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Course Criteria
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3.00 Credits
Bifurcations, normal forms, pattern formations, mixing, Lagrangian chaos, and applications to fluid dynamics.
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3.00 Credits
Sobolev spaces; incompressible Euler and Navier-Stokes equations; weak and strong solutions; attractors and the connection with turbulence; geophysical applications. Completion of a course in Differential Equations II is strongly recommended prior to enrollment in this course.
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3.00 Credits
Bounded linear and compact operators on Hilbert spaces. Linear integral equations, Fredholm and Hilbert-Schmidt theory, and approximate methods. Distributions. Completion of a course in Applied Analysis is strongly recommended prior to enrollment in this course.
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3.00 Credits
Regular and singular perturbation methods for ordinary and partial differential equations, Boundary layer theory, matched asymptotic expansions, multiple-scale, homogenization, and WKB methods. Application to nonlinear oscillations, bifurcation and stability problems. Completion of a course in Differential Equations II or Partial Differential Equations in Engineering is strongly recommended prior to enrollment in this course.
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3.00 Credits
Existence and uniqueness theorems, boundary value and initial value problems, characteristics, Green's functions, maximum principle, distributions, and weak solutions.
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3.00 Credits
Continuation of APM 576. Completion of a course in the Theory of Partial Differential Equations is strongly recommended prior to enrollment in this course.
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3.00 Credits
Manifolds, tangent and cotangent bundle, Lie theory, integrability and controllability, and feedback control. Students should have previously taken coursework in differential equations, applied analysis, applied probability, and stochastic processes.
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3.00 Credits
Variational principles, Euler-Lagrange equations, Hamiltonian systems, optimal control, connections and curvature. Students should have previously taken coursework in differential equations, applied analysis, applied probability, and stochastic processes.
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1.00 - 12.00 Credits
A small class emphasizing discussion, presentations by students, and written research papers.
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1.00 - 4.00 Credits
Topical courses not offered in regular course rotation--e.g., new courses not in the catalog, courses by visiting faculty, courses on timely topics, highly specialized courses responding to unique student demand.
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