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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

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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18.311 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.

Subjects

partial differential equation | hyperbolic equations | dimensional analysis | perturbation methods | hyperbolic systems | diffusion and reaction processes | continuum models | equilibrium models | continuous applied mathematics | traffic flow | fluids | elasticity | granular flows | 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) | sonic booms | Mach cone | caustics | lattices | dispersion | group velocity

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

Site sourced from

https://ocw.mit.edu/rss/all/mit-allcourses.xml

Attribution

Click to get HTML | Click to get attribution | Click to get URL

All metadata

See all metadata