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18.086 Mathematical Methods for Engineers II (MIT) 18.086 Mathematical Methods for Engineers II (MIT)

Description

Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization. Includes audio/video content: AV lectures. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Optimization: network flows | linear programming

License

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8.311 Electromagnetic Theory (MIT) 8.311 Electromagnetic Theory (MIT)

Description

Electromagnetic Theory covers the basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional e.m.f. and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. This is a graduate level subject which uses appropriate mathematics but whose emphasis is on physical phenomena and principles. Electromagnetic Theory covers the basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional e.m.f. and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. This is a graduate level subject which uses appropriate mathematics but whose emphasis is on physical phenomena and principles.

Subjects

electromagnetism | electromagnetism | electrostatics | electrostatics | magnetic fields of steady currents | magnetic fields of steady currents | motional e.m.f. | motional e.m.f. | electromagnetic induction | electromagnetic induction | Maxwell's equations | Maxwell's equations | propagation and radiation | propagation and radiation | electromagnetic waves | electromagnetic waves | electric properties of matter | electric properties of matter | magnetic properties of matter | magnetic properties of matter | conservation laws | conservation laws | electromagnetic waves | electric properties of matter | electromagnetic waves | electric properties of matter | conservation laws. | conservation laws.

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8.01 Physics I (MIT) 8.01 Physics I (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics. Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.

Subjects

classical mechanics | classical mechanics | Space and time | Space and time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | experimental basis of Newton's laws | experimental basis of Newton's laws | particle dynamics | particle dynamics | universal gravitation | universal gravitation | collisions and conservation laws | collisions and conservation laws | work and potential energy | work and potential energy | vibrational motion | vibrational motion | conservative forces | conservative forces | central force motions | central force motions | inertial forces and non-inertial frames | inertial forces and non-inertial frames | rigid bodies and rotational dynamics | rigid bodies and rotational dynamics | forces and equilibrium | forces and equilibrium | space | space | time | time | space-time | space-time | planar motion | planar motion | forces | forces | equilibrium | equilibrium | Newton?s laws | Newton?s laws | collisions | collisions | conservation laws | conservation laws | work | work | potential energy | potential energy | inertial forces | inertial forces | non-inertial forces | non-inertial forces | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics

License

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16.07 Dynamics (MIT) 16.07 Dynamics (MIT)

Description

Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics. Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.

Subjects

Curvilinear motion | Curvilinear motion | carteian coordinates | carteian coordinates | dynamics | dynamics | equations of motion | equations of motion | intrinsic coordinates | intrinsic coordinates | coordinate systems | coordinate systems | work | work | energy | energy | conservative forces | conservative forces | potential energy | potential energy | linear impulse | linear impulse | mommentum | mommentum | angular impulse | angular impulse | relative motion | relative motion | rotating axes | rotating axes | translating axes | translating axes | Newton's second law | Newton's second law | inertial forces | inertial forces | accelerometers | accelerometers | Newtonian relativity | Newtonian relativity | gravitational attraction | gravitational attraction | 2D rigid body kinematics | 2D rigid body kinematics | conservation laws for systems of particles | conservation laws for systems of particles | 2D rigid body dynamics | 2D rigid body dynamics | pendulums | pendulums | 3D rigid body kinematics | 3D rigid body kinematics | 3d rigid body dynamics | 3d rigid body dynamics | inertia tensor | inertia tensor | gyroscopic motion | gyroscopic motion | torque-free motion | torque-free motion | spin stabilization | spin stabilization | variable mass systems | variable mass systems | rocket equation | rocket equation | central foce motion | central foce motion | Keppler's laws | Keppler's laws | orbits | orbits | orbit transfer | orbit transfer | vibration | vibration | spring mass systems | spring mass systems | forced vibration | forced vibration | isolation | isolation | coupled oscillators | coupled oscillators | normal modes | normal modes | wave propagation | wave propagation | cartesian coordinates | cartesian coordinates | momentum | momentum | central force motion | central force motion

License

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1.020 Ecology II: Engineering for Sustainability (MIT) 1.020 Ecology II: Engineering for Sustainability (MIT)

Description

This course covers the use of ecological and thermodynamic principles to examine interactions between humans and the natural environment. Topics include conservation and constitutive laws, box models, feedback, thermodynamic concepts, energy in natural and engineered systems, basic transport concepts, life cycle analysis and related economic methods.Topics such as renewable energy, sustainable agriculture, green buildings, and mitigation of climate change are illustrated with quantitative case studies. Case studies are team-oriented and may include numerical simulations and design exercises. Some programming experience is desirable but not a prerequisite. Instruction and practice in oral and written communication are provided. This course covers the use of ecological and thermodynamic principles to examine interactions between humans and the natural environment. Topics include conservation and constitutive laws, box models, feedback, thermodynamic concepts, energy in natural and engineered systems, basic transport concepts, life cycle analysis and related economic methods.Topics such as renewable energy, sustainable agriculture, green buildings, and mitigation of climate change are illustrated with quantitative case studies. Case studies are team-oriented and may include numerical simulations and design exercises. Some programming experience is desirable but not a prerequisite. Instruction and practice in oral and written communication are provided.

Subjects

systems | systems | conservation laws | conservation laws | constitutive laws | constitutive laws | box models | box models | mass conservation | mass conservation | perturbation methods | perturbation methods | thermodymanics | thermodymanics | heat transfer | heat transfer | enthalpy | enthalpy | entropy | entropy | multiphase systems | multiphase systems | mass and energy balances | mass and energy balances | energy supply options | energy supply options | economic value | economic value | natural resources | natural resources | multiobjective analysis | multiobjective analysis | life cycle analysis | life cycle analysis | mass and energy transport | mass and energy transport | green buildings | green buildings | transportation modeling | transportation modeling | renewable energy | renewable energy | climate modeling | climate modeling

License

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18.086 Mathematical Methods for Engineers II (MIT) 18.086 Mathematical Methods for Engineers II (MIT)

Description

This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site. MATLAB® software is required to run the .m files found on this course site. This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site. MATLAB® software is required to run the .m files found on this course site.

Subjects

Scientific computing: Fast Fourier Transform | Scientific computing: Fast Fourier Transform | finite differences | finite differences | finite elements | finite elements | spectral method | spectral method | numerical linear algebra | numerical linear algebra | Complex variables and applications | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | wave equation versus heat equation | conservation laws and shocks | conservation laws and shocks | dissipation and dispersion | dissipation and dispersion | Optimization: network flows | Optimization: network flows | linear programming | linear programming

License

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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc. Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | Nonlinear dynamical systems | nonlinear waves | nonlinear waves | diffusion | diffusion | stability | stability | characteristics | characteristics | nonlinear steepening | nonlinear steepening | breaking and shock formation | breaking and shock formation | conservation laws | conservation laws | first-order partial differential equations | first-order partial differential equations | finite differences | finite differences | numerical stability | numerical stability | traffic problems | traffic problems | flows in rivers | flows in rivers | internal waves | internal waves | mechanical vibrations | mechanical vibrations

License

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2.26 Compressible Fluid Dynamics (MIT) 2.26 Compressible Fluid Dynamics (MIT)

Description

2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Mey 2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Mey

Subjects

conservation laws | conservation laws | isentropic flows | isentropic flows | normal shock wave relations | normal shock wave relations | oblique shock waves | oblique shock waves | weak shock | weak shock | strong shock | strong shock | ducts | ducts | heat transfer | heat transfer | unsteady flows | unsteady flows | Riemann invariants | Riemann invariants | piston | piston | shock tube | shock tube | steady 2D supersonic flow | steady 2D supersonic flow | Prandtl-Meyer function | Prandtl-Meyer function | self-similar compressible flows | self-similar compressible flows

License

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8.01T Physics I (MIT) 8.01T Physics I (MIT)

Description

This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation. This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation.

Subjects

classical mechanics | classical mechanics | Space and time | Space and time | straight-line kinematics | straight-line kinematics | motion in a plane | motion in a plane | forces and equilibrium | forces and equilibrium | experimental basis of Newton's laws | experimental basis of Newton's laws | particle dynamics | particle dynamics | universal gravitation | universal gravitation | collisions and conservation laws | collisions and conservation laws | work and potential energy | work and potential energy | vibrational motion | vibrational motion | conservative forces | conservative forces | inertial forces and non-inertial frames | inertial forces and non-inertial frames | central force motions | central force motions | rigid bodies | rigid bodies | rotational dynamics | rotational dynamics | rigid bodies and rotational dynamics | rigid bodies and rotational dynamics

License

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18.152 Introduction to Partial Differential Equations (MIT) 18.152 Introduction to Partial Differential Equations (MIT)

Description

This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications. This course introduces three main types of partial differential equations: diffusion, elliptic, and hyperbolic. It includes mathematical tools, real-world examples and applications.

Subjects

diffusion | diffusion | elliptic | elliptic | hyperbolic | hyperbolic | partial differential equation | partial differential equation | Initial and boundary value problems for ordinary differential equations | Initial and boundary value problems for ordinary differential equations | Sturm-Liouville theory and eigenfunction expansions | Sturm-Liouville theory and eigenfunction expansions | initial value problems | initial value problems | wave equation;heat equation | wave equation;heat equation | Dirichlet problem | Dirichlet problem | Laplace operator and potential theory | Laplace operator and potential theory | Black-Scholes equation | Black-Scholes equation | water waves | water waves | scalar conservation laws | scalar conservation laws | first order equations | first order equations

License

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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

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8.01 Physics I (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.

Subjects

classical mechanics | Space and time | straight-line kinematics | motion in a plane | experimental basis of Newton's laws | particle dynamics | universal gravitation | collisions and conservation laws | work and potential energy | vibrational motion | conservative forces | central force motions | inertial forces and non-inertial frames | rigid bodies and rotational dynamics | forces and equilibrium | space | time | space-time | planar motion | forces | equilibrium | Newton?s laws | collisions | conservation laws | work | potential energy | inertial forces | non-inertial forces | rigid bodies | rotational dynamics

License

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18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT)

Description

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity. 18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

Subjects

partial differential equation | partial differential equation | hyperbolic equations | hyperbolic equations | dimensional analysis | dimensional analysis | perturbation methods | perturbation methods | hyperbolic systems | hyperbolic systems | diffusion and reaction processes | diffusion and reaction processes | continuum models | continuum models | equilibrium models | equilibrium models | continuous applied mathematics | continuous applied mathematics | traffic flow | traffic flow | fluids | fluids | elasticity | elasticity | granular flows | granular flows | continuum limit | continuum limit | conservation laws | conservation laws | quasi-equilibrium | quasi-equilibrium | kinematic waves | kinematic waves | characteristics | characteristics | simple waves | simple waves | shocks | shocks | diffusion (linear and nonlinear) | diffusion (linear and nonlinear) | numerical solution of wave equations | numerical solution of wave equations | finite differences | finite differences | consistency | consistency | stability | stability | discrete and fast Fourier transforms | discrete and fast Fourier transforms | spectral methods | spectral methods | transforms and series (Fourier | Laplace) | transforms and series (Fourier | Laplace) | sonic booms | sonic booms | Mach cone | Mach cone | caustics | caustics | lattices | lattices | dispersion | dispersion | group velocity | group velocity

License

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8.311 Electromagnetic Theory (MIT)

Description

Electromagnetic Theory covers the basic principles of electromagnetism: experimental basis, electrostatics, magnetic fields of steady currents, motional e.m.f. and electromagnetic induction, Maxwell's equations, propagation and radiation of electromagnetic waves, electric and magnetic properties of matter, and conservation laws. This is a graduate level subject which uses appropriate mathematics but whose emphasis is on physical phenomena and principles.

Subjects

electromagnetism | electrostatics | magnetic fields of steady currents | motional e.m.f. | electromagnetic induction | Maxwell's equations | propagation and radiation | electromagnetic waves | electric properties of matter | magnetic properties of matter | conservation laws | electromagnetic waves | electric properties of matter | conservation laws.

License

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8.01 Physics I (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.

Subjects

classical mechanics | Space and time | straight-line kinematics | motion in a plane | experimental basis of Newton's laws | particle dynamics | universal gravitation | collisions and conservation laws | work and potential energy | vibrational motion | conservative forces | central force motions | inertial forces and non-inertial frames | rigid bodies and rotational dynamics | forces and equilibrium | space | time | space-time | planar motion | forces | equilibrium | Newton?s laws | collisions | conservation laws | work | potential energy | inertial forces | non-inertial forces | rigid bodies | rotational dynamics

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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18.086 Mathematical Methods for Engineers II (MIT)

Description

This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.

Subjects

Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming | Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming

License

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8.01 Physics I (MIT)

Description

Physics I is a first-year physics course which introduces students to classical mechanics. Topics include: space and time; straight-line kinematics; motion in a plane; forces and equilibrium; experimental basis of Newton's laws; particle dynamics; universal gravitation; collisions and conservation laws; work and potential energy; vibrational motion; conservative forces; inertial forces and non-inertial frames; central force motions; rigid bodies and rotational dynamics.

Subjects

classical mechanics | Space and time | straight-line kinematics | motion in a plane | experimental basis of Newton's laws | particle dynamics | universal gravitation | collisions and conservation laws | work and potential energy | vibrational motion | conservative forces | central force motions | inertial forces and non-inertial frames | rigid bodies and rotational dynamics | forces and equilibrium | space | time | space-time | planar motion | forces | equilibrium | Newton?s laws | collisions | conservation laws | work | potential energy | inertial forces | non-inertial forces | rigid bodies | rotational dynamics

License

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8.01SC Physics I: Classical Mechanics (MIT)

Description

Physics I is a first-year, first-semester course that provides an introduction to Classical Mechanics. It covers the basic concepts of Newtonian mechanics, fluid mechanics, and kinetic gas theory.

Subjects

classical mechanics | space and time | straight-line kinematics | motion in a plane | forces and equilibrium | experimental basis of Newton's laws | particle dynamics | universal gravitation | collisions and conservation laws | work and potential energy | vibrational motion | conservative forces | inertial forces and non-inertial frames | central force motions | rigid bodies | rotational dynamics | rigid bodies and rotational dynamics

License

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8.01T Physics I (MIT)

Description

This freshman-level course is an introduction to classical mechanics. The subject is taught using the TEAL (Technology Enabled Active Learning) format which features small group interaction via table-top experiments utilizing laptops for data acquisition and problem solving workshops. Acknowledgements The TEAL project is supported by The Alex and Brit d'Arbeloff Fund for Excellence in MIT Education, MIT iCampus, the Davis Educational Foundation, the National Science Foundation, the Class of 1960 Endowment for Innovation in Education, the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, and the Helena Foundation.

Subjects

classical mechanics | Space and time | straight-line kinematics | motion in a plane | forces and equilibrium | experimental basis of Newton's laws | particle dynamics | universal gravitation | collisions and conservation laws | work and potential energy | vibrational motion | conservative forces | inertial forces and non-inertial frames | central force motions | rigid bodies | rotational dynamics | rigid bodies and rotational dynamics

License

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Enhancing Physics Knowledge for Teaching – Mechanics

Description

The approach we’ll be taking in this session will set the structure for the whole of the module. We’ll begin by introducing a problem that will cover the main learning objectives of the session. We’ll then look at what is required to solve this problem; We’ll build up this knowledge step by step, applying it to the solution of the problem as we proceed. When we get to the end we will have found a solution to the problem. Then we’ll invite you to try some problems covering again some of the topics that have arisen during the session, either on your own or with guidance. We’ll also invite you to raise any issues with these problems in the tutorial.

Subjects

sfsoer | ukoer | forces | kinematics | dynamics | conservation laws | Physical sciences | F000

License

Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales Attribution-Noncommercial-Share Alike 2.0 UK: England & Wales http://creativecommons.org/licenses/by-nc-sa/2.0/uk/ http://creativecommons.org/licenses/by-nc-sa/2.0/uk/

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16.07 Dynamics (MIT)

Description

Dynamics starts with fundamentals of Newtonian mechanics. Further topics include kinematics, particle dynamics, motion relative to accelerated reference frames, work and energy, impulse and momentum, systems of particles and rigid body dynamics. Applications to aerospace engineering are discussed, including introductory topics in orbital mechanics, flight dynamics, inertial navigation and attitude dynamics.

Subjects

Curvilinear motion | carteian coordinates | dynamics | equations of motion | intrinsic coordinates | coordinate systems | work | energy | conservative forces | potential energy | linear impulse | mommentum | angular impulse | relative motion | rotating axes | translating axes | Newton's second law | inertial forces | accelerometers | Newtonian relativity | gravitational attraction | 2D rigid body kinematics | conservation laws for systems of particles | 2D rigid body dynamics | pendulums | 3D rigid body kinematics | 3d rigid body dynamics | inertia tensor | gyroscopic motion | torque-free motion | spin stabilization | variable mass systems | rocket equation | central foce motion | Keppler's laws | orbits | orbit transfer | vibration | spring mass systems | forced vibration | isolation | coupled oscillators | normal modes | wave propagation | cartesian coordinates | momentum | central force motion

License

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1.020 Ecology II: Engineering for Sustainability (MIT)

Description

This course covers the use of ecological and thermodynamic principles to examine interactions between humans and the natural environment. Topics include conservation and constitutive laws, box models, feedback, thermodynamic concepts, energy in natural and engineered systems, basic transport concepts, life cycle analysis and related economic methods.Topics such as renewable energy, sustainable agriculture, green buildings, and mitigation of climate change are illustrated with quantitative case studies. Case studies are team-oriented and may include numerical simulations and design exercises. Some programming experience is desirable but not a prerequisite. Instruction and practice in oral and written communication are provided.

Subjects

systems | conservation laws | constitutive laws | box models | mass conservation | perturbation methods | thermodymanics | heat transfer | enthalpy | entropy | multiphase systems | mass and energy balances | energy supply options | economic value | natural resources | multiobjective analysis | life cycle analysis | mass and energy transport | green buildings | transportation modeling | renewable energy | climate modeling

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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18.086 Mathematical Methods for Engineers II (MIT)

Description

This graduate-level course is a continuation of Mathematical Methods for Engineers I (18.085). Topics include numerical methods; initial-value problems; network flows; and optimization.Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .zip files found on this course site. MATLAB® software is required to run the .m files found on this course site.

Subjects

Scientific computing: Fast Fourier Transform | finite differences | finite elements | spectral method | numerical linear algebra | Complex variables and applications | Initial-value problems: stability or chaos in ordinary differential equations | wave equation versus heat equation | conservation laws and shocks | dissipation and dispersion | Optimization: network flows | linear programming

License

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18.311 Principles of Applied Mathematics (MIT)

Description

Discussion of computational and modeling issues. Nonlinear dynamical systems; nonlinear waves; diffusion; stability; characteristics; nonlinear steepening, breaking and shock formation; conservation laws; first-order partial differential equations; finite differences; numerical stability; etc. Applications to traffic problems, flows in rivers, internal waves, mechanical vibrations and other problems in the physical world.Technical RequirementsMATLAB® software is required to run the .m files found on this course site. MATLAB® is a trademark of The MathWorks, Inc.

Subjects

Nonlinear dynamical systems | nonlinear waves | diffusion | stability | characteristics | nonlinear steepening | breaking and shock formation | conservation laws | first-order partial differential equations | finite differences | numerical stability | traffic problems | flows in rivers | internal waves | mechanical vibrations

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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2.26 Compressible Fluid Dynamics (MIT)

Description

2.26 is a 6-unit Honors-level subject serving as the Mechanical Engineering department's sole course in compressible fluid dynamics. The prerequisites for this course are undergraduate courses in thermodynamics, fluid dynamics, and heat transfer. The goal of this course is to lay out the fundamental concepts and results for the compressible flow of gases. Topics to be covered include: appropriate conservation laws; propagation of disturbances; isentropic flows; normal shock wave relations, oblique shock waves, weak and strong shocks, and shock wave structure; compressible flows in ducts with area changes, friction, or heat addition; heat transfer to high speed flows; unsteady compressible flows, Riemann invariants, and piston and shock tube problems; steady 2D supersonic flow, Prandtl-Mey

Subjects

conservation laws | isentropic flows | normal shock wave relations | oblique shock waves | weak shock | strong shock | ducts | heat transfer | unsteady flows | Riemann invariants | piston | shock tube | steady 2D supersonic flow | Prandtl-Meyer function | self-similar compressible flows

License

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