MA 502 Boundary Value Problems 3 Credits
Basic techniques of solving boundary-value problems of partial differential equations by employing the methods of Fourier series orthogonal functions, operational calculus including Laplace transforms, other integral transforms, and Cauchy's residue calculus. Applications to heat transfer, fluid mechanics, elasticity, and mechanical vibrations. Computer applications.
Prerequisites: MA 441.
MA 504 Theory of the Potential 3 Credits
Potential theory and Green's function. Method of characteristics and solution of Cauchy's initial value problem for first and second order equations. Numerical methods. Application to fluid mechanics, electromagnetic fields, heat conduction, and other areas. Computer applications.
Prerequisites: MA 502.
MA 505 Statistics I 3 Credits
Descriptive statistics and graphical depiction of data; confidence intervals and hypothesis testing for the mean, difference between two means, variance, ratio of two variances, proportion, and difference between two proportions; simple and multiple regression, including model development, inferences, residual analysis, outlier identification, and verification of assumptions; fundamental concepts of design of experiments; justification of linear models; construction and analysis of basic designs including one-way, block designs, and Latin squares; multiple comparisons.
Prerequisites: MA 243.
MA 506 Probability for Engineers 3 Credits
Foundations, combinations, conditional probability, expectations, and applications to discrete sample spaces. Random variable in one or more dimensions. Various continuum distributions. Characteristic functions. Applications to engineering problems. Computer applications.
Prerequisites: MA 441.
MA 510 Fundamentals of Optimization 3 Credits
Overview of several important general types of optimization problems; development of mathematical models; linear programming; the simplex method; introduction to sensitivity analysis, networks; applications involving Maple and Excel.
Prerequisites: MA 243.
MA 520 Mathematical Programming and Decision-Making 3 Credits
A continuation of MA 510. Development of mathematical modeling techniques with an emphasis on integer programming, nonlinear programming, and multiple-criteria decision-making techniques; case studies from aviation/aerospace involving mathematical programming and decision-making.
Prerequisites: MA 510.
MA 540 Data Mining 3 Credits (3,0)
Data Mining is to gather, assimilate, and make sense of large amounts of data. The course includes techniques, algorithms, and open-source software to automatically classify data, to discover novel and useful patterns, and to help predict future outcomes. Prerequisites are Statistics, Multivariate Calculus, and familiarity with either Java, C/C++, MATLAB or R.
MA 541 Introduction to Mathematical Analysis 3 Credits
Careful treatment of the theoretical aspects of the calculus of functions of a real variable. Topics include the real number system, limits, continuity, derivatives, the Riemann integral, elementary notions of topology and metric spaces.
MA 543 Complex Variables 3 Credits
Algebra of complex numbers; complex functions, analytic functions; mapping by elementary functions; conformal mappings and their applications; additional topics may include complex integration, power series expansion.
MA 544 Scientific Visualization 3 Credits
Scientific visualization is the representation of data graphically as a means of gaining understanding and insight into the data. This course will introduce different aspects of scientific visualization: computer graphics and related mathematics concepts, application packages for interactive display and analysis of data.
MA 550 Partial Differential Equations 3 Credits
Physical models leading to partial differential equations. Fourier series and Fourier transforms. Solution of linear partial differential equations, including solutions of the wave, heat and Laplace's equation.
MA 553 High Performance Scientific Computing 3 Credits
This course is an introduction to high performance computing in computational mathematics and sciences with practical applications. The course provides an overview of parallel computing and study of program efficiency on high performance computers. It concentrates on the two major parallelization paradigms: shared-memory parallelization with OpenMP and distributed-memory parallel programming with MPI. The main focus of the course will be on applications of parallel computing in the sciences (Engineering, Physics, Mathematics, etc.).
Prerequisites: MA 305 or MA 348.
MA 588 Numerical Methods in Fluids 3 Credits
This course explores the theory and applications of numerical methods in fluid mechanics. The topics covered will include numerical methods for incompressible flows; primitive variable and vorticity stream function on formulation; numerical treatment for inviscid and viscous flows, including restricted to incompressible flow. Emphasis will be placed on numerical methods based on finite difference, finite volume, or finite element formulations.
MA 605 Statistical Quality Analysis 3 Credits
Fundamental concepts of statistical quality control, including Shewhart charts, cusum charts, EWMA charts, multivariate charts, tolerance limits, and capability analysis. Further development of concepts in statistical design of experiments including use of factorial designs, fractional factorial designs, and use of central composite designs. Several nonparametric statistical techniques, including sign test, signed rank test, rank-sum test, Kruskal-Wallis test, runs test, and Kendall's Tau. Advanced regression topics, including the use of transformations, weighted least squares regression, and detection of influential points. Throughout the course, industrial applications will be emphasized, including the use of several case studies.
Prerequisites: MA 505.
MA 610 Multivariate Optimization 3 Credits
Multiple objective optimization with an emphasis on response surface methodologies and goal programming; inclusion of group decision-making techniques in model development; case studies from aviation/aerospace emphasizing multivariate model development, and determination of optimal solutions.
Prerequisites: MA 520 and MA 605.
MA 690 Graduate Research Project 3 Credits
An applied problem on an aviation/aerospace topic that requires the use of optimization and/or quality- improvement skills.
MA 699 Special Topics in Mathematics 1-6 Credit
Students may elect to perform a special, directed analysis and/or independent study in an aviation area of particular interest. A detailed proposal of the desired project must be developed and presented to the department chair or center director for faculty review and recommendation, three weeks prior to the end of registration for the term.
MA 700 Thesis Research 1-9 Credit
Written and defended documentation of a research project conducted under the supervision of a faculty committee. The research must be at the level of a published paper in an appropriate journal, as determined by the faculty committee.