ENME Ph.D. Approved Math Courses

ENME 605: Advanced Systems Control (3 Credits) Prerequisite: ENME462; or permission of instructor.

  Modern control theory for both continuous and discrete systems. State space representation is reviewed and the concepts of controllability and observability are discussed. Design methods of deterministic observers are presented and optimal control theory is formulated. Control techniques for modifying system characteristics are discussed.

ENME 610: Engineering Optimization (3 Credits).

Overview of applied single- and multi- objective optimization and decision making concepts and techniques with applications in engineering design and/or manufacturing problems. Topics include formulation examples, concepts, optimality conditions, unconstrained/constrained methods, and post-optimality sensitivity analysis. Students are expected to work on a semester-long real-world multi-objective engineering project.

ENME 625: Multidisciplinary Optimization (3 Credits).

Overview of single- and multi-level design optimization concepts and techniques with emphasis on multidisciplinary engineering design problems. Topics include single and multilevel optimality conditions, hierarchic and nonhierarchic modes and multilevel post optimality sensitivity analysis. Students are expected to work on a semester-long project.

ENME 700: Advanced Mechanical Engineering Analysis (3 Credits)

An advanced, unified approach to the solution of mechanical engineering problems, emphasis is on the formulation and solution of equilibrium, eigenvalue and propagation problems. Review and extension of undergraduate material in applied mathematics with emphasis on problems in heat transfer, vibrations, fluid flow and stress analysis which may be formulated and solved by classical procedures.

***ENME 722: Equilibrium Programming in Engineering (3 Credits)

Provide motivation and introduction to equilibrium models involving economics and engineering. We will concentrate on models involving markets (Nash-Cournot, etc.), those wherein the activities are spatially diverse, and those involving energy activities or traffic flow. 

***ENME 725: Probabilistic Optimization (3 Credits)

Prerequisite: An advanced undergraduate course in probability and a graduate course in optimization or permission of the instructor required. Also offered as: ENCE725. Credit only granted for: ENME725 or ENCE725.   Provide an introduction to optimization under uncertainty. Chance-constrained programming, reliability programming, value of information, two stage problems with recourse, decomposition methods, nonlinear and linear programming theory, probability theory. The objectives of this course are to provide understanding for studying problems that involve optimization under uncertainty, learn about various stochastic programming formulations (chance constrained programs, two stage methods with recourse, etc.) relevant to engineering and economic settings, present theory for solutions to such problems, and present algorithms to solve these problems.

***ENME741: Operations Research Models in Engineering (3 Credits)

The course will cover the fundamentals of Management Science techniques in Project Management including: linear and integer programming, goal programming, multi-objective optimization, simulation, Analytic Hierarchy Process (AHP), deterministic and stochastic dynamic programming.  Applications will be drawn from the Critical Path Method (CPM), resource management, and other areas of Project management.

***ENME 741 is the first graduate level course in the 3-optimization course series of ENME 741, 722 and 725.  ENME 741 provides an overview of both linear and nonlinear programming/game theory/equilibrium problems with both theory and plenty of engineering and economic examples as well as some algorithms.  Then, in ENME 722 the nonlinear programming/game theory/equilibrium problems are explored more deeply with engineering and economics examples.  In ENME 725, stochastic optimization problems and algorithms are presented. For both ENME 722 and ENME 725,  it’s assumed a background in a first-year, graduate optimization course like ENME 741.  Lastly, either ENME 722 or ENME 725 can follow after ENME 741 (or an equivalent course).

ENME 745: Computational Methods in Science and Engineering (3 Credits)

Credit only granted for: ENME745 and ENME808B. Formerly: ENME808B.   Fundamental aspects of how to apply analytical mathematical concepts to discrete data. The course is aimed at graduate students in any area of engineering, and treats the material in a general manner that is not specific to any application or field of specialization.

ENRE 620: Mathematical Techniques of Reliability Engineering (3 Credits). Prerequisites: MATH 246 or permission of department.

Basic probability and statistics Application of selected mathematical techniques to the analysis and solution of reliability engineering problems.  Applications of matrices, vectors, tensors, differential equations, integral transforms, and probability methods to a wide range of reliability-related problems

ENRE 655: Advanced Methods in Reliability Modeling (3 Credits)

Prerequisite: ENRE602. Credit only granted for: ENRE655 or ENRE665. Formerly: ENRE665.   Bayesian methods and applications, estimation of rare event frequencies uncertainty analysis and propagation methods, reliability analysis of dynamic systems, analysis of dependent failures, reliability of repairable systems, human reliability analysis methods and theory of logic diagrams and application to systems reliability

Any MATH, STAT, or AMSC course at the 600 level or above