RSS Feed for perturbation methods https://solvonauts.org/%3Faction%3Drss_search%26term%3Dperturbation+methods RSS Feed for perturbation methods 1.020 Ecology II: Engineering for Sustainability (MIT) 1.020 Ecology II: Engineering for Sustainability (MIT) 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 http://dspace.mit.edu/handle/1721.1/52323 http://dspace.mit.edu/handle/1721.1/52323 18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT) This course is about mathematical analysis of continuum models of various natural phenomena Such models are generally described by partial differential equations PDE and for this reason much of the course is devoted to the analysis of PDE Examples of applications come from physics chemistry biology complex systems traffic flows shock waves hydraulic jumps bio fluid flows chemical reactions diffusion heat transfer population dynamics and pattern formation This course is about mathematical analysis of continuum models of various natural phenomena Such models are generally described by partial differential equations PDE and for this reason much of the course is devoted to the analysis of PDE Examples of applications come from physics chemistry biology complex systems traffic flows shock waves hydraulic jumps bio fluid flows chemical reactions diffusion heat transfer population dynamics and pattern formation http://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2009 http://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2009 18.369 Mathematical Methods in Nanophotonics (MIT) 18.369 Mathematical Methods in Nanophotonics (MIT) Find out what solid state physics has brought to Electromagnetism in the last 20 years This course surveys the physics and mathematics of nanophotonics electromagnetic waves in media structured on the scale of the wavelength Topics include computational methods combined with high level algebraic techniques borrowed from solid state quantum mechanics linear algebra and eigensystems group theory Bloch s theorem and conservation laws perturbation methods and coupled mode theories to understand surprising optical phenomena from band gaps to slow light to nonlinear filters Note An earlier version of this course was published on OCW as 18 325 Topics in Applied Mathematics Mathematical Methods in Nanophotonics Fall 2005 Find out what solid state physics has brought to Electromagnetism in the last 20 years This course surveys the physics and mathematics of nanophotonics electromagnetic waves in media structured on the scale of the wavelength Topics include computational methods combined with high level algebraic techniques borrowed from solid state quantum mechanics linear algebra and eigensystems group theory Bloch s theorem and conservation laws perturbation methods and coupled mode theories to understand surprising optical phenomena from band gaps to slow light to nonlinear filters Note An earlier version of this course was published on OCW as 18 325 Topics in Applied Mathematics Mathematical Methods in Nanophotonics Fall 2005 http://ocw.mit.edu/courses/mathematics/18-369-mathematical-methods-in-nanophotonics-spring-2008 http://ocw.mit.edu/courses/mathematics/18-369-mathematical-methods-in-nanophotonics-spring-2008 18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT) 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 http://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2014 http://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2014 18.311 Principles of Applied Mathematics (MIT) 18.311 Principles of Applied Mathematics (MIT) This course is about mathematical analysis of continuum models of various natural phenomena Such models are generally described by partial differential equations PDE and for this reason much of the course is devoted to the analysis of PDE Examples of applications come from physics chemistry biology complex systems traffic flows shock waves hydraulic jumps bio fluid flows chemical reactions diffusion heat transfer population dynamics and pattern formation This course is about mathematical analysis of continuum models of various natural phenomena Such models are generally described by partial differential equations PDE and for this reason much of the course is devoted to the analysis of PDE Examples of applications come from physics chemistry biology complex systems traffic flows shock waves hydraulic jumps bio fluid flows chemical reactions diffusion heat transfer population dynamics and pattern formation http://dspace.mit.edu/handle/1721.1/97754 http://dspace.mit.edu/handle/1721.1/97754 18.311 Principles of Applied Mathematics (MIT) This course is about mathematical analysis of continuum models of various natural phenomena Such models are generally described by partial differential equations PDE and for this reason much of the course is devoted to the analysis of PDE Examples of applications come from physics chemistry biology complex systems traffic flows shock waves hydraulic jumps bio fluid flows chemical reactions diffusion heat transfer population dynamics and pattern formation https://dspace.mit.edu/handle/1721.1/97754 https://dspace.mit.edu/handle/1721.1/97754 1.020 Ecology II: Engineering for Sustainability (MIT) 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 https://dspace.mit.edu/handle/1721.1/52323 https://dspace.mit.edu/handle/1721.1/52323 18.311 Principles of Applied Mathematics (MIT) 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 https://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2014 https://ocw.mit.edu/courses/mathematics/18-311-principles-of-applied-mathematics-spring-2014 18.369 Mathematical Methods in Nanophotonics (MIT) Find out what solid state physics has brought to Electromagnetism in the last 20 years This course surveys the physics and mathematics of nanophotonics electromagnetic waves in media structured on the scale of the wavelength Topics include computational methods combined with high level algebraic techniques borrowed from solid state quantum mechanics linear algebra and eigensystems group theory Bloch s theorem and conservation laws perturbation methods and coupled mode theories to understand surprising optical phenomena from band gaps to slow light to nonlinear filters Note An earlier version of this course was published on OCW as 18 325 Topics in Applied Mathematics Mathematical Methods in Nanophotonics Fall 2005 https://ocw.mit.edu/courses/mathematics/18-369-mathematical-methods-in-nanophotonics-spring-2008 https://ocw.mit.edu/courses/mathematics/18-369-mathematical-methods-in-nanophotonics-spring-2008