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

Description

This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project. This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

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2.29 Numerical Fluid Dynamics (MIT) 2.29 Numerical Fluid Dynamics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs). This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

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

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

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2.782J Design of Medical Devices and Implants (MIT) 2.782J Design of Medical Devices and Implants (MIT)

Description

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

Subjects

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

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16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLAB&#1 This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLAB&#1

Subjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derviative | substantial derviative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamics | Incompressible | Incompressible

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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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4.105 Geometric Disciplines and Architecture Skills: Reciprocal Methodologies (MIT) 4.105 Geometric Disciplines and Architecture Skills: Reciprocal Methodologies (MIT)

Description

This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students. This course is an intensive introduction to architectural design tools and process, and is taught through a series of short exercises. The conceptual basis of each exercise is in the interrogation of the geometric principles that lie at the core of each skill. Skills covered in this course range from techniques of hand drafting, to generation of 3D computer models, physical model-building, sketching, and diagramming. Weekly lectures and pin-ups address the conventions associated with modes of architectural representation and their capacity to convey ideas. This course is tailored and offered only to first-year M.Arch students.

Subjects

geometry | geometry | representation | representation | architecture | architecture | drawing | drawing | projection | projection | perspective | perspective | planes | planes | axonometric | axonometric | stereotomy | stereotomy | volume | volume | surface | surface | curvature | curvature | curves | curves | discretization | discretization | generation | generation | construction | construction | publication | publication | presentation | presentation

License

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1.725J Chemicals in the Environment: Fate and Transport (MIT) 1.725J Chemicals in the Environment: Fate and Transport (MIT)

Description

This core class in the Environmental M.Eng. program is for all students interested in the behavior of chemicals in the environment. The emphasis is on man-made chemicals; their movement through water, air, and soil; and their eventual fate. Physical transport, as well as chemical and biological sources and sinks, are discussed. Linkages to health effects, sources and control, and policy aspects are discussed and debated. This core class in the Environmental M.Eng. program is for all students interested in the behavior of chemicals in the environment. The emphasis is on man-made chemicals; their movement through water, air, and soil; and their eventual fate. Physical transport, as well as chemical and biological sources and sinks, are discussed. Linkages to health effects, sources and control, and policy aspects are discussed and debated.

Subjects

control volumes | control volumes | mass balance | mass balance | advective/dispersive transport | advective/dispersive transport | chemical equilibria | chemical equilibria | mass action | mass action | electroneutrality | electroneutrality | mass conservation | mass conservation | chemical kinetics and partitioning | chemical kinetics and partitioning | river transport | river transport | lakes and wetlands and estuaries | lakes and wetlands and estuaries | sediment transport | sediment transport | bottom sediments | bottom sediments | paleolimnology | paleolimnology | air-water exchange | air-water exchange | major ion chemistry of natural waters | major ion chemistry of natural waters | D'Arcy's Law | D'Arcy's Law | 1.725 | 1.725

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2.782J Design of Medical Devices and Implants (MIT) 2.782J Design of Medical Devices and Implants (MIT)

Description

This design course targets the solution of clinical problems by use of implants and other medical devices. Topics include the systematic use of cell-matrix control volumes; the role of stress analysis in the design process; anatomic fit, shape and size of implants; selection of biomaterials; instrumentation for surgical implantation procedures; preclinical testing for safety and efficacy, including risk/benefit ratio assessment evaluation of clinical performance and design of clinical trials. Student project materials are drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants. This design course targets the solution of clinical problems by use of implants and other medical devices. Topics include the systematic use of cell-matrix control volumes; the role of stress analysis in the design process; anatomic fit, shape and size of implants; selection of biomaterials; instrumentation for surgical implantation procedures; preclinical testing for safety and efficacy, including risk/benefit ratio assessment evaluation of clinical performance and design of clinical trials. Student project materials are drawn from orthopedic devices, soft tissue implants, artificial organs, and dental implants.

Subjects

2.782 | 2.782 | 3.961 | 3.961 | 20.451 | 20.451 | HST.524 | HST.524 | clinical problems | clinical problems | implants | implants | medical devices | medical devices | cell-matrix control volumes | cell-matrix control volumes | stress analysis | stress analysis | anatomic fit | anatomic fit | biomaterials | biomaterials | surgical implantation procedures | surgical implantation procedures | Preclinical testing | Preclinical testing | risk/benefit ratio assessment | risk/benefit ratio assessment | clinical performance | clinical performance | clinical trials | clinical trials | orthopedic devices | orthopedic devices | soft tissue implants | soft tissue implants | artificial organs | artificial organs | dental implants | dental implants | stent | stent | prosthesis | prosthesis | scaffold | scaffold | bio-implant | bio-implant | scar | scar | genetics | genetics | skin | skin | nerve | nerve | bone | bone | tooth | tooth | joint | joint | FDA | FDA | FDA approval | FDA approval | cartilage | cartilage | ACL | ACL | health | health | regulation | regulation | healthcare | healthcare | medicine | medicine | bioengineering | bioengineering

License

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6.243J Dynamics of Nonlinear Systems (MIT) 6.243J Dynamics of Nonlinear Systems (MIT)

Description

This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems. This course provides an introduction to nonlinear deterministic dynamical systems. Topics covered include: nonlinear ordinary differential equations; planar autonomous systems; fundamental theory: Picard iteration, contraction mapping theorem, and Bellman-Gronwall lemma; stability of equilibria by Lyapunov's first and second methods; feedback linearization; and application to nonlinear circuits and control systems.

Subjects

nonlinear systems | nonlinear systems | deterministic dynamical systems | deterministic dynamical systems | ordinary differential equations | ordinary differential equations | planar autonomous systems | planar autonomous systems | Picard iteration | Picard iteration | contraction mapping theorem | contraction mapping theorem | Bellman-Gronwall lemma | Bellman-Gronwall lemma | Lyapunov methods | Lyapunov methods | feedback linearization | feedback linearization | nonlinear circuits | nonlinear circuits | control systems | control systems | local controllability | local controllability | volume evolution | volume evolution | system analysis | system analysis | singular perturbations | singular perturbations | averaging | averaging | local behavior | local behavior | trajectories | trajectories | equilibria | equilibria | storage functions | storage functions | stability analysis | stability analysis | continuity | continuity | differential equations | differential equations | system models | system models | parameters | parameters | input/output | input/output | state-space | state-space | 16.337 | 16.337

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16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem.

Subjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derivative | substantial derivative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamics

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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

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16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT) 16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT)

Description

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations). A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Subjects

numerical methods | numerical methods | differential equations | differential equations | linear | linear | nonlinear | nonlinear | elliptic | elliptic | parabolic | parabolic | hyperbolic | hyperbolic | partial differential equations | partial differential equations | integral equations | integral equations | mathematical formulations | mathematical formulations | mathematics | mathematics | finite difference | finite difference | finite volume | finite volume | discretisation | discretisation | finite element | finite element | boundary element | boundary element | iteration | iteration | 16.920 | 16.920 | 2.097 | 2.097 | 6.339 | 6.339

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18.336 Numerical Methods for Partial Differential Equations (MIT) 18.336 Numerical Methods for Partial Differential Equations (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

advection equation | advection equation | heat equation | heat equation | wave equation | wave equation | Airy equation | Airy equation | convection-diffusion problems | convection-diffusion problems | KdV equation | KdV equation | hyperbolic conservation laws | hyperbolic conservation laws | Poisson equation | Poisson equation | Stokes problem | Stokes problem | Navier-Stokes equations | Navier-Stokes equations | interface problems | interface problems | consistency | consistency | stability | stability | convergence | convergence | Lax equivalence theorem | Lax equivalence theorem | error analysis | error analysis | Fourier approaches | Fourier approaches | staggered grids | staggered grids | shocks | shocks | front propagation | front propagation | preconditioning | preconditioning | multigrid | multigrid | Krylov spaces | Krylov spaces | saddle point problems | saddle point problems | finite differences | finite differences | finite volumes | finite volumes | finite elements | finite elements | ENO/WENO | ENO/WENO | spectral methods | spectral methods | projection approaches for incompressible ows | projection approaches for incompressible ows | level set methods | level set methods | particle methods | particle methods | direct and iterative methods | direct and iterative 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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22.058 Principles of Medical Imaging (MIT) 22.058 Principles of Medical Imaging (MIT)

Description

An introduction to the principles of tomographic imaging and its applications. It includes a series of lectures with a parallel set of recitations that provide demonstrations of basic principles. Both ionizing and non-ionizing radiation are covered, including x-ray, PET, MRI, and ultrasound. Emphasis on the physics and engineering of image formation. An introduction to the principles of tomographic imaging and its applications. It includes a series of lectures with a parallel set of recitations that provide demonstrations of basic principles. Both ionizing and non-ionizing radiation are covered, including x-ray, PET, MRI, and ultrasound. Emphasis on the physics and engineering of image formation.

Subjects

general imaging principles | | general imaging principles | | linear optics | | linear optics | | ray tracing | | ray tracing | | Linear Imaging Systems | | Linear Imaging Systems | | Space Invariance | | Space Invariance | | Pin-hole camera | | Pin-hole camera | | Fourier Transformations | | Fourier Transformations | | Modulation Transfer Functions | | Modulation Transfer Functions | | Fourier convolution | | Fourier convolution | | Sampling | | Sampling | | Nyquist | | Nyquist | | counting statistics | | counting statistics | | additive noise | | additive noise | | optical imaging | | optical imaging | | Radiation types | | Radiation types | | Radiation detection | | Radiation detection | | photon detection | | photon detection | | spectra | | spectra | | attenuation | | attenuation | | Planar X-ray imaging | | Planar X-ray imaging | | Projective Imaging | | Projective Imaging | | X-ray CT | | X-ray CT | | Ultrasound | | Ultrasound | | microscopy | k-space | | microscopy | k-space | | NMR pulses | | NMR pulses | | f2-D gradient | | f2-D gradient | | spin echoes | | spin echoes | | 3-D methods of MRI | | 3-D methods of MRI | | volume localized spectroscopy | volume localized spectroscopy

License

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HST.542J Quantitative Physiology: Organ Transport Systems (MIT) HST.542J Quantitative Physiology: Organ Transport Systems (MIT)

Description

This course elaborates on the application of the principles of energy and mass flow to major human organ systems. It discusses mechanisms of regulation and homeostasis. It also discusses anatomical, physiological, and pathophysiological features of the cardiovascular, respiratory, and renal systems. There is emphasis on those systems, features, and devices that are most illuminated by the methods of physical sciences. This course elaborates on the application of the principles of energy and mass flow to major human organ systems. It discusses mechanisms of regulation and homeostasis. It also discusses anatomical, physiological, and pathophysiological features of the cardiovascular, respiratory, and renal systems. There is emphasis on those systems, features, and devices that are most illuminated by the methods of physical sciences.

Subjects

electrocardiogram | electrocardiogram | cardiovascular system | cardiovascular system | cardiovascular physiology | cardiovascular physiology | electrophysiology | electrophysiology | myocardial cells | myocardial cells | electrocardiography | electrocardiography | physiological fluid mechanics | physiological fluid mechanics | respiratory physiology | respiratory physiology | renal physiology | renal physiology | quantitative physiology | quantitative physiology | pulmonary mechanics | pulmonary mechanics | heart | heart | arrhythmia | arrhythmia | pulmonary modeling | pulmonary modeling | clinical electrocardiography | clinical electrocardiography | ECG | ECG | EKG | EKG | ischemia | ischemia | infarction | infarction | vector cardiogram | vector cardiogram | purkinje fibers | purkinje fibers | QRS waveform | QRS waveform | tachycardia | tachycardia | action potential | action potential | depolarization | depolarization | afterdepolarization | afterdepolarization | total lung capacity | total lung capacity | systolic | systolic | diastolic | diastolic | residual volume | residual volume | vital capacity | vital capacity | HST.542 | HST.542 | 2.792 | 2.792 | 20.371J20.371 | 20.371J20.371 | 6.022 | 6.022

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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Using a Spacer

Description

Please visit the My Lungs My Life resource for more advice, support and information regarding chest illness http://mylungsmylife.org

Subjects

CHSS | COPD | asthma | Chronic Obstructive Pulmonary Disease | inhaler | spacer | small volume spacer | large volume spacer | HEALTH CARE / MEDICINE / HEALTH and SAFETY | P

License

Attribution-NonCommercial-NoDerivatives 4.0 International Attribution-NonCommercial-NoDerivatives 4.0 International http://creativecommons.org/licenses/by-nc-nd/4.0/ http://creativecommons.org/licenses/by-nc-nd/4.0/

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2.29 Numerical Fluid Mechanics (MIT)

Description

This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.

Subjects

errors | condition numbers and roots of equations | Navier-Stokes | direct and iterative methods for linear systems | finite differences for elliptic | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | finite volume methods | time marching methods | Navier-Stokes solvers | grid generation | finite volumes on complex geometries | finite element methods | spectral methods | boundary element and panel methods | turbulent flows | boundary layers | Lagrangian Coherent Structures

License

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2.29 Numerical Fluid Mechanics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the

Subjects

errors | condition numbers and roots of equations | Navier-Stokes | direct and iterative methods for linear systems | finite differences for elliptic | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | finite volume methods | time marching methods | Navier-Stokes solvers | grid generation | finite volumes on complex geometries | finite element methods | spectral methods | boundary element and panel methods | turbulent flows | boundary layers | Lagrangian Coherent Structures

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

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Pretvarjanje mer (dl, l, hl do 100) Converting units of measurment (dl, l, hl)

Description

Zbirka vaj za pretvarjanje mer za prostornino (dl, l in hl). Collection of exercises to drill conversion between different units of measurements for volume (dl, l, hl).

Subjects

znanstvene vede | sciences | matematika | mathematics | liter | litre | pretvorba | conversion | prostornina | volume | merska enota | unit of measurement

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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Prostornina kvadra Volume of cuboid

Description

PowerPointova diaprojekcija je pripravljena dovolj intuitivno, da jo lahko uporabi vsakdo. Presentation of how to measure volume of cuboid whit the use of unit cube with volume 1.

Subjects

znanstvene vede | sciences | matematika | mathematics | prostornina | volume | kvader | cuboid | kocka | cube

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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Površina in prostornina pokončne prizme Area and volume of a right prism

Description

PowerPointova predstavitev geometrijske izpeljave in tabele formul za računanje površine in prostornine pokončnih prizem in valja. Calculating area and volume of a right prism.

Subjects

znanstvene vede | sciences | matematika | mathematics | površina | area | prostornina | volume | pokončna prizma | right prism | prizma | prism

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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Površina in prostornina pokončne piramide Area and volume of a right pyramid

Description

PowerPointova diaprojekcija geometrijske izpeljave in tabela formul za računanje površine in prostornine pokončnih piramid in stožca. Calculating area and volume of a right pyramid.

Subjects

znanstvene vede | sciences | matematika | mathematics | površina | area | prostornina | volume | pokončna piramida | right pyramid | piramida | pyramid

License

http://creativecommons.org/licenses/by-nc-sa/2.5/si/ http://creativecommons.org/licenses/by-nc-sa/2.5/si/

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