2003-2005 - Graduate School - The University of Alabama

170 The University of AlabamaMATH 528 Introduction to Optimal Control. Three hours.Prerequisite: MATH 238.Corequisite: MATH 510 or permission of the department.Introduction to the theory and applications of deterministic systems and their controls.Major topics include calculus of variations, the Pontryagin maximum principle, dynamicprogramming, stability, controllability, and numerical aspects of control problems.MATH 532 Graph Theory and Applications. Three hours.Prerequisites: MATH 237 or MATH 257, and MATH 382 or permission of theinstructor.Survey of several of the main ideas of general graph theory with applications to networktheory. Topics include oriented and nonoriented linear graphs, spanning trees, branchingsand connectivity, accessibility, planar graphs, networks and fl ows, matchings, andapplications.MATH 537 Special Topics in Applied Mathematics I. Three hours.Prerequisite: Permission of the department.MATH 538 Special Topics in Applied Mathematics II. Three hours.Prerequisite: Permission of the department.MATH 541 Boundary Value Problems. Three hours.Prerequisites: MATH 343 and MATH 382, or permission of the department.Emphasis on boundary-value problems for classical partial differential equations ofphysical sciences and engineering. Other topics include boundary-value problems forordinary differential equations and for systems of partial differential equations.MATH 542 Integral Transforms and Asymptotics. Three hours.Prerequisite: MATH 441, MATH 541, or permission of the department.Introduction to complex variable methods, integral transforms, asymptotic expansions,WKB method, matched asymptotics, and boundary layers.MATH 544 Singular Perturbations. Three hours.Prerequisites: MATH 382 and MATH 441 (or MATH 541), or permission of the department.Topics include regular perturbation methods for solving partial differential equations,matched asymptotic methods for differential equations, and the methods of strainedcoordinates and multiple scales, with applications to problems in combustion theory,fl uid dynamics, and biology.MATH 545 Theoretical Foundations of Fluid Dynamics I. Three hours.Prerequisite: MATH 343, AEM 264 or equivalent, or permission of the department.Introduction to continuum mechanics and tensors. Local fl uid motion. Equations governing fl uid fl ow and boundary conditions. Some exact solutions of the Navier-Stokesequations. Vortex motion. Potential fl ow and aerofoil theory.MATH 546 Theoretical Foundations of Fluid Dynamics II. Three hours.Prerequisite: MATH 545 or equivalent, or permission of the department.Introduction to asymptotic methods and other approximate methods applied to classicalproblems in boundary-layer theory, low Reynolds number fl ows, surface gravity waves,shallow-water theory, and hydrodynamic stability.MATH 551 Mathematical Sta tis tics with Ap pli ca tions I. Three hours.Prerequisites: MATH 237 and MATH 355.Introduction to mathematical statistics. Topics include bivariate and multivariate probabil i ty distributions; functions of random variables; sampling distributions and the centrallimit theorem; concepts and properties of point estimators; various methods of pointes ti ma tion; interval estimation; tests of hypotheses; and Neyman-Pearson lemma withsome applications. Credit for this course will not be counted toward an advanced degreein math e mat ics.MATH 552 Mathematical Statistics with Applications II. Three hours.Prerequisite: MATH 551.Considers further applications of the Neyman-Pearson lemma, likelihood ratio tests,chi-square test for goodness of fi t, estimation and test of hypothesis for linear statisticalmodels, the analysis of variance, analysis of enumerative data, and some topics innonparametric statistics. Credit for this course will not be counted toward an advanceddegree in mathematics.