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Course Criteria
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3.00 Credits
Applications of mathematics to problems in chemical engineering; vector calculus; properties and methods of solution of first and second order partial differential equations; similarity transforms, separation of variables, Laplace and Fourier transforms. Offered: jointly with CHEM E 512; A.
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3.00 Credits
Networks and directed graphs. Paths and trees. Feasible and optimal flows and potentials. Transportation problems, matching and assignment problems. Algorithms and applications. Offered: jointly with MATH 514.
Prerequisite:
MATH 308 or AMATH 352 and MATH 324
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5.00 Credits
Maximization and minimization of functions of finitely many variables subject to constraints. Basic problem types and examples of applications; linear, convex, smooth, and nonsmooth programming. Optimality conditions. Saddlepoints and dual problems. Penalties, decomposition. Overview of computational approaches. Offered: jointly with IND E 515/MATH 515.
Prerequisite:
linear algebra and advanced calculus
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3.00 Credits
Methods of solving optimization problems in finitely many variables, with or without constraints. Steepest descent, quasi-Newton methods. Quadratic programming and complementarity. Exact penalty methods, multiplier methods. Sequential quadratic programming. Cutting planes and nonsmooth optimization. Offered: jointly with MATH 516.
Prerequisite:
AMATH 515
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3.00 Credits
Sequential optimization problems involving random variables. Dynamic programming, stochastic programming. Control of uncertain dynamic systems in finite, discrete time. Risk, feedback, adaptivity. Problems with imperfect state information. Applications to optimal stopping, inventory control, resource management. Offered: jointly with MATH 517.
Prerequisite:
AMATH 506 (or an introduction to basic concepts of probability such as STAT 390 or 394, 395), MATH 308 and 324
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5.00 Credits
In-depth study of an application topic in applied mathematics. Topics may include special studies in geophysical fluid dynamics, hydrodynamic stability, turbulence, analytic dynamics, solid mechanics, applied optimization, tensor analysis, stochastic analysis, and nonlinear optics and lasers. Offered: W.
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5.00 Credits
DNA-folding, patter-forming systems, stochastic analysis. Offered: Sp.
Prerequisite:
AMATH 402 or equivalent
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3.00 Credits
Nonlinear first-order partial differential equations: characteristics, applications to geometrical optics and Hamilton-Jacobi theory. Linear and quasilinear hyperbolic equations: conservation laws, characteristics, shocks, examples from fluid dynamics. Approximate solution methods: regular, singular, and multiple-scale perturbations. Offered: odd years.
Prerequisite:
AMATH 569
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3.00 Credits
Nonlinear first-order partial differential equations: characteristics, applications to geometrical optics and Hamilton-Jacobi theory. Linear and quasilinear hyperbolic equations: conservation laws, characteristics, shocks, examples from fluid dynamics. Approximate solution methods: regular, singular, and multiple-scale perturbations. Offered: odd years.
Prerequisite:
AMATH 569
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5.00 Credits
Complex variable and associated topics. Branch cuts, series and product expansions. Contour integration, numerical implications. Harmonic functions. Complex potential (and singularities) in physical problems. Conformal mapping; applications and examples. Fourier and Laplace transforms and applications. Recommended: 401 or equivalent. Offered: A.
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