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Course Criteria
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3.00 Credits
Prereq., graduate status in engineering or arts and sciences, or instructor consent. Same as APPM 4360.
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3.00 Credits
Same as APPM 4380.
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3.00 Credits
Reviews basic ideas of complex analysis, including solutions of ODEs and PDEs of physical interest via complex analysis; conformal mapping, including Schwarz-Christoffel transformations and generalizations; computational methods; Riemann-Hilbert problems; and topics in asymptotic methods. Prereq., APPM 4360 or 5360, or instructor consent.
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3.00 Credits
Discusses the elements of basic real and complex analysis, Banach spaces, LP spaces, and many relevant inequalities. Includes applications of existence and uniqueness of solutions to various types of ordinary differential equations, partial differential equations, and integral equations. Prereqs., MATH 4310 and 4320, or equivalent; MATH 3130 or equivalent; or instructor consent.
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3.00 Credits
Continuation of APPM 5440. Prereq., APPM 5440 or instructor consent.
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3.00 Credits
Introduces the theory and applications of dynamical systems through solutions to differential equations. Covers existence and uniqueness theory, local stability properties, qualitative analysis, global phase portraits, perturbation theory, and bifurcation theory. Special topics may include Melnikov methods, averaging methods, bifurcations to chaos, and Hamiltonian systems. Prereqs., undergraduate courses equivalent to APPM 2360, 3310, and MATH 4310.
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3.00 Credits
Studies properties and solutions of partial differential equations. Covers methods of characteristics for partial differential equations, well-posed problems, main results for the well-known equations, Green's functions, and related integral equations. Prereqs., APPM 4350 and 4360, or MATH 4430, or equivalent.
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3.00 Credits
Covers asymptotic evaluation of integrals (stationary phase and steepest descent), perturbation methods (regular and singular methods, and inner and outer expansions), multiple scale methods, and applications to differential and integral equations. Prereq., APPM 5470 or instructor consent.
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3.00 Credits
Same as APPM 4520 and MATH 5520.
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3.00 Credits
Same as APPM 4540 and MATH 5540.
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