with the biology of cells of higher organisms: The structure, function, and biosynthesis of cellular membranes and organelles; cell growth and oncogenic transformation; transport, receptors, and cell signaling; the cytoskeleton, the extracellular matrix, and cell movements; chromatin structure and RNA synthesis.Subjects

Biology | Biology | cells | cells | organisms | organisms | biosynthesis | biosynthesis | cellular membranes | cellular membranes | organelles | organelles | cell growth | cell growth | oncogenic transformation | oncogenic transformation | transport | transport | receptors | receptors | cell signaling | cell signaling | cytoskeleton | cytoskeleton | extracellular matrix | extracellular matrix | matrix | matrix | cell movements | cell movements | chromatin | chromatin | RNA | RNA | RNA synthesis | RNA synthesisLicense

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 is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computingLicense

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

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See all metadata2.785J Cell-Matrix Mechanics (MIT) 2.785J Cell-Matrix Mechanics (MIT)

Description

Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine. Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine.Subjects

2.785 | 2.785 | 3.97 | 3.97 | 20.411 | 20.411 | HST.523 | HST.523 | cell | cell | matrix | matrix | mechanics | mechanics | tissue | tissue | organ | organ | development | development | injury | injury | stress field | stress field | cell function | cell function | deformed cells | deformed cells | biosynthetic activity | biosynthetic activity | unit cell | unit cell | connective tissue | connective tissue | cell biology | cell biology | physiology | physiology | medicine | medicine | cytoplasm | cytoplasm | extracellular matrix | extracellular matrix | skeleton | skeleton | bone | boneLicense

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See all metadataHST.523J Cell-Matrix Mechanics (MIT) HST.523J Cell-Matrix Mechanics (MIT)

Description

Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine. Mechanical forces play a decisive role during development of tissues and organs, during remodeling following injury as well as in normal function. A stress field influences cell function primarily through deformation of the extracellular matrix to which cells are attached. Deformed cells express different biosynthetic activity relative to undeformed cells. The unit cell process paradigm combined with topics in connective tissue mechanics form the basis for discussions of several topics from cell biology, physiology, and medicine.Subjects

cell | cell | tissue | tissue | organ | organ | unit cell process | unit cell process | cell matrix | cell matrix | tissue structure | tissue structure | extracellular matrix | extracellular matrix | adhesion protein | adhesion protein | integrin | integrin | cell force | cell force | cell contraction | cell contraction | healing | healing | skin | skin | scar | scar | tendon | tendon | ligament | ligament | cartilage | cartilage | bone | bone | collagen | collagen | muscle | muscle | nerve | nerve | implant | implant | HST.523 | HST.523 | 2.785 | 2.785 | 3.97 | 3.97 | 20.411 | 20.411License

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 is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems. This course is organized around algorithmic issues that arise in machine learning. Modern machine learning systems are often built on top of algorithms that do not have provable guarantees, and it is the subject of debate when and why they work. In this class, we focus on designing algorithms whose performance we can rigorously analyze for fundamental machine learning problems.Subjects

Machine learning | Machine learning | nonnegative matrix factorization | nonnegative matrix factorization | tensor decomposition | tensor decomposition | tensor rank | tensor rank | border rank | border rank | sparse coding | sparse coding | sparse recovery | sparse recovery | learning mixture model | learning mixture model | matrix completion | matrix completionLicense

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 is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic. This course is a student-presented seminar in combinatorics, graph theory, and discrete mathematics in general. Instruction and practice in written and oral communication is emphasized, with participants reading and presenting papers from recent mathematics literature and writing a final paper in a related topic.Subjects

discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math; discrete mathematics; discrete; math; mathematics; seminar; presentations; student presentations; oral; communication; stable marriage; dych; emergency; response vehicles; ambulance; game theory; congruences; color theorem; four color; cake cutting; algorithm; RSA; encryption; numberical integration; sorting; post correspondence problem; PCP; ramsey; van der waals; fibonacci; recursion; domino; tiling; towers; hanoi; pigeonhole; principle; matrix; hamming; code; hat game; juggling; zero-knowledge; proof; repeated games; lewis carroll; determinants; infinitude of primes; bridges; konigsberg; koenigsberg; time series analysis; GARCH; rational; recurrence; relations; digital; image; compression; quantum computing | discrete math | discrete math | discrete mathematics | discrete mathematics | discrete | discrete | math | math | mathematics | mathematics | seminar | seminar | presentations | presentations | student presentations | student presentations | oral | oral | communication | communication | stable marriage | stable marriage | dych | dych | emergency | emergency | response vehicles | response vehicles | ambulance | ambulance | game theory | game theory | congruences | congruences | color theorem | color theorem | four color | four color | cake cutting | cake cutting | algorithm | algorithm | RSA | RSA | encryption | encryption | numberical integration | numberical integration | sorting | sorting | post correspondence problem | post correspondence problem | PCP | PCP | ramsey | ramsey | van der waals | van der waals | fibonacci | fibonacci | recursion | recursion | domino | domino | tiling | tiling | towers | towers | hanoi | hanoi | pigeonhole | pigeonhole | principle | principle | matrix | matrix | hamming | hamming | code | code | hat game | hat game | juggling | juggling | zero-knowledge | zero-knowledge | proof | proof | repeated games | repeated games | lewis carroll | lewis carroll | determinants | determinants | infinitude of primes | infinitude of primes | bridges | bridges | konigsberg | konigsberg | koenigsberg | koenigsberg | time series analysis | time series analysis | GARCH | GARCH | rational | rational | recurrence | recurrence | relations | relations | digital | digital | image | image | compression | compression | quantum computing | quantum computingLicense

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 metadata18.996 Random Matrix Theory and Its Applications (MIT)

Description

This course is an introduction to the basics of random matrix theory, motivated by engineering and scientific applications.Subjects

Random matrix theory | Matrix Jacobians | Wishart Matrices | Wigner's Semi-Circular laws | Matrix beta ensembles | free probability | spherical coordinates | wedging | Plucker coordinates | matrix factorizations | householder transformations | Stiefel manifold | Cauchey-Binet theorem | Telatar's paper | level densities | orthogonal polynomials | matrix integrals | hypergeometric functions | wireless communictions | eigenvalue density | sample covariance matrices | Marcenko-Pastur theorem | wireless communicationsLicense

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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6.241 examines linear, discrete- and continuous-time, and multi-input-output systems in control and related areas. Least squares and matrix perturbation problems are considered. Topics covered include: state-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, minimality, internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, observer-based compensators, measures of control performance, and robustness issues using singular values of transfer functions. Nonlinear systems are also introduced. 6.241 examines linear, discrete- and continuous-time, and multi-input-output systems in control and related areas. Least squares and matrix perturbation problems are considered. Topics covered include: state-space models, modes, stability, controllability, observability, transfer function matrices, poles and zeros, minimality, internal stability of interconnected systems, feedback compensators, state feedback, optimal regulation, observers, observer-based compensators, measures of control performance, and robustness issues using singular values of transfer functions. Nonlinear systems are also introduced.Subjects

control | control | linear | linear | discrete | discrete | continuous-time | continuous-time | multi-input-output | multi-input-output | least squares | least squares | matrix perturbation | matrix perturbation | state-space models | stability | controllability | observability | transfer function matrices | poles | state-space models | stability | controllability | observability | transfer function matrices | poles | zeros | zeros | minimality | minimality | feedback | feedback | compensators | compensators | state feedback | state feedback | optimal regulation | optimal regulation | observers | transfer functions | observers | transfer functions | nonlinear systems | nonlinear systems | linear systems | linear systemsLicense

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

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See all metadata18.022 Calculus (MIT) 18.022 Calculus (MIT)

Description

This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra. This is an undergraduate course on calculus of several variables. It covers all of the topics covered in Calculus II (18.02), but presents them in greater depth. These topics are vector algebra in 3-space, determinants, matrices, vector-valued functions of one variable, space motion, scalar functions of several variables, partial differentiation, gradient, optimization techniques, double integrals, line integrals in the plane, exact differentials, conservative fields, Green's theorem, triple integrals, line and surface integrals in space, the divergence theorem, and Stokes' theorem. Additional topics covered in 18.022 are geometry, vector fields, and linear algebra.Subjects

vector algebra | vector algebra | determinant | determinant | matrix | matrix | matrices | matrices | vector-valued | vector-valued | functions | functions | space motion | space motion | scalar functions | scalar functions | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differentials | exact differentials | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem | divergence theorem | Stokes' theorem | Stokes' theorem | geometry | geometry | vector fields | vector fields | linear algebra | linear algebraLicense

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 is an introduction to principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Topics include methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. It also covers mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Other areas include tissue and organ regeneration; design of implants and prostheses based on control of biomaterials-tissue interactions; comparative analysis of intact, biodegradable, and bioreplaceable implants by reference to This course is an introduction to principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Topics include methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. It also covers mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Other areas include tissue and organ regeneration; design of implants and prostheses based on control of biomaterials-tissue interactions; comparative analysis of intact, biodegradable, and bioreplaceable implants by reference toSubjects

medical implants | medical implants | artificial organs | artificial organs | tissue engineering | tissue engineering | matrix | matrix | biomaterials | biomaterials | protein adsorption | protein adsorption | unit cell process | unit cell process | wound healing | wound healing | tissue remodeling | tissue remodeling | tissue regeneration | tissue regeneration | organ regeneration | organ regeneration | prosthesis | prosthesis | biodegradable | biodegradable | bioreplaceable implants | bioreplaceable implants | BE.441 | BE.441 | 2.79 | 2.79 | 3.96 | 3.96 | HST.522 | HST.522License

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See all metadata18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. This is a basic subject on matrix theory and linear algebra. Emphasis is given to topics that will be useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices.Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equations | linear algebra | linear algebra | determinants | determinants | eigenvalues | eigenvalues | similarity | similarity | least-squares approximations | least-squares approximations | stability of differential equations | stability of differential equations | networks | networksLicense

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 lab-oriented course introduces the student to the subject of X-ray spectrometry and micro-scale chemical quantitative analysis of solid samples through an intensive series of hands-on laboratory exercises that use the electron microprobe. This lab-oriented course introduces the student to the subject of X-ray spectrometry and micro-scale chemical quantitative analysis of solid samples through an intensive series of hands-on laboratory exercises that use the electron microprobe.Subjects

x-ray microanalysis | x-ray microanalysis | electron microprobe | electron microprobe | ZAF matrix corrections | ZAF matrix corrections | wavelength and energy dispersive spectrometry | wavelength and energy dispersive spectrometry | scanning backscattered electron | scanning backscattered electron | secondary electron | secondary electron | cathodoluminescence | cathodoluminescence | and X-ray imaging | and X-ray imagingLicense

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

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See all metadata8.323 Relativistic Quantum Field Theory I (MIT) 8.323 Relativistic Quantum Field Theory I (MIT)

Description

In 8.323, Relativistic Quantum Field Theory I, concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Topics include: Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields and spin 1/2 fields. Interacting fields and Feynman diagrams. In 8.323, Relativistic Quantum Field Theory I, concepts and basic techniques are developed through applications in elementary particle physics, and condensed matter physics.Topics include: Classical field theory, symmetries, and Noether's theorem. Quantization of scalar fields and spin 1/2 fields. Interacting fields and Feynman diagrams.Subjects

Quantum physics | Quantum physics | Classical field theory | Classical field theory | symmetries | symmetries | and Noether's theorem | and Noether's theorem | Quantization of scalar fields | Quantization of scalar fields | spin fields | spin fields | and Gauge bosons | and Gauge bosons | Feynman graphs | Feynman graphs | analytic properties of amplitudes and unitarity of the S-matrix | analytic properties of amplitudes and unitarity of the S-matrix | Calculations in quantum electrodynamics (QED) | Calculations in quantum electrodynamics (QED) | Introduction to renormalization | Introduction to renormalizationLicense

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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Solution of clinical problems by use of implants and other medical devices. Systematic use of cell-matrix control volumes. The role of stress analysis in the design process. Anatomic fit: shape and size of implants. Selection of biomaterials. Instrumentation for surgical implantation procedures. Preclinical testing for safety and efficacy: risk/benefit ratio assessment. Evaluation of clinical performance: design of clinical trials. Project materials drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants. Solution of clinical problems by use of implants and other medical devices. Systematic use of cell-matrix control volumes. The role of stress analysis in the design process. Anatomic fit: shape and size of implants. Selection of biomaterials. Instrumentation for surgical implantation procedures. Preclinical testing for safety and efficacy: risk/benefit ratio assessment. Evaluation of clinical performance: design of clinical trials. Project materials drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants.Subjects

clinical problems | clinical problems | implants | implants | medical devices | medical devices | cell-matrix control volumes | cell-matrix control volumes | stress analysis | stress analysis | Anatomic fit | Anatomic fit | biomaterials | biomaterials | surgical implantation procedures | surgical implantation procedures | Preclinical testing | Preclinical testing | risk/benefit ratio assessment | risk/benefit ratio assessment | clinical performance | clinical performance | clinical trials | clinical trials | orthopedic devices | orthopedic devices | soft tissue implants | soft tissue implants | artificial organs | artificial organs | dental implants | dental implants | BE.451J | BE.451J | 2.782 | 2.782 | 3.961 | 3.961 | BE.451 | BE.451 | HST.524 | HST.524 | 20.451 | 20.451License

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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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 .epSubjects

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 | 6.337License

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This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms). This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5503 (Analysis and Design of Algorithms).Subjects

algorithms | algorithms | efficient algorithms | efficient algorithms | sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide-and-conquer | divide-and-conquer | dynamic programming | dynamic programming | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest paths | network flow | network flow | computational geometry | computational geometry | number-theoretic algorithms | number-theoretic algorithms | polynomial and matrix calculations | polynomial and matrix calculations | caching | caching | parallel computing | parallel computing | SMA 5503 | SMA 5503 | 6.046 | 6.046License

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This course, intended for both graduate and upper level undergraduate students, will focus on understanding of the basic molecular structural principles of biological materials. It will address the molecular structures of various materials of biological origin, such as several types of collagen, silk, spider silk, wool, hair, bones, shells, protein adhesives, GFP, and self-assembling peptides. It will also address molecular design of new biological materials applying the molecular structural principles. The long-term goal of this course is to teach molecular design of new biological materials for a broad range of applications. A brief history of biological materials and its future perspective as well as its impact to the society will also be discussed. Several experts will be invited to gi This course, intended for both graduate and upper level undergraduate students, will focus on understanding of the basic molecular structural principles of biological materials. It will address the molecular structures of various materials of biological origin, such as several types of collagen, silk, spider silk, wool, hair, bones, shells, protein adhesives, GFP, and self-assembling peptides. It will also address molecular design of new biological materials applying the molecular structural principles. The long-term goal of this course is to teach molecular design of new biological materials for a broad range of applications. A brief history of biological materials and its future perspective as well as its impact to the society will also be discussed. Several experts will be invited to giSubjects

protein | protein | hydration | hydration | amino acid | amino acid | ECM | ECM | extracellular matrix | extracellular matrix | peptide | peptide | helix | helix | DNA | DNA | RNA | RNA | biomaterial | biomaterial | biotech | biotech | biotechnology | biotechnology | nanomaterial | nanomaterial | beta-sheet | beta-sheet | beta sheet | beta sheet | molecular structure | molecular structure | bioengineering | bioengineering | silk | silk | biomimetic | biomimetic | self-assembly | self-assembly | keratin | keratin | collagen | collagen | adhesive | adhesive | GFP | GFP | fluorescent | fluorescent | polymer | polymer | lipid | lipidLicense

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See all metadataBE.441 Biomaterials-Tissue Interactions (MIT) BE.441 Biomaterials-Tissue Interactions (MIT)

Description

This course is an introduction to principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Topics include methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. It also covers mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Other areas include tissue and organ regeneration; design of implants and prostheses based on control of biomaterials-tissue interactions; comparative analysis of intact, biodegradable, and bioreplaceable implants by reference to This course is an introduction to principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Topics include methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. It also covers mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Other areas include tissue and organ regeneration; design of implants and prostheses based on control of biomaterials-tissue interactions; comparative analysis of intact, biodegradable, and bioreplaceable implants by reference toSubjects

medical implants | medical implants | artificial organs | artificial organs | tissue engineering | tissue engineering | matrix | matrix | biomaterials | biomaterials | protein adsorption | protein adsorption | unit cell process | unit cell process | wound healing | wound healing | tissue remodeling | tissue remodeling | tissue regeneration | tissue regeneration | organ regeneration | organ regeneration | prosthesis | prosthesis | biodegradable | biodegradable | bioreplaceable implants | bioreplaceable implants | 2.79J | 2.79J | 3.96J | 3.96J | HST.522J | HST.522J | 2.79 | 2.79 | 3.96 | 3.96 | HST.522 | HST.522License

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 metadata6.046J Introduction to Algorithms (MIT) 6.046J Introduction to Algorithms (MIT)

Description

This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing. This course teaches techniques for the design and analysis of efficient algorithms, emphasizing methods useful in practice. Topics covered include: sorting; search trees, heaps, and hashing; divide-and-conquer; dynamic programming; amortized analysis; graph algorithms; shortest paths; network flow; computational geometry; number-theoretic algorithms; polynomial and matrix calculations; caching; and parallel computing.Subjects

algorithms | algorithms | efficient algorithms | efficient algorithms | sorting | sorting | search trees | search trees | heaps | heaps | hashing | hashing | divide-and-conquer | divide-and-conquer | dynamic programming | dynamic programming | amortized analysis | amortized analysis | graph algorithms | graph algorithms | shortest paths | shortest paths | network flow | network flow | computational geometry | computational geometry | number-theoretic algorithms | number-theoretic algorithms | polynomial and matrix calculations | polynomial and matrix calculations | caching | caching | parallel computing | parallel computing | 6.046 | 6.046 | 18.410 | 18.410License

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 metadata1.050 Solid Mechanics (MIT) 1.050 Solid Mechanics (MIT)

Description

This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking.Technical RequirementsJava® Virtual Machine software (automatically installed in most major web browsers) is required to run the .class files found on this course site. Java® plug-in software is required to run the This course introduces students to the fundamental principles and methods of structural mechanics. Topics covered include: static equilibrium, force resultants, support conditions, analysis of determinate planar structures (beams, trusses, frames), stresses and strains in structural elements, states of stress (shear, bending, torsion), statically indeterminate systems, displacements and deformations, introduction to matrix methods, elastic stability, and approximate methods. Design exercises are used to encourage creative student initiative and systems thinking.Technical RequirementsJava® Virtual Machine software (automatically installed in most major web browsers) is required to run the .class files found on this course site. Java® plug-in software is required to run theSubjects

elastic stability | elastic stability | matrix methods | matrix methods | statically indeterminate systems | statically indeterminate systems | torsion | torsion | bending | bending | shearing | shearing | strains in structural elements | strains in structural elements | stress | stress | beams | beams | frames | frames | determinate planar structures | determinate planar structures | support conditions | support conditions | static equilibrium | static equilibriumLicense

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 metadata18.06 Linear Algebra (MIT) 18.06 Linear Algebra (MIT)

Description

Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc. Basic subject on matrix theory and linear algebra, emphasizing topics useful in other disciplines, including systems of equations, vector spaces, determinants, eigenvalues, similarity, and positive definite matrices. Applications to least-squares approximations, stability of differential equations, networks, Fourier transforms, and Markov processes. Uses MATLAB®. Compared with 18.700 [also Linear Algebra], more emphasis on matrix algorithms and many applications. MATLAB® is a trademark of The MathWorks, Inc.Subjects

Generalized spaces | Generalized spaces | Linear algebra | Linear algebra | Algebra | Universal | Algebra | Universal | Mathematical analysis | Mathematical analysis | Calculus of operations | Calculus of operations | Line geometry | Line geometry | Topology | Topology | matrix theory | matrix theory | systems of equations | systems of equations | vector spaces | vector spaces | systems determinants | systems determinants | eigen values | eigen values | positive definite matrices | positive definite matrices | Markov processes | Markov processes | Fourier transforms | Fourier transforms | differential equations | differential equationsLicense

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

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See all metadata12.141 Electron Microprobe Analysis (MIT) 12.141 Electron Microprobe Analysis (MIT)

Description

Introduction to the theory of x-ray microanalysis through the electron microprobe including ZAF matrix corrections. Techniques to be discussed are wavelength and energy dispersive spectrometry, scanning backscattered electron, secondary electron, cathodoluminescence, and X-ray imaging. Lab sessions involve hands-on use of the electron microprobe.Offered for undergraduate credit, but persons interested in an in-depth discussion of quantitative x-ray analysis are invited to participate. Students will be required to complete lab exercises to obtain credit. Introduction to the theory of x-ray microanalysis through the electron microprobe including ZAF matrix corrections. Techniques to be discussed are wavelength and energy dispersive spectrometry, scanning backscattered electron, secondary electron, cathodoluminescence, and X-ray imaging. Lab sessions involve hands-on use of the electron microprobe.Offered for undergraduate credit, but persons interested in an in-depth discussion of quantitative x-ray analysis are invited to participate. Students will be required to complete lab exercises to obtain credit.Subjects

x-ray microanalysis | x-ray microanalysis | electron microprobe | electron microprobe | ZAF matrix corrections | ZAF matrix corrections | wavelength and energy dispersive spectrometry | wavelength and energy dispersive spectrometry | scanning backscattered electron | scanning backscattered electron | secondary electron | secondary electron | cathodoluminescence | cathodoluminescence | X-ray imaging | X-ray imagingLicense

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See all metadata2.003SC Engineering Dynamics (MIT) 2.003SC Engineering Dynamics (MIT)

Description

Includes audio/video content: AV lectures. This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange's equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems. Includes audio/video content: AV lectures. This course is an introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Topics covered include kinematics, force-momentum formulation for systems of particles and rigid bodies in planar motion, work-energy concepts, virtual displacements and virtual work. Students will also become familiar with the following topics: Lagrange's equations for systems of particles and rigid bodies in planar motion, and linearization of equations of motion. After this course, students will be able to evaluate free and forced vibration of linear multi-degree of freedom models of mechanical systems and matrix eigenvalue problems.Subjects

dynamics and vibrations | dynamics and vibrations | lumped-parameter models | lumped-parameter models | kinematics | kinematics | momentum | momentum | systems of particles and rigid bodies | systems of particles and rigid bodies | work-energy concepts | work-energy concepts | virtual displacements and virtual work | virtual displacements and virtual work | Lagrange's equations | Lagrange's equations | equations of motion | equations of motion | linear stability analysis | linear stability analysis | free and forced vibration | free and forced vibration | linear multi-degree of freedom models | linear multi-degree of freedom models | matrix eigenvalue problems | matrix eigenvalue problemsLicense

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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