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18.022 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 mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers. This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers.Subjects

optimization | optimization | multidisciplinary design optimization | multidisciplinary design optimization | MDO | MDO | subsystem identification | subsystem identification | interface design | interface design | linear constrained optimization fomulation | linear constrained optimization fomulation | non-linear constrained optimization formulation | non-linear constrained optimization formulation | scalar optimization | scalar optimization | vector optimization | vector optimization | systems engineering | systems engineering | complex systems | complex systems | heuristic search methods | heuristic search methods | tabu search | tabu search | simulated annealing | simulated annealing | genertic algorithms | genertic algorithms | sensitivity | sensitivity | tradeoff analysis | tradeoff analysis | goal programming | goal programming | isoperformance | isoperformance | pareto optimality | pareto optimality | flowchart | flowchart | design vector | design vector | simulation model | simulation model | objective vector | objective vector | input | input | discipline | discipline | output | output | coupling | coupling | multiobjective optimization | multiobjective optimization | optimization algorithms | optimization algorithms | tradespace exploration | tradespace exploration | numerical techniques | numerical techniques | direct methods | direct methods | penalty methods | penalty methods | heuristic techniques | heuristic techniques | SA | SA | GA | GA | approximation methods | approximation methods | sensitivity analysis | sensitivity analysis | isoperformace | isoperformace | output evaluation | output evaluation | MSDO framework | MSDO frameworkLicense

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 of Several Variables (MIT) 18.022 Calculus of Several Variables (MIT)

Description

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts. This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.Subjects

vector algebra | vector algebra | determinant | determinant | matrix | matrix | matrices | matrices | vector-valued functions | vector-valued 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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See all metadataMAS.622J Pattern Recognition and Analysis (MIT) MAS.622J Pattern Recognition and Analysis (MIT)

Description

This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class. This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class.Subjects

MAS.622 | MAS.622 | 1.126 | 1.126 | pattern recognition | pattern recognition | feature detection | feature detection | classification | classification | probability theory | probability theory | pattern analysis | pattern analysis | conditional probability | conditional probability | bayes rule | bayes rule | random vectors | decision theory | random vectors | decision theory | ROC curves | ROC curves | likelihood ratio test | likelihood ratio test | fisher discriminant | fisher discriminant | template-based recognition | template-based recognition | feature extraction | feature extraction | eigenvector and multilinear analysis | eigenvector and multilinear analysis | linear discriminant | linear discriminant | perceptron learning | perceptron learning | optimization by gradient descent | optimization by gradient descent | support vecotr machines | support vecotr machines | K-nearest-neighbor classification | K-nearest-neighbor classification | parzen estimation | parzen estimation | unsupervised learning | unsupervised learning | clustering | clustering | vector quantization | vector quantization | K-means | K-means | Expectation-Maximization | Expectation-Maximization | Hidden markov models | Hidden markov models | viterbi algorithm | viterbi algorithm | Baum-Welch algorithm | Baum-Welch algorithm | linear dynamical systems | linear dynamical systems | Kalman filtering | Kalman filtering | Bayesian networks | Bayesian networks | decision trees | decision trees | reinforcement learning | reinforcement learning | genetic algorithms | genetic algorithmsLicense

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 metadataMathematical Methods II Mathematical Methods II

Description

This course consists of a introduction to linear algebra. This course consists of a introduction to linear algebra.Subjects

Bachelor in Statistics and Business | Bachelor in Statistics and Business | Algebra | Algebra | Prerequisites | Prerequisites | Systems of linear equations | Systems of linear equations | Eigenvalues and eigenvectors | Eigenvalues and eigenvectors | General information | General information | Orthogonality and least-square problems | Orthogonality and least-square problems | Singular value decomposition | Singular value decomposition | ística y Empresa | ística y Empresa | Real vector spaces | Real vector spaces | Matrices and determinants | Matrices and determinants | Diagonalization | Diagonalization | 2012 | 2012License

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Curso centrado en los fundamentos de los problemas lineales: algebra matricial y espacios vectoriales. Curso centrado en los fundamentos de los problemas lineales: algebra matricial y espacios vectoriales.Subjects

ía Telemática | ía Telemática | Autovalores y autovectores | Autovalores y autovectores | Espacios vectoriales | Espacios vectoriales | 2009 | 2009 | Matrices | Matrices | ínimos cuadrados | ínimos cuadradosLicense

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See all metadata8.033 Relativity (MIT) 8.033 Relativity (MIT)

Description

Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay. Relativity is normally taken by physics majors in their sophomore year. Topics include: Einstein's postulates; consequences for simultaneity, time dilation, length contraction, clock synchronization; Lorentz transformation; relativistic effects and paradoxes; Minkowski diagrams; invariants and four-vectors; momentum, energy and mass; and particle collisions. Also covered is: Relativity and electricity; Coulomb's law; and magnetic fields. Brief introduction to Newtonian cosmology. There is also an introduction to some concepts of General Relativity; principle of equivalence; the Schwarzchild metric; gravitational red shift, particle and light trajectories, geodesics, and Shapiro delay.Subjects

Einstein's postulates | Einstein's postulates | consequences for simultaneity | time dilation | length contraction | clock synchronization | consequences for simultaneity | time dilation | length contraction | clock synchronization | Lorentz transformation | Lorentz transformation | relativistic effects and paradoxes | relativistic effects and paradoxes | Minkowski diagrams | Minkowski diagrams | invariants and four-vectors | invariants and four-vectors | momentum | energy and mass | momentum | energy and mass | particle collisions | particle collisions | Relativity and electricity | Relativity and electricity | Coulomb's law | Coulomb's law | magnetic fields | magnetic fields | Newtonian cosmology | Newtonian cosmology | General Relativity | General Relativity | principle of equivalence | principle of equivalence | the Schwarzchild metric | the Schwarzchild metric | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | particle and light trajectories | geodesics | Shapiro delay | gravitational red shift | gravitational red shift | particle trajectories | particle trajectories | light trajectories | light trajectories | invariants | invariants | four-vectors | four-vectors | momentum | momentum | energy | energy | mass | mass | relativistic effects | relativistic effects | paradoxes | paradoxes | electricity | electricity | time dilation | time dilation | length contraction | length contraction | clock synchronization | clock synchronization | Schwarzchild metric | Schwarzchild metric | geodesics | geodesics | Shaprio delay | Shaprio delay | relativistic kinematics | relativistic kinematics | relativistic dynamics | relativistic dynamics | electromagnetism | electromagnetism | hubble expansion | hubble expansion | universe | universe | equivalence principle | equivalence principle | curved space time | curved space time | Ether Theory | Ether Theory | constants | constants | speed of light | speed of light | c | c | graph | graph | pythagorem theorem | pythagorem theorem | triangle | triangle | arrows | arrowsLicense

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 metadata6.823 Computer System Architecture (MIT) 6.823 Computer System Architecture (MIT)

Description

6.823 is a study of the evolution of computer architecture and the factors influencing the design of hardware and software elements of computer systems. Topics may include: instruction set design; processor micro-architecture and pipelining; cache and virtual memory organizations; protection and sharing; I/O and interrupts; in-order and out-of-order superscalar architectures; VLIW machines; vector supercomputers; multithreaded architectures; symmetric multiprocessors; and parallel computers. 6.823 is a study of the evolution of computer architecture and the factors influencing the design of hardware and software elements of computer systems. Topics may include: instruction set design; processor micro-architecture and pipelining; cache and virtual memory organizations; protection and sharing; I/O and interrupts; in-order and out-of-order superscalar architectures; VLIW machines; vector supercomputers; multithreaded architectures; symmetric multiprocessors; and parallel computers.Subjects

computer architecture | | computer architecture | | computer system architecture | | computer system architecture | | hardware | | hardware | | hardware design | | hardware design | | software | | software | | software design | | software design | | instruction set design | | instruction set design | | processor micro-architecture | | processor micro-architecture | | pipelining | | pipelining | | cache memory | | cache memory | | irtual memory | | irtual memory | | I/O | | I/O | | input/output | | input/output | | interrupts | | interrupts | | superscalar architectures | | superscalar architectures | | VLIW machines | | VLIW machines | | vector supercomputers | | vector supercomputers | | multithreaded architectures | | multithreaded architectures | | symmetric multiprocessors | | symmetric multiprocessors | | parallel computers | parallel computers | computer architecture | computer architecture | computer system architecture | computer system architecture | hardware | hardware | hardware design | hardware design | software | software | software design | software design | instruction set design | instruction set design | processor micro-architecture | processor micro-architecture | pipelining | pipelining | cache memory | cache memory | virtual memory | virtual memory | I/O | I/O | input/output | input/output | interrupts | interrupts | superscalar architectures | superscalar architectures | VLIW machines | VLIW machines | vector supercomputers | vector supercomputers | multithreaded architectures | multithreaded architectures | symmetric multiprocessors | symmetric multiprocessorsLicense

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 metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods | Laplace transform methods | Matrix systems | Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagrams | constant coefficients | constant coefficients | complex numbers | complex numbers | exponentials | exponentials | eigenvalues | eigenvalues | eigenvectors | eigenvectorsLicense

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.S997 Introduction To MATLAB Programming (MIT) 18.S997 Introduction To MATLAB Programming (MIT)

Description

Includes audio/video content: AV lectures. This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular. Includes audio/video content: AV lectures. This course is intended to assist undergraduates with learning the basics of programming in general and programming MATLAB® in particular.Subjects

MATLAB | programming | MATLAB | programming | variables | variables | plotting | plotting | scripts | scripts | functions | functions | flow control | flow control | statistics | statistics | data structures | data structures | images | images | vectors | vectors | matrices | matrices | root-finding | root-finding | Newton's Method | Newton's Method | Secant Method | Secant Method | Basins of Attraction | Basins of Attraction | Conway Game of Life | Conway Game of Life | Game of Life | Game of Life | vectorization | vectorization | debugging | debugging | scope | scope | function block | function blockLicense

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 metadata7.01SC Fundamentals of Biology (MIT) 7.01SC Fundamentals of Biology (MIT)

Description

Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and recombinant DNA. These principles are necessary to understanding the basic mechanisms of life and anchor the biological knowledge that is required to understand many of the challenges in everyday life, from human health and disease to loss of biodiversity and environmental quality. Fundamentals of Biology focuses on the basic principles of biochemistry, molecular biology, genetics, and recombinant DNA. These principles are necessary to understanding the basic mechanisms of life and anchor the biological knowledge that is required to understand many of the challenges in everyday life, from human health and disease to loss of biodiversity and environmental quality.Subjects

amino acids | amino acids | carboxyl group | carboxyl group | amino group | amino group | side chains | side chains | polar | polar | hydrophobic | hydrophobic | primary structure | primary structure | secondary structure | secondary structure | tertiary structure | tertiary structure | quaternary structure | quaternary structure | x-ray crystallography | x-ray crystallography | alpha helix | alpha helix | beta sheet | beta sheet | ionic bond | ionic bond | non-polar bond | non-polar bond | van der Waals interactions | van der Waals interactions | proton gradient | proton gradient | cyclic photophosphorylation | cyclic photophosphorylation | sunlight | sunlight | ATP | ATP | chlorophyll | chlorophyll | chlorophyll a | chlorophyll a | electrons | electrons | hydrogen sulfide | hydrogen sulfide | biosynthesis | biosynthesis | non-cyclic photophosphorylation | non-cyclic photophosphorylation | photosystem II | photosystem II | photosystem I | photosystem I | cyanobacteria | cyanobacteria | chloroplast | chloroplast | stroma | stroma | thylakoid membrane | thylakoid membrane | Genetics | Genetics | Mendel | Mendel | Mendel's Laws | Mendel's Laws | cloning | cloning | restriction enzymes | restriction enzymes | vector | vector | insert DNA | insert DNA | ligase | ligase | library | library | E.Coli | E.Coli | phosphatase | phosphatase | yeast | yeast | transformation | transformation | ARG1 gene | ARG1 gene | ARG1 mutant yeast | ARG1 mutant yeast | yeast wild-type | yeast wild-type | cloning by complementation | cloning by complementation | Human Beta Globin gene | Human Beta Globin gene | protein tetramer | protein tetramer | vectors | vectors | antibodies | antibodies | human promoter | human promoter | splicing | splicing | mRNA | mRNA | cDNA | cDNA | reverse transcriptase | reverse transcriptase | plasmid | plasmid | electrophoresis | electrophoresis | DNA sequencing | DNA sequencing | primer | primer | template | template | capillary tube | capillary tube | laser detector | laser detector | human genome project | human genome project | recombinant DNA | recombinant DNA | clone | clone | primer walking | primer walking | subcloning | subcloning | computer assembly | computer assembly | shotgun sequencing | shotgun sequencing | open reading frame | open reading frame | databases | databases | polymerase chain reaction (PCR) | polymerase chain reaction (PCR) | polymerase | polymerase | nucleotides | nucleotides | Thermus aquaticus | Thermus aquaticus | Taq polymerase | Taq polymerase | thermocycler | thermocycler | resequencing | resequencing | in vitro fertilization | in vitro fertilization | pre-implantation diagnostics | pre-implantation diagnostics | forensics | forensics | genetic engineering | genetic engineering | DNA sequences | DNA sequences | therapeutic proteins | therapeutic proteins | E. coli | E. coli | disease-causing mutations | disease-causing mutations | cleavage of DNA | cleavage of DNA | bacterial transformation | bacterial transformation | recombinant DNA revolution | recombinant DNA revolution | biotechnology industry | biotechnology industry | Robert Swanson | Robert Swanson | toxin gene | toxin gene | pathogenic bacterium | pathogenic bacterium | biomedical research | biomedical research | S. Pyogenes | S. Pyogenes | origin of replication | origin of replicationLicense

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 metadata18.02SC Multivariable Calculus (MIT) 18.02SC Multivariable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics. Includes audio/video content: AV lectures. This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.Subjects

calculus | calculus | calculus of several variables | calculus of several variables | vector algebra | vector algebra | determinants | determinants | matrix | matrix | matrices | matrices | vector-valued function | vector-valued function | space motion | space motion | scalar function | scalar function | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differential | exact differential | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem Stokes' theorem | divergence theorem Stokes' theorem | applications | applicationsLicense

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 metadata18.02 Multivariable Calculus (MIT) 18.02 Multivariable Calculus (MIT)

Description

Includes audio/video content: AV lectures. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates. Includes audio/video content: AV lectures. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.Subjects

calculus | calculus | calculus of several variables | calculus of several variables | vector algebra | vector algebra | determinants | determinants | matrix | matrix | matrices | matrices | vector-valued function | vector-valued function | space motion | space motion | scalar function | scalar function | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differential | exact differential | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem Stokes' theorem | divergence theorem Stokes' theorem | applications | applicationsLicense

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 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 metadata18.02 Multivariable Calculus (MIT) 18.02 Multivariable Calculus (MIT)

Description

This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space. This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.Subjects

Calculus | Calculus | calculus of several variables | calculus of several variables | vector algebra | vector algebra | determinants | determinants | matrix | matrix | matrices | matrices | vector-valued function | vector-valued function | space motion | space motion | scalar function | scalar function | partial differentiation | partial differentiation | gradient | gradient | optimization techniques | optimization techniques | double integrals | double integrals | line integrals | line integrals | exact differential | exact differential | conservative fields | conservative fields | Green's theorem | Green's theorem | triple integrals | triple integrals | surface integrals | surface integrals | divergence theorem Stokes' theorem | divergence theorem Stokes' theorem | applications | applicationsLicense

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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Includes audio/video content: AV selected lectures. This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Includes audio/video content: AV selected lectures. This course is about the mathematics that is most widely used in the mechanical engineering core subjects: An introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations.Subjects

differential equations | differential equations | linear algebra | linear algebra | linear differential equations | linear differential equations | ordinary | ordinary | partial | partial | vector space | vector space | first order | first order | second order | second order | Heaviside | Heaviside | delta | delta | Dirac | Dirac | exponential | exponential | sinusoid | sinusoid | real | real | complex | complex | forced oscillations | forced oscillations | Laplace transform | Laplace transform | graph | graph | nonlinear | nonlinear | source | source | sink | sink | saddle | saddle | spiral | spiral | Euler | Euler | linearization | linearization | Guassian | Guassian | matrix | matrix | mechanical engineer | mechanical engineer | eigenvector | eigenvector | eigenvalue | eigenvalue | exponentiation | exponentiation | least squares | least squaresLicense

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 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 | determinant | matrix | matrices | vector-valued | functions | space motion | scalar functions | partial differentiation | gradient | optimization techniques | double integrals | line integrals | exact differentials | conservative fields | Green's theorem | triple integrals | surface integrals | divergence theorem | Stokes' theorem | geometry | vector fields | 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 https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadata16.888 Multidisciplinary System Design Optimization (MIT)

Description

This course is mainly focused on the quantitative aspects of design and presents a unifying framework called "Multidisciplinary System Design Optimization" (MSDO). The objective of the course is to present tools and methodologies for performing system optimization in a multidisciplinary design context, focusing on three aspects of the problem: (i) The multidisciplinary character of engineering systems, (ii) design of these complex systems, and (iii) tools for optimization. There is a version of this course (16.60s) offered through the MIT Professional Institute, targeted at professional engineers.Subjects

optimization | multidisciplinary design optimization | MDO | subsystem identification | interface design | linear constrained optimization fomulation | non-linear constrained optimization formulation | scalar optimization | vector optimization | systems engineering | complex systems | heuristic search methods | tabu search | simulated annealing | genertic algorithms | sensitivity | tradeoff analysis | goal programming | isoperformance | pareto optimality | flowchart | design vector | simulation model | objective vector | input | discipline | output | coupling | multiobjective optimization | optimization algorithms | tradespace exploration | numerical techniques | direct methods | penalty methods | heuristic techniques | SA | GA | approximation methods | sensitivity analysis | isoperformace | output evaluation | MSDO frameworkLicense

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 metadata18.022 Calculus of Several Variables (MIT)

Description

This is a variation on 18.02 Multivariable Calculus. It covers the same topics as in 18.02, but with more focus on mathematical concepts.Subjects

vector algebra | determinant | matrix | matrices | vector-valued functions | space motion | scalar functions | partial differentiation | gradient | optimization techniques | double integrals | line integrals | exact differentials | conservative fields | Green's theorem | triple integrals | surface integrals | divergence theorem | Stokes' theorem | geometry | vector fields | 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 https://ocw.mit.edu/terms/index.htmSite sourced from

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See all metadataMAS.622J Pattern Recognition and Analysis (MIT)

Description

This class deals with the fundamentals of characterizing and recognizing patterns and features of interest in numerical data. We discuss the basic tools and theory for signal understanding problems with applications to user modeling, affect recognition, speech recognition and understanding, computer vision, physiological analysis, and more. We also cover decision theory, statistical classification, maximum likelihood and Bayesian estimation, nonparametric methods, unsupervised learning and clustering. Additional topics on machine and human learning from active research are also talked about in the class.Subjects

MAS.622 | 1.126 | pattern recognition | feature detection | classification | probability theory | pattern analysis | conditional probability | bayes rule | random vectors | decision theory | ROC curves | likelihood ratio test | fisher discriminant | template-based recognition | feature extraction | eigenvector and multilinear analysis | linear discriminant | perceptron learning | optimization by gradient descent | support vecotr machines | K-nearest-neighbor classification | parzen estimation | unsupervised learning | clustering | vector quantization | K-means | Expectation-Maximization | Hidden markov models | viterbi algorithm | Baum-Welch algorithm | linear dynamical systems | Kalman filtering | Bayesian networks | decision trees | reinforcement learning | genetic algorithmsLicense

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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Se estudian tanto los convertidores estáticos de potencia ac/dc para accionamientos de corriente continua (rectificadores y troceadores (choppers)), como la regulación de los mismo aplicados a la máquina de corriente continua. Tambien se trata el funcionamiento de los convertidores estáticos de potencia para accionamientos de corriente alterna. Pero el contenido fundamental de la asignatura se centra en el control vectorial, tanto el de un inversor en cuatro cuadrantes, de la máquina síncrona como el de máquinas asíncronas de jaula. Se estudian tanto los convertidores estáticos de potencia ac/dc para accionamientos de corriente continua (rectificadores y troceadores (choppers)), como la regulación de los mismo aplicados a la máquina de corriente continua. Tambien se trata el funcionamiento de los convertidores estáticos de potencia para accionamientos de corriente alterna. Pero el contenido fundamental de la asignatura se centra en el control vectorial, tanto el de un inversor en cuatro cuadrantes, de la máquina síncrona como el de máquinas asíncronas de jaula.Subjects

Control vectorial de inversor | Control vectorial de inversor | 2009 | 2009 | áquinas de corriente continua | áquinas de corriente continua | Convertidores de corriente continua y corriente alterna | Convertidores de corriente continua y corriente alterna | áquinas electricas | áquinas electricas | ía Industrial | ía Industrial | íncrona | íncrona | áquinas de inducción | áquinas de inducción | ía Eléctrica | ía EléctricaLicense

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See all metadata18.024 Calculus with Theory II (MIT) 18.024 Calculus with Theory II (MIT)

Description

This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. 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 and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-Taylor This course is a continuation of 18.014. It covers the same material as 18.02 (Calculus), but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.Topics include: Calculus of several variables. 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 and line integrals in the plane; exact differentials and conservative fields; Green's theorem and applications, triple integrals, line and surface integrals in space, Divergence theorem, Stokes' theorem; applications. Dr. Lachowska wishes to acknowledge Andrew Brooke-TaylorSubjects

linear algebra | linear algebra | vector integral calculus | vector integral calculus | Calculus of several variables | Calculus of several variables | Vector algebra in 3-space | Vector algebra in 3-space | determinants | determinants | matrices | matrices | Vector-valued functions of one variable | Vector-valued functions of one variable | space motion | space motion | Scalar functions of several variables: partial differentiation | Scalar functions of several variables: partial differentiation | gradient | gradient | optimization techniques | optimization techniques | Double integrals and line integrals in the plane | Double integrals and line integrals in the plane | exact differentials and conservative fields | exact differentials and conservative fields | Green's theorem and applications | Green's theorem and applications | triple integrals | triple integrals | line and surface integrals in space | line and surface integrals in space | Divergence theorem | Divergence theorem | Stokes' theorem | Stokes' theorem | applications | applicationsLicense

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 metadata18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues andSubjects

Ordinary Differential Equations | Ordinary Differential Equations | ODE | ODE | modeling physical systems | modeling physical systems | first-order ODE's | first-order ODE's | Linear ODE's | Linear ODE's | second order ODE's | second order ODE's | second order ODE's with constant coefficients | second order ODE's with constant coefficients | Undetermined coefficients | Undetermined coefficients | variation of parameters | variation of parameters | Sinusoidal signals | Sinusoidal signals | exponential signals | exponential signals | oscillations | oscillations | damping | damping | resonance | resonance | Complex numbers and exponentials | Complex numbers and exponentials | Fourier series | Fourier series | periodic solutions | periodic solutions | Delta functions | Delta functions | convolution | convolution | Laplace transform methods Matrix systems | Laplace transform methods Matrix systems | first order linear systems | first order linear systems | eigenvalues and eigenvectors | eigenvalues and eigenvectors | Non-linear autonomous systems | Non-linear autonomous systems | critical point analysis | critical point analysis | phase plane diagrams | phase plane diagramsLicense

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 metadata18.701 Algebra I (MIT) 18.701 Algebra I (MIT)

Description

This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups. This undergraduate level Algebra I course covers groups, vector spaces, linear transformations, symmetry groups, bilinear forms, and linear groups.Subjects

Group Theory | Group Theory | Linear Algebra | and Geometry | Linear Algebra | and Geometry | groups | groups | vector spaces | vector spaces | linear transformations | linear transformations | symmetry groups | symmetry groups | bilinear | bilinear | bilinear forms | and linear groups | bilinear forms | and linear groupsLicense

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

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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