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APM 560: Applied Dynamical Systems
3.00 Credits
Arizona State University
Bifurcations, normal forms, pattern formations, mixing, Lagrangian chaos, and applications to fluid dynamics.
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APM 560 - Applied Dynamical Systems
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APM 561: Nonlinear Analysis of PDEs in Fluids
3.00 Credits
Arizona State University
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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APM 561 - Nonlinear Analysis of PDEs in Fluids
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APM 570: Applied Linear Operators
3.00 Credits
Arizona State University
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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APM 570 - Applied Linear Operators
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APM 575: Perturbation Methods in Applied Mathematics
3.00 Credits
Arizona State University
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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APM 575 - Perturbation Methods in Applied Mathematics
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APM 576: Theory of Partial Differential Equations
3.00 Credits
Arizona State University
Existence and uniqueness theorems, boundary value and initial value problems, characteristics, Green's functions, maximum principle, distributions, and weak solutions.
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APM 576 - Theory of Partial Differential Equations
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APM 577: Theory of Partial Differential Equations
3.00 Credits
Arizona State University
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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APM 577 - Theory of Partial Differential Equations
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APM 581: Geometry and Control of Dynamical Systems I
3.00 Credits
Arizona State University
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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APM 581 - Geometry and Control of Dynamical Systems I
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APM 582: Geometry and Control of Dynamical Systems II
3.00 Credits
Arizona State University
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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APM 582 - Geometry and Control of Dynamical Systems II
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APM 591: Seminar
1.00 - 12.00 Credits
Arizona State University
A small class emphasizing discussion, presentations by students, and written research papers.
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APM 591 - Seminar
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APM 598: Special Topics
1.00 - 4.00 Credits
Arizona State University
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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APM 598 - Special Topics
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