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Course Criteria
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0.00 - 4.00 Credits
Methods of mathematical analysis for the solution of problems in physics and engineering. Topics include an introduction to functional analysis, linear analysis & eigenvalue problems for matrices & operators, Sturm-Liouville theory, Green's functions for the solution of linear ordinary differential equations and Poisson's equation, and the calculus of variations, and the inverse and implicit function theorems.
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0.00 - 4.00 Credits
A laboratory course that focuses on basic electronics techniques, digital electronics, and data acquisition and analysis. Topics include introduction to digital and analog electronics, digital-to-analog and analog-to-digital conversion, microcomputer sampling, and data analysis. There are four laboratory hours and two lecture hours per week. There is one project.
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0.00 - 4.00 Credits
A one-semester research project under the supervision of a faculty member. The topic is developed by the student and faculty supervisor. Course culminates in a final report in the style of a research paper. Post generals students that have not already taken that course may take this course, however, they must take it with a faculty member other than their research advisor on a different research topic. P/D/F for Ph.D. candidates, graded for MSE and MEng candidates.
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0.00 - 4.00 Credits
Continuation of MAE 513. Directed study for Master of Engineering students. The topic is proposed by the student and must be approved by the student's research advisor and have received approval from the MAE Graduate Committee.
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0.00 - 4.00 Credits
An introduction to principles of lasers. Topics include propagation theory, interaction of light and matter, Fourier optics, and a description of operational characteristics of lasers, light scattering, and nonlinear optics.
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0.00 - 4.00 Credits
Physical and chemical topics of basic importance in modern fluid mechanics, plasma dynamics, and combustion science: statistical calculations of thermodynamic properties of gases; physical equilibria; quantum mechanical analysis of atomic and molecular structure including rotational and vibrational transitions; atomic-scale collision phenomena adn excitation and ionization; emission, absorption, and propagation of radiation. Analyses of major greenhouse gases from point of view of molecular absorption and emission properties; discussion of affect of greenhouse gases concentration and disribution on climate equilibria.
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0.00 - 4.00 Credits
Chemical thermodynamics and kinetics, oxidation of hydrogen, hydrocarbons and alternate fuels, pollutant chemistry and control, transport phenomena, laminar premixed and nonpremixed flames, turbulent flames, ignition, extinction, and flammability phenomena, flame stabilization and blowoff, detonation and blast waves, droplet, spray and coal particle combustion, principles of engine operation.
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0.00 - 4.00 Credits
Theoretical aspects of combustion: the conservation equations of chemically-reacting flows; activation energy asymptotics; chemical and dynamic structures of laminar premixed and nonpremixed flames; aerodynamics and stabilization of flames; pattern formation and geometry of flame surfaces; ignition, extinction, and flammability phenomena; turbulent combustion; boundary layer combustion; droplet, particle, and spray combustion; and detonation and flame stabilization in supersonic flows.
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0.00 - 4.00 Credits
Phase-plane methods and single-degree-of-freedom nonlinear oscillators; invariant manifolds, local and global analysis, structural stability and bifurcation, center manifolds, and normal forms; averaging and perturbation methods, forced oscillations, homoclinic orbits, and chaos; and Melnikov's method, the Smale horseshoe, symbolic dynamics, and strange attractors.
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0.00 - 4.00 Credits
Principles and methods for formulating and analyzing mathematical models of physical systems; Newtonian, Lagrangian, and Hamiltonian formulations of particle and rigid and elastic body dynamics; canonical transformations, Hamilton-Jacobi theory; and integrable and nonintegrable systems. Additional topics are explored at the discretion of the instructor.
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