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18.03 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 and

Subjects

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 diagrams

License

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18.03 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 and

Subjects

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 | eigenvectors

License

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

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18.03SC Differential Equations (MIT) 18.03SC Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering. Includes audio/video content: AV lectures. The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Subjects

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

License

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

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18.03 Differential Equations (MIT) 18.03 Differential Equations (MIT)

Description

Includes audio/video content: AV lectures. 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. Includes audio/video content: AV lectures. 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.

Subjects

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

License

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

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18.03 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.

Subjects

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

License

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

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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

Subjects

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

License

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

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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

Subjects

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

License

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

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18.03SC Differential Equations (MIT)

Description

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Subjects

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

License

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

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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.

Subjects

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

License

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

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18.336 Numerical Methods of Applied Mathematics II (MIT) 18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

Linear systems | Linear systems | Fast Fourier Transform | Fast Fourier Transform | Wave equation | Wave equation | Von Neumann analysis | Von Neumann analysis | Conditions for stability | Conditions for stability | Dissipation | Dissipation | Multistep schemes | Multistep schemes | Dispersion | Dispersion | Group Velocity | Group Velocity | Propagation of Wave Packets | Propagation of Wave Packets | Parabolic Equations | Parabolic Equations | The Du Fort Frankel Scheme | The Du Fort Frankel Scheme | Convection-Diffusion equation | Convection-Diffusion equation | ADI Methods | ADI Methods | Elliptic Equations | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | Jacobi | Gauss-Seidel and SOR(w) | ODEs | ODEs | finite differences | finite differences | spectral methods | spectral methods | well-posedness and stability | well-posedness and stability | boundary and nonlinear instabilities | boundary and nonlinear instabilities | Finite Difference Schemes | Finite Difference Schemes | Partial Differential Equations | Partial Differential Equations

License

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

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18.336 Numerical Methods of Applied Mathematics II (MIT) 18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.

Subjects

Linear systems | Linear systems | Fast Fourier Transform | Fast Fourier Transform | Wave equation | Wave equation | Von Neumann analysis | Von Neumann analysis | Conditions for stability | Conditions for stability | Dissipation | Dissipation | Multistep schemes | Multistep schemes | Dispersion | Dispersion | Group Velocity | Group Velocity | Propagation of Wave Packets | Propagation of Wave Packets | Parabolic Equations | Parabolic Equations | The Du Fort Frankel Scheme | The Du Fort Frankel Scheme | Convection-Diffusion equation | Convection-Diffusion equation | ADI Methods | ADI Methods | Elliptic Equations | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | Jacobi | Gauss-Seidel and SOR(w) | ODEs | ODEs | finite differences | finite differences | spectral methods | spectral methods | well-posedness and stability | well-posedness and stability | boundary and nonlinear instabilities | boundary and nonlinear instabilities | Finite Difference Schemes | Finite Difference Schemes | Partial Differential Equations | Partial Differential Equations

License

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

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

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

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2.997 Decision Making in Large Scale Systems (MIT) 2.997 Decision Making in Large Scale Systems (MIT)

Description

This course is an introduction to the theory and application of large-scale dynamic programming. Topics include Markov decision processes, dynamic programming algorithms, simulation-based algorithms, theory and algorithms for value function approximation, and policy search methods. The course examines games and applications in areas such as dynamic resource allocation, finance and queueing networks. This course is an introduction to the theory and application of large-scale dynamic programming. Topics include Markov decision processes, dynamic programming algorithms, simulation-based algorithms, theory and algorithms for value function approximation, and policy search methods. The course examines games and applications in areas such as dynamic resource allocation, finance and queueing networks.

Subjects

algorithm | algorithm | markov decision process | markov decision process | dynamic programming | dynamic programming | stochastic models | stochastic models | policy iteration | policy iteration | Q-Learning | Q-Learning | reinforcement learning | reinforcement learning | Lyapunov function | Lyapunov function | ODE | ODE | TD-Learning | TD-Learning | value function approximation | value function approximation | linear programming | linear programming | policy search | policy search | policy gradient | policy gradient | actor-critic | actor-critic | experts algorithm | experts algorithm | regret minimization and calibration | regret minimization and calibration | games. | games.

License

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3.016 Mathematics for Materials Scientists and Engineers (MIT) 3.016 Mathematics for Materials Scientists and Engineers (MIT)

Description

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

Subjects

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 | simulation

License

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14.02 Principles of Macroeconomics (MIT) 14.02 Principles of Macroeconomics (MIT)

Description

This course provides an overview of the following macroeconomic issues: the determination of output, employment, unemployment, interest rates, and inflation. Monetary and fiscal policies are discussed, as are public debt and international economic issues. This course also introduces basic models of macroeconomics and illustrates principles with the experience of the United States and other economies. This course provides an overview of the following macroeconomic issues: the determination of output, employment, unemployment, interest rates, and inflation. Monetary and fiscal policies are discussed, as are public debt and international economic issues. This course also introduces basic models of macroeconomics and illustrates principles with the experience of the United States and other economies.

Subjects

macroeconomics | macroeconomics | economics | economics | output | output | employment | employment | determination | determination | unemployment | unemployment | interest rates | interest rates | Federal Reserve | Federal Reserve | inflation | inflation | monetary policy | monetary policy | fiscal policy | fiscal policy | public debt | public debt | international economics | international economics | goods market | goods market | market | market | financial markets | financial markets | open economy | open economy | exchange rate | exchange rate | labor market | labor market | phillips curve | phillips curve | growth | growth | Solow's model | Solow's model | MACROECONOMICS | MACROECONOMICS | ECONOMICS | ECONOMICS | OUTPUT | OUTPUT | Macroeconomics | Macroeconomics | EMPLOYMENT | EMPLOYMENT | DETERMINATION | DETERMINATION | UNEMPLOYMENT | UNEMPLOYMENT | INTEREST RATES | INTEREST RATES | FEDERAL RESERVE | FEDERAL RESERVE | INFLATION | INFLATION | MONETARY POLICY | MONETARY POLICY | FISCAL POLICY | FISCAL POLICY | PUBLIC DEBT | PUBLIC DEBT | INTERNATIONAL ECONOMICS | INTERNATIONAL ECONOMICS | GOODS MARKET | GOODS MARKET | MARKET | MARKET | FINANCIAL MARKETS | FINANCIAL MARKETS | OPEN ECONOMY | OPEN ECONOMY | EXCHANGE RATE | EXCHANGE RATE | LABOR MARKET | LABOR MARKET | PHILLIPS CURVE | PHILLIPS CURVE | GROWTH | GROWTH | SOLOW'S MODEL | SOLOW'S MODEL | Economics | Economics | Output | Output | Employment | Employment | Determination | Determination | Unemployment | Unemployment | Interest Rates | Interest Rates | Inflation | Inflation | Monetary Policy | Monetary Policy | Fiscal Policy | Fiscal Policy | Public Debt | Public Debt | International Economics | International Economics | Goods Market | Goods Market | Market | Market | Financial Markets | Financial Markets | Open Economy | Open Economy | Exchange Rate | Exchange Rate | Labor Market | Labor Market | Phillips Curve | Phillips Curve | Growth | Growth | Solow's Model | Solow's Model

License

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

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

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

Description

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

Subjects

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

License

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RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (MIT) RES.18-009 Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler (MIT)

Description

Includes audio/video content: AV lectures. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos w Includes audio/video content: AV lectures. Learn Differential Equations: Up Close with Gilbert Strang and Cleve Moler is an in-depth series of videos about differential equations and the MATLAB® ODE suite. These videos are suitable for students and life-long learners to enjoy.About the Instructors Gilbert Strang is the MathWorks Professor of Mathematics at MIT. His research focuses on mathematical analysis, linear algebra and PDEs. He has written textbooks on linear algebra, computational science, finite elements, wavelets, GPS, and calculus.Cleve Moler is chief mathematician, chairman, and cofounder of MathWorks. He was a professor of math and computer science for almost 20 years at the University of Michigan, Stanford University, and the University of New Mexico. These videos w

Subjects

differential equations | differential equations | ODE | MATLAB | ODE | MATLAB | first order equations | first order equations | second order equations | second order equations | matrices | matrices | Laplace transform | Laplace transform | linear algebra | linear algebra | eigenvalues | eigenvalues | eigenvectors | eigenvectors | Fourier series | Fourier series | Runge-Kutta | Runge-Kutta | Tumbling box | Tumbling box | predator-prey equations | predator-prey equations | Lorenz Attractor | Lorenz Attractor

License

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

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

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S.I.G. - II (2010)

Description

Conocer los softwares de Sistemas de Información Geográfica open source utilizados en la administración local Conocer el marco legal nacional y europeo de la cartografía aplicada a los Sistemas de Información Geográfica. Desarrollar la creatividad para el desarrollo de posibles proyectos SIG. Incrementar el refuerzo personal a la hora de liderar proyectos o defenderlos públicamente. Ser capaz de la implantación de un SIG en cualquier institución y en concreto en la Administración Local. Profundizar en los conocimientos prácticos utilizando la última versión del software más extendido en la actualidad.

Subjects

INGENIERIA CARTOGRAFICA | GEODESIA Y FOTOGRAMETRIA | ArcInfo | Ayuntamiento | ía | Proyecto SIG | SIG

License

http://creativecommons.org/licenses/by-nc-nd/2.5/es/

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ÓN LOCAL (2011)

Description

Se realizará un proyecto SIG dentro de las competencias de una administración local. Desde el análisis hasta la programación. Se estudiará en profundidad las necesidades de las administraciones locales en el mundo de los Sistemas de Información Geográfica.

Subjects

INGENIERIA CARTOGRAFICA | GEODESIA Y FOTOGRAMETRIA | ón local | Ayuntamiento | ía | IDE | SIG

License

http://creativecommons.org/licenses/by-nc-nd/2.5/es/

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ÓN CARTOGRÁFICA (2010)

Description

Conocer el modelo de datos de la Base Topográfica Armonizada (BTA) Conocer las fases de la producción cartográfica de una serie. Ser capaz de realizar una hoja cartográfica desde el inicio hasta el final. Entender y desarrollar un pliego de condiciones técnicas para la generación de cartografía. Potenciar el trabajo en equipo. Conocer los criterios necesarios para crear un proyecto empresarial y Desarrollar la creatividad para ser capaz de generar nuevas empresas de cartografía. Incrementar el refuerzo personal a la hora de liderar proyectos o defenderlos públicamente. Profundizar en los conocimientos prácticos utilizando GEOMEDIA.

Subjects

INGENIERIA CARTOGRAFICA | GEODESIA Y FOTOGRAMETRIA | ía | BTA | geodatabase | áfica | plan de empresa

License

http://creativecommons.org/licenses/by-nc-nd/2.5/es/

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2.997 Decision Making in Large Scale Systems (MIT)

Description

This course is an introduction to the theory and application of large-scale dynamic programming. Topics include Markov decision processes, dynamic programming algorithms, simulation-based algorithms, theory and algorithms for value function approximation, and policy search methods. The course examines games and applications in areas such as dynamic resource allocation, finance and queueing networks.

Subjects

algorithm | markov decision process | dynamic programming | stochastic models | policy iteration | Q-Learning | reinforcement learning | Lyapunov function | ODE | TD-Learning | value function approximation | linear programming | policy search | policy gradient | actor-critic | experts algorithm | regret minimization and calibration | games.

License

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18.336 Numerical Methods of Applied Mathematics II (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

Linear systems | Fast Fourier Transform | Wave equation | Von Neumann analysis | Conditions for stability | Dissipation | Multistep schemes | Dispersion | Group Velocity | Propagation of Wave Packets | Parabolic Equations | The Du Fort Frankel Scheme | Convection-Diffusion equation | ADI Methods | Elliptic Equations | Jacobi | Gauss-Seidel and SOR(w) | ODEs | finite differences | spectral methods | well-posedness and stability | boundary and nonlinear instabilities | Finite Difference Schemes | Partial Differential Equations

License

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

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