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Course Criteria
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0.00 Credits
Lectures and discussions of topics of current interest in applied mathematics. May not be offered every quarter; content may vary from one offering to another.
Prerequisite:
permission of instructor
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1.00 Credits
Special topics and selected problems of current interest in applied mathematics. Credit/ no credit only. Offered: AWSp.
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1.00 Credits
The clinic provides consulting service for problems from different academic units requiring assistance in formulation, analysis, and interpretation of mathematical models. Students learn to delineate sources of difficulties, identify or devise a method of solution, and effectively communicate it to clients. Credit/no credit only. Offered: AWSp.
Prerequisite:
AMATH 568, AMATH 569, and AMATH 584
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3.00 Credits
Mathematical modeling in biomedical sciences (mainly ecology, epidemiology, physiology, and zoology). Topics covered include modeling (continuous and discrete), population interactions, dynamic diseases, reaction kinetics, biological oscillators, oscillator generated wave phenomena, epidemics, and the dynamics of infectious diseases. Offered: A.
Prerequisite:
AMATH 402 or equivalent knowledge of ordinary differential equations
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3.00 Credits
Mathematical modeling in the biomedical sciences (mainly ecology, epidemiology, and zoology). Topics include spatial spread of populations, traveling wave phenomena in biology, reaction diffusion theory, biological pattern formation mechanisms, mechanochemical theory of morphogenesis, spatial spread of epidemics. (May be taken independently of 503.) Offered: W.
Prerequisite:
AMATH 402, AMATH 403 or equivalents; ordinary, partial differential equations
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4.00 Credits
Eulerian equations for mass-motion; Navier- Stokes equation for viscous fluids, Cartesion tensors, stress-strain relations; Kelvin’s theorem, vortex dynamics; potential flows, flows with highlow Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory. Offered: jointly with ATM S 505/OCEAN 511; A.
Prerequisite:
AMATH 403 or permission of instructor
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4.00 Credits
Discreet and continuous random variables, independence and conditional probability, central limit theorem, elementary statistical estimation and inference, linear regression. Emphasis on physical applications. Offered: jointly with STAT 506.
Prerequisite:
some advanced calculus and linear algebra
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5.00 Credits
Necessary and sufficient conditions for a weak and strong extremum. Legendre transformation, Hamiltonian systems. Constraints and Lagrange multipliers. Space-time problems with examples from elasticity, electromagnetics, and fluid mechanics. Sturm-Liouville problems. Approximate methods.
Prerequisite:
AMATH 351 or MATH 307; MATH 324, 327; recommended: AMATH 402 and AMATH 403 or MATH 428 and 429
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3.00 Credits
Trajectories obtained from ordinary differential equations with control variables. Controllability, optimality, the maximum principle. Relaxation and the existence of solutions. Techniques of nonsmooth analysis. Offered: jointly with MATH 509; even years.
Prerequisite:
real analysis on the level of MATH 426; background in optimization corresponding to AMATH 507 or AMATH 515
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3.00 Credits
Zabinsky Discussion of issues arising in applications of optimization to engineering design. Emphasis on formulating problems and selecting appropriate solution techniques. Random search methods for problems otherwise computationally intractable. Individual projects in engineering optimal design. Offered: jointly with IND E 516.
Prerequisite:
AMATH/MATH/IND E 515 and MATH 328 or permission of instructor
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