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

Description

This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods. This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.

Subjects

numerical methods | numerical methods | interpolation | interpolation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | finite difference methods | finite difference methods | boundary integral equation panel methods | boundary integral equation panel methods | numerical lifting surface computations | numerical lifting surface computations | Fast Fourier Transforms | Fast Fourier Transforms | Numerical representation | Numerical representation | deterministic and random sea waves | deterministic and random sea waves | Integral boundary layer equations | Integral boundary layer equations | numerical solutions | numerical solutions

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.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

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

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™ This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™

Subjects

numerical methods | numerical methods | interpolation | interpolation | differentiation | differentiation | integration | integration | systems of linear equations | systems of linear equations | differential equations | differential equations | numerical integration | numerical integration | partial differential | partial differential | boundary integral equation panel methods | boundary integral equation panel methods | deterministic and random sea waves | deterministic and random sea waves | Fast Fourier Transforms | Fast Fourier Transforms | finite difference methods | finite difference methods | Integral boundary layer equations | Integral boundary layer equations | numerical lifting surface computations | numerical lifting surface computations | Numerical representation | Numerical representation | numerical solutions | numerical solutions | partial differential equations of inviscid hydrodynamics | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | incompressible fluid mechanics | calculus | calculus | complex numbers | complex numbers | root finding | root finding | curve fitting | curve fitting | numerical differentiation | numerical differentiation | numerical errors | numerical errors | panel methods | panel methods | oscillating rigid objects | oscillating rigid objects | 2.29 | 2.29

License

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RES.2-002 Finite Element Procedures for Solids and Structures (MIT) RES.2-002 Finite Element Procedures for Solids and Structures (MIT)

Description

Includes audio/video content: AV lectures. Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses. These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study. Includes audio/video content: AV lectures. Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses. These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study.

Subjects

finite element method | finite element method | statics | statics | dynamics | dynamics | linear analysis | linear analysis | nonlinear analysis | nonlinear analysis | computer modeling | computer modeling | engineering design | engineering design | solids | solids | structures | structures | wave propagation | wave propagation | vibration | vibration | collapse | collapse | buckling | buckling | Lagrangian formulation | Lagrangian formulation | truss | truss | beam | beam | plate | plate | shell | shell | elastic materials | elastic materials | plastic materials | plastic materials | creep | creep | ADINA | ADINA | numerical integration methods | numerical integration methods | mode superposition | mode superposition

License

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

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

Description

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

Subjects

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

License

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

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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 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

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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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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2.29 Numerical Fluid Mechanics (MIT)

Description

This course introduces students to MATLAB®. Numerical methods include number representation and errors, interpolation, differentiation, integration, systems of linear equations, and Fourier interpolation and transforms. Students will study partial and ordinary differential equations as well as elliptic and parabolic differential equations, and solutions by numerical integration, finite difference methods, finite element methods, boundary element methods, and panel methods.

Subjects

numerical methods | interpolation | integration | systems of linear equations | differential equations | numerical integration | partial differential equations of inviscid hydrodynamics | finite difference methods | boundary integral equation panel methods | numerical lifting surface computations | Fast Fourier Transforms | Numerical representation | deterministic and random sea waves | Integral boundary layer equations | numerical solutions

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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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.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | omputational methods | aerospace engineering | 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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13.024 Numerical Marine Hydrodynamics (MIT)

Description

This course is an introduction to numerical methods: interpolation, differentiation, integration, and systems of linear equations. It covers the solution of differential equations by numerical integration, as well as partial differential equations of inviscid hydrodynamics: finite difference methods, boundary integral equation panel methods. Also addressed are introductory numerical lifting surface computations, fast Fourier transforms, the numerical representation of deterministic and random sea waves, as well as integral boundary layer equations and numerical solutions.Technical RequirementMATLAB® software is required to run the .m files found on this course site. The .FIN and .OUT are simply data offest tables. They can be viewed with any text reader. RealOne™

Subjects

numerical methods | interpolation | differentiation | integration | systems of linear equations | differential equations | numerical integration | partial differential | boundary integral equation panel methods | deterministic and random sea waves | Fast Fourier Transforms | finite difference methods | Integral boundary layer equations | numerical lifting surface computations | Numerical representation | numerical solutions | partial differential equations of inviscid hydrodynamics | incompressible fluid mechanics | calculus | complex numbers | root finding | curve fitting | numerical differentiation | numerical errors | panel methods | oscillating rigid objects | 2.29

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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2.29 Numerical Marine Hydrodynamics (13.024) (MIT)

Description

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

Subjects

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

License

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

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RES.2-002 Finite Element Procedures for Solids and Structures (MIT)

Description

Finite element analysis is now widely used for solving complex static and dynamic problems encountered in engineering and the sciences. In these two video courses, Professor K. J. Bathe, a researcher of world renown in the field of finite element analysis, teaches the basic principles used for effective finite element analysis, describes the general assumptions, and discusses the implementation of finite element procedures for linear and nonlinear analyses. These videos were produced in 1982 and 1986 by the MIT Center for Advanced Engineering Study.

Subjects

finite element method | statics | dynamics | linear analysis | nonlinear analysis | computer modeling | engineering design | solids | structures | wave propagation | vibration | collapse | buckling | Lagrangian formulation | truss | beam | plate | shell | elastic materials | plastic materials | creep | ADINA | numerical integration methods | mode superposition

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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16.90 Computational Methods in Aerospace Engineering (MIT)

Description

This course provides an introduction to numerical methods and computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques covered include numerical integration of systems of ordinary differential equations; numerical discretization of partial differential equations; and probabilistic methods for quantifying the impact of variability. Specific emphasis is given to finite volume methods in fluid mechanics, and finite element methods in structural mechanics.Acknowledgement: Prof. David Darmofal taught this course in prior years, and created some of the materials found in this OCW site.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | computational methods | aerospace engineering | Monte Carlo | Fourier stability analysis | Matrix stability analysis | Runge-Kutta | convergence | accuracy | stiffness | weighted residual | statistical sampling | sensitivity analysis

License

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

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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.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | omputational methods | aerospace engineering | 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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10.34 Numerical Methods Applied to Chemical Engineering (MIT)

Description

Numerical methods for solving problems arising in heat and mass transfer, fluid mechanics, chemical reaction engineering, and molecular simulation. Topics: Numerical linear algebra, solution of nonlinear algebraic equations and ordinary differential equations, solution of partial differential equations (e.g. Navier-Stokes), numerical methods in molecular simulation (dynamics, geometry optimization). All methods are presented within the context of chemical engineering problems. Familiarity with structured programming is assumed.

Subjects

linear algebra | optimization | ODE-IVP | numerical integration | differential-algebraic equations | boundary value problems | partial differential equations | probability theory | operator splitting | Monte Carlo methods | stochastic chemical kinetics | systems of nonlinear 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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