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18.303 Linear Partial Differential Equations (MIT) 18.303 Linear Partial Differential Equations (MIT)

Description

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized.Technical RequirementsSpecial software is required to use some of the files in this course: .m. This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized.Technical RequirementsSpecial software is required to use some of the files in this course: .m.

Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functions | Bessel functions

License

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18.303 Linear Partial Differential Equations (MIT) 18.303 Linear Partial Differential Equations (MIT)

Description

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.

Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functions | Bessel functions

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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2.003SC Engineering Dynamics (MIT) 2.003SC Engineering Dynamics (MIT)

Description

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

Subjects

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

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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2.003J Dynamics and Control I (MIT) 2.003J Dynamics and Control I (MIT)

Description

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems. Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

Subjects

dynamics and vibrations of lumped-parameter models | dynamics and vibrations of lumped-parameter models | mechanical systems | mechanical systems | Kinematics | Kinematics | Force-momentum formulation | Force-momentum formulation | systems of particles | systems of particles | rigid bodies in planar motion | rigid bodies in planar motion | Work-energy concepts | Work-energy concepts | Virtual displacements | Virtual displacements | virtual work | virtual work | Lagrange's equations | Lagrange's equations | Linearization of equations of motion | Linearization of equations of motion | Linear stability analysis | Linear stability analysis | Free vibration | Free vibration | forced vibration | forced vibration | linear multi-degree of freedom models | linear multi-degree of freedom models | matrix eigenvalue problems | matrix eigenvalue problems | numerical methods | numerical methods | MATLAB | MATLAB

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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18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT) 18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)

Description

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.

Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functionsORDS | Bessel functionsORDS

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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18.303 Linear Partial Differential Equations (MIT) 18.303 Linear Partial Differential Equations (MIT)

Description

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions. This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.

Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functions | Bessel functions

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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18.335J Introduction to Numerical Methods (MIT) 18.335J Introduction to Numerical Methods (MIT)

Description

The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems. The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems.

Subjects

linear algebra | linear algebra | ordinary differential equations | ordinary differential equations | linear systems of equations | linear systems of equations | least square problems | least square problems | eigenvalue problems | eigenvalue problems | singular value problems | singular value problems

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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18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT) 18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)

Description

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples. This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.

Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functionsORDS | Bessel functionsORDS

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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18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT) 18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)

Description

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.

Subjects

diffusion | diffusion | Laplace equations | Laplace equations | Poisson | Poisson | wave equations | wave equations | separation of variables | separation of variables | Fourier series | Fourier series | Fourier transforms | Fourier transforms | eigenvalue problems | eigenvalue problems | Green's function | Green's function | Heat Equation | Heat Equation | Sturm-Liouville Eigenvalue problems | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | quasilinear PDEs | Bessel functionsORDS | Bessel functionsORDS

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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18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)

Description

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems.

Subjects

diffusion | Laplace equations | Poisson | wave equations | separation of variables | Fourier series | Fourier transforms | eigenvalue problems | Green's function | Heat Equation | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | Bessel functionsORDS

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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18.303 Linear Partial Differential Equations (MIT)

Description

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized.Technical RequirementsSpecial software is required to use some of the files in this course: .m.

Subjects

diffusion | Laplace equations | Poisson | wave equations | separation of variables | Fourier series | Fourier transforms | eigenvalue problems | Green's function | Heat Equation | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | Bessel functions

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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18.303 Linear Partial Differential Equations (MIT)

Description

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods of solution, such as separation of variables, Fourier series and transforms, eigenvalue problems. Green's function methods are emphasized.Technical RequirementsMATLAB® software is required to run the .m files found on this course site.

Subjects

diffusion | Laplace equations | Poisson | wave equations | separation of variables | Fourier series | Fourier transforms | eigenvalue problems | Green's function | Heat Equation | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | Bessel functions

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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2.003SC Engineering Dynamics (MIT)

Description

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

Subjects

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

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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2.003J Dynamics and Control I (MIT)

Description

Introduction to the dynamics and vibrations of lumped-parameter models of mechanical systems. Kinematics. Force-momentum formulation for systems of particles and rigid bodies in planar motion. Work-energy concepts. Virtual displacements and virtual work. Lagrange's equations for systems of particles and rigid bodies in planar motion. Linearization of equations of motion. Linear stability analysis of mechanical systems. Free and forced vibration of linear multi-degree of freedom models of mechanical systems; matrix eigenvalue problems. Introduction to numerical methods and MATLAB® to solve dynamics and vibrations problems.

Subjects

dynamics and vibrations of lumped-parameter models | mechanical systems | Kinematics | Force-momentum formulation | systems of particles | rigid bodies in planar motion | Work-energy concepts | Virtual displacements | virtual work | Lagrange's equations | Linearization of equations of motion | Linear stability analysis | Free vibration | forced vibration | linear multi-degree of freedom models | matrix eigenvalue problems | numerical methods | MATLAB

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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18.303 Linear Partial Differential Equations: Analysis and Numerics (MIT)

Description

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.

Subjects

diffusion | Laplace equations | Poisson | wave equations | separation of variables | Fourier series | Fourier transforms | eigenvalue problems | Green's function | Heat Equation | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | Bessel functionsORDS

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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18.303 Linear Partial Differential Equations (MIT)

Description

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.

Subjects

diffusion | Laplace equations | Poisson | wave equations | separation of variables | Fourier series | Fourier transforms | eigenvalue problems | Green's function | Heat Equation | Sturm-Liouville Eigenvalue problems | quasilinear PDEs | Bessel functions

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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18.335J Introduction to Numerical Methods (MIT)

Description

The focus of this course is on numerical linear algebra and numerical methods for solving ordinary differential equations. Topics include linear systems of equations, least square problems, eigenvalue problems, and singular value problems.

Subjects

linear algebra | ordinary differential equations | linear systems of equations | least square problems | eigenvalue problems | singular value problems

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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