# Courses

#### Engineering (ENGR)

**5011. Engineering Mathematics I (3 s.h.)**

This mathematics course is for those studying engineering at the master’s level. Topics include real-variable theory (limits, series, functions of several variables, vector field theory); complex variable theory; linear analysis (systems of linear equations, eigenvalue problems, Sturm-Liouville theory); and recipes for the numerical solution of any first- or second-order linear differential equation. MATLAB programming is introduced.

5012.
**Engineering Mathematics II (3 s.h.)**

*Prerequisite: ENGR 5011.*

This course provides students with the analytical and numerical tools needed to solve partial differential equations of the type found in engineering practice. Topics include the UNIX programming environment; the C programming language; separation of variables methods in Cartesian and non-Cartesian coordinate systems; integral transform methods; root finding; integration/differentiation; interpolation of tabulated data; initial-value and boundary-value problems; and partial differential equations.

5022. **Engineering Analysis and Applications (3 s.h.)**

This course covers vector space, basis, projection, null space, function space, L2 and space of continuous functions, Hilbert space, orthogonality, generalized Fourier series, linear transformation, adjoint transformation, eigenvalue problems, linear functional, Gâteaux and Fréchet differential, constrained optimization, infinite dimensional systems, and complex analysis.

**5032. Probability, Statistics, and Stochastic Methods (3 s.h.)**

This course presents a balanced approach to probability, statistics, stochastic models, and stochastic differential equations with special emphasis on engineering applications. It also covers random variables, probability distributions, Monte Carlo simulation models, statistical inference theory, design of engineering experiments, reliability and risk assessment, fitting data to probability distributions, ANOVA, stochastic processes, Brownian motion, white noise, random walk, and colored noise processes. Also discussed are differential equations subject to random initial conditions, random forcing functions, and random parameters; partial differential equations subject to stochastic boundary conditions; and new techniques for non-linear differential equations. Students engage in computer simulation with MAPLE and other symbolic algebra software.

**5033. Probability and Random Processes (3 s.h.)**

This course covers sets and events, random variables, distribution and density functions, functions of multiple random variables, moments and conditional statistics, information entropy, stochastic processes, wide-sense stationary process, ergodicity, correlation, the power spectrum of stationary processes, applications to sampling theory, and signal modulation and detection.

5116. **Spacecraft Systems Engineering (3 s.h.)**

The concept of systems engineering is introduced using a satellite application. Systems engineering is a top-down approach to the design, implementation, testing, and deployment of large-scale systems to meet the needs of users. Topics include systems engineering methodology, dynamics of spacecraft, and celestial mechanics. This course also introduces the notions of invention and innovation and how they relate to issues of intellectual property.

5117. **Experimental Methods (3 s.h.)**

This course emphasizes application and design of experimental techniques and measurement systems used in engineering laboratories; introduction to the DMM, digital scope, and computer-based data acquisition systems for measurements of force, motion, pressure, temperature, and flow in steady and unsteady systems; data transmission, data analysis and presentation, and computer interfacing techniques; statistical methods and uncertainty analysis; and hands-on experience with state-of-the-art instrumentation systems.

**5311. Deformation and Fracture of Engineering Materials (3 s.h.)**

This course presents elastic and plastic deformation of materials; an introduction to dislocation theory; and failure analysis. Topics include loading real-life situations, variable loading, failure theories, buckling and instability, fatigue analysis, and fracture mechanics. Case histories are introduced from a variety of industries, including automotive, aerospace, utilities, oil and gas, petrochemical, and biomedical. Helpful techniques, such as operating stress maps, are introduced.

5314. **Continuum Mechanics (3 s.h.)**

Prerequisite: MATH 3041.

This course covers tensors, kinematics of a continuum, stress, integral formulations, linear isotropic elastic solid, and an introduction to Newtonian Fluid (CLO 3).

5334. **Dynamical Systems (3 s.h.)**

Prerequisite: MATH 3041.

The objectives of this course are to establish the theoretical basis for the description of regular and chaotic dynamical systems; understand the basic ideas of dynamical systems and the nature of chaotic behavior; gain the ability to apply these ideas to particular systems; and learn how to choose the appropriate modeling techniques and hypothesis to establish a mathematical model of a qualitatively described phenomenon. The discussed applications include examples from biology, fluid mechanics, and physics.

5511. **Fluid Dynamics (3 s.h.)**

Prerequisite: ENGR 3553 and MATH 3041.

This course deals with Navier-Stokes equations; laminar and turbulent flow; boundary layer phenomena; and compressible fluid flow, including isotropic flow, shock waves, friction flow, and flow with heat transfer.

5512.** **Compressible Fluid Dynamics (3 s.h.)

Prerequisite: ENGR 3553 and MATH 3041.

This course introduces students to the subject of high speed gas dynamics. Compressible flows exhibit fundamentally different behavior from those in low speed, constant density fluids. Such flows are found in aerodynamics, combustors, turbines, jets, gas pipelines, and wind tunnel facilities. Students study phenomena associated with supersonic flows, including normal and oblique shocks, expansion fans, and compressible flows with friction and/or heat transfer. An introduction to high temperature and rarified gas dynamics is also included.

5576. **Computational Fluid Dynamics (3 s.h.)**

Prerequisite: ENGR 3751, MATH 2010, and MATH 3041.

This course provides an introduction to numerical methods for solution of initial and boundary value problems with special emphasis on finite element and finite difference discretization methods. Students learn to implement the algorithm by using MATLAB programming to solve problems in heat transfer and fluid flow.

**5719. Introduction to Bioengineering (3 s.h.)**

This course offers an introduction to current topics in bioengineering as presented by experts and researchers in the field.

**5721. Cell Biology for Engineers (3 s.h.)**

This course introduces engineering students to biological concepts in modern cellular and molecular biology. Topics include the chemical composition of cells, bioenergetics and metabolism, structure and function of the plasma membrane, transport across membranes, the cytoplasmic membrane system, the extracellular matrix, interactions between cells and their environment, the cytoskeleton and cell motility, sensory systems, and cell signaling. In addition, an introduction to basic anatomy and physiology of vertebrates includes the skeletal, muscle, cardiovascular, and nervous systems.

5737. **Systems Physiology for Engineers (3 s.h.)**

This course is designed for graduate students majoring in engineering and for others interested in studying physiological processes from the molecular level to the organ/system level. Among the topics covered are scaling, respiration, circulation, cardiac process, renal function, muscle function, neuromuscular function, neural processes, and temperature regulation. The course stresses the application of energetic and informational principles to the study of the body.

**5741. Biomaterials for Engineers (3 s.h.)**

This course introduces engineering students to materials as they interact with biological systems, primarily in medicine. Topics include a review of properties of materials, the classes of materials, tissues that come into contact with materials, the degradation of materials in the biological environment, the application of materials for specific uses, tissue engineering, and biomaterials standards and regulations.

9182. **Independent Study I (3 s.h.)**

Special study is undertaken in a particular aspect of engineering under the direct supervision of a graduate faculty member. This course may be taken once by master's students and once by Ph.D. students.

**9282. Independent Study II (3 s.h.)**

Special study is undertaken in a particular aspect of engineering under the direct supervision of a graduate faculty member. This course may be taken once by Ph.D. students.

9990. **Engineering Seminar (1-6 s.h.)**

Students present their research results at an open seminar. The seminars may be arranged on a biweekly basis over the semester. Active participation of all graduate students is expected.

9991. **Directed Research (1-6 s.h.)**

Under the guidance of a faculty member, the student conducts independent research on a selected topic in engineering.

9994. **Preliminary Examination Preparation (1-6 s.h.)**

This course is intended for Ph.D. students who have completed their coursework but who have not yet passed the Ph.D. Qualifying and Preliminary Examinations.

9998. **Pre-Dissertation Research (1-6 s.h.)**

This course is intended for Ph.D. students who have passed both the Qualifying and Preliminary Examinations but who have not been elevated to candidacy.

9999. **Dissertation Research (1-6 s.h.)**

This course is intended only for those students who have achieved Ph.D. candidacy status. A minimum of 6 semester hours is required for graduation.

Updated 6.7.10