Course Descriptions

Engineering Core
Aerospace and Mechanical Engineering
Biomedical Engineering
Manufacturing Engineering
Electrical and Computer Engineering
RELATED COURSES

The following key is used to designate the core courses and departmental courses.

EK Engineering core

AM Aerospace and Mechanical Engineering

BE Biomedical Engineering

MN Manufacturing Engineering

SC Electrical and Computer Engineering

The course number indicates the course's level of difficulty. Courses at the 500 and 600 levels are open to both undergraduate and graduate students; those listed in this bulletin are approved for both MS and PhD credit. Graduate students in these courses are often expected to complete extra work in the form of special projects. Students should consult the course instructor about any special requirements.

Other course levels are as follows:

700–899 Primarily for graduate students

900–999 For graduate students only

Credits are awarded on the semester-hour basis. A credit requires three to four hours per week of an average student's time. The distribution of that time between class activities (such as lecture, recitation, laboratory, field trips, etc.) and outside preparation varies from course to course.

Class denotes periods of classroom work per week, including lecture, recitation, class discussion, demonstration, or combinations of these.

Pract denotes periods of practicum work per week, including laboratory, shop, studio, drafting room, field trips, etc.

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Engineering Core

ENG EK 500 Probability with Statistical Applications

ENG EK 520 Computer-Aided Design and Manufacture

Prereq: junior or senior standing, or consent of instructor. Introduction to computer-aided design and manufacturing (CAD/CAM). Topics include solid modeling, manufacturing databases, process monitoring and control, process planning and optimization, reliability and quality control, testing, group technology, and flexible manufacturing. Projects selected from various engineering areas. Includes lab with extensive use of ProE. 4 cr.

ENG EK 697E Graduate Part-time Co-op Experience

Prereq: acceptance into the Co-operative Education Program. Students work part-time, as defined by their employing company, while registering for 8–11 credits. Registration for 12 or more credits requires the written approval of the director. 0 cr.

ENG EK 698E Graduate Co-op Experience

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Aerospace and Mechanical Engineering

ENG AM 501/SC 501 Dynamic System Theory

Prereq: familiarity with differential equations and matrices at the level of ENG AM 404 or CAS MA 242, or consent of instructor. Introduction to analytical concepts and examples of dynamic systems and control. Mathematical description and state space formulation of dynamic systems: modeling, controllability and observability. Eigenvector and transform analysis of linear systems including canonical forms. Performance specifications. State feedback: pole placement and the linear quadratic regulator. Introduction to MIMO design and robust control. Experience in controller design and system identification using computer tools and laboratory experiments. Student may not receive credit for both. 4 cr.

ENG AM 502 Special Topics in Aerospace Engineering

Prereq: graduate standing or consent of instructor. Specific prerequisites vary according to topic, but do not extend beyond what is covered in the core courses in the undergraduate curriculum in aerospace engineering. Format is similar to that of regular classroom courses, with in-depth coverage of an announced topic of current interest in aerospace engineering. Subject matter varies from year to year. 4 cr.

ENG AM 503 Special Topics in Mechanical Engineering

Prereq: graduate standing or consent of instructor. Specific prerequisites vary according to topic, but do not extend beyond what is covered in the core courses in the undergraduate curriculum in mechanical engineering. Format is similar to that of regular classroom courses, with in-depth coverage of an announced topic of current interest in mechanical engineering. Subject matter varies from year to year. 4 cr.

ENG AM 504 Numerical Methods for Engineers

Prereq: graduate standing or consent of instructor. Survey of numerical methods with examples selected from aerospace and mechanical engineering. Numerical solution of systems of linear and non-linear algebraic equations, interpolation and extrapolation, computation of eigenvalues and eigenvectors, numerical integration, techniques for numerical solution of ordinary differential equations and partial differential equations. Required projects involve extensive student use of computers. 4 cr.

ENG AM 505 Engineering Analysis

Prereq: ENG AM 400 or equivalent. Mathematical methods in aerospace and mechanical engineering; vectors and tensors; partial differential equations of heat and mass transfer, wave motion and potential theory, classification of second order PDEs; eigenfunction expansions, method of characteristics, Fourier and Laplace transforms; complex variable theory, residue integration, conformal mapping; Green’s functions, integral equations, variational methods; perturbation methods for non-linear differential equations. 4 cr.

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EMG AM 506 Statistical Mechanics Concepts in Engineering

Prereq: graduate standing or consent of instructor. Specific prerequisites vary according to topic, but do not extend beyond what is covered in the core courses in the undergraduate curriculum in mechanical engineering. Elementary introduction to selected fundamental concepts in probability, random processes, signal processing, and statistical mechanics with strong emphasis on their applications to aerospace and mechanical engineering. Examples taken from acoustics, mechanics, thermodynamics, and fluid dynamics. 4 cr.

ENG AM 513 Compressible Aerodynamics

Prereq: ENG EK 304, ENG AM 400, and either ENG AM 420 as prereq or AM 422. Aerodynamics and thermodynamics of compressible fluid flow. Laval nozzles, Prandtl-Meyer flow, normal and oblique shock waves. Linearized theory. Application to external and internal flow problems such as airfoils. Cannot be taken for credit in addition to ENG AM 423. 4 cr.

ENG AM 515 Vibration of Complex Mechanical Systems

Prereq: CAS MA 226, CAS PY 313, ENG EK 302, ENG EK 307, ENG AM 307 or 308, and ENG AM 400. Introductory course in mechanical vibrations for graduate students and for undergraduate students with substantial mastery of core undergraduate subjects in mechanics and mathematics. Course includes an elementary introduction to applicable concepts in linear algebra. Potential and kinetic energy functions of single- and multidegree of freedom systems. Matrix formulations of forced vibrations of linear systems. Natural frequencies, resonance, and forced vibration response. Natural modes and mode shapes. Rayleigh’s principle. Rayleigh’s dissipation function, transient and forced responses of damped vibrations. Random excitation of vibrations. Impedance matrix. O’Hara-Cunniff theorem, modal masses, modal analysis. Vibrations of simple continuous systems such as strings, beams, rods, and torsional shafts. This course cannot be taken for credit in addition to ENG AM 441. 4 cr.

ENG AM 519 Theory of Heat Transfer

Prereq: ENG AM 419, AM 420, or AM 422. Analytical, numerical, and physical aspects of heat transfer phenomena, with emphasis on nondimensionalization and scaling. Mathematical treatment of steady and unsteady conduction, including finite difference methods. Forced and natural convection in internal and external flows. Thermal radiation and multimode heat transfer. Melting and solidification. Applications to aerospace heat transfer, energy systems, manufacturing, and biological heat transfer. 4 cr.

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ENG AM 520 Acoustics I

Prereq: ENG EK 302, EK 303, EK 304, and AM 400. Introduction to wave propagation and sound. General concepts such as quantitative measures of sound, plane waves, and acoustic energy density and intensity. Derivation of wave equation. Sound radiation from vibrating bodies. Basic ray-acoustic concepts: reflection, refraction, diffraction and scattering of acoustic waves. Other topics may include flow-induced sound, Helmholtz resonators, sound transmission through ducts and mufflers, room acoustics, and absorption and attenuation of sound waves in fluids. 4 cr.

ENG AM 521/BE 521 Continuum Mechanics/Continuum Mechanics for Biomedical Engineers

Prereq: EK 424 or AM 308 and either EK 304, AM 420, AM 422, BE 420, BE 436, or consent of instructor. The main goal of this course is to present a unified, mathematically rigorous approach to two classical branches of mechanics: the mechanics of fluids and the mechanics of solids. Topics will include kinematics, stress analysis, balance laws (mass, momentum, and energy), the entropy inequality, and constitutive equations in the framework of Cartesian vectors and tensors. Emphasis will be placed on mechanical principles that apply to all materials by using the unifying mathematical framework of Cartesian vectors and tensors. Illustrative examples from biology and physiology will be used to describe basic concepts in continuum mechanics. The course will end at the point from which specialized courses devoted to problems in fluid mechanics (e.g., biotransport) and solid mechanics (e.g., cellular biomechanics) could logically proceed; students may not receive credit for both. 4 cr.

ENG AM 522 Underwater Acoustics

Prereq: ENG AM 400 or equivalent. The ocean environment. Physical processes in deep and shallow water. Time and frequency domain wave equations for homogeneous and in-homogeneous acoustics. Spectral and ray methods for wave propagation in layered fluid and elastic media. Uncoupled and adiabatic normal mode theory. Parabolic equations and computational techniques for fluids and solids. Noise sources and surface effects. Sensors, transducers, and signal processing techniques. 4 cr.

ENG AM 524/BE 524 Skeletal Tissue Mechanics

ENG AM 530 Introduction to Micro- and Nanomechanics of Solids

Prereq: undergraduate mechanics (ENG AM 307/308 or equivalent) or undergraduate solid-state physics (CAS PY 313/314 or equivalent) or consent of instructor. Mechanics and physics of solids at the nanometer scale: introductory graduate-level course for students with background in undergraduate engineering mechanics (or solid-state physics) and mathematics. Review of continuum solid mechanics fundamentals. Introduction to dislocation theory. Continuum elastic theory of dislocations. Mechanics of thin films. Review of fundamentals of solid-state physics. Electron motion in a periodic potential. Derivative of bulk material properties from free-election and free-atom models. Phonons. Introduction to atomistic computational methods. 4 cr.

ENG AM 540 Advanced Aerodynamics

Prereq: CAS MA 226, 412, ENG AM 420 or ENG AM 422. Presentation of basic fluid dynamics concepts relevant to understanding the theory of flight. Partial differential and integral equations of incompressible and compressible flow. Discussion of idealized two-dimensional flows using mathematics of complex variables and conformal mapping. Flow around wings and slender bodies. Lifting line theory, numerical panel methods, supersonic flows, unsteady aerodynamics. 4 cr.

ENG AM 541 Classical Thermodynamics

Prereq: ENG EK 304. Principles and formulation of classical thermodynamics: concept of equilibrium, postulates of macroscopic thermodynamics, Euler equations and Gibbs-Duhem relation, alternative formulations, Maxwell's relations, gas mixtures, phase transitions, applications to processes, cycles and engines. Introduction to irreversible thermodynamics: theory of fluctuations, entropy generation, availability, and second law analysis. 4 cr.

ENG AM 542 Advanced Fluid Mechanics

Prereq: ENG AM 422. Incompressible fluid flow. Review of control-volume approach to fluids engineering problems, with advanced applications. Differential analysis of fluid motion. Derivation of full Navier-Stokes, Euler, and Bernoulli equations. Unsteady Bernoulli equation. Velocity potential and its application to steady 2D flows. Vorticity and vortex motion. Eulerian vs Lagrangian analysis. 4 cr.

ENG AM 560 Introduction to Robotics

Prereq: CAS MA 242 or equivalent. An introduction to the kinematics, dynamics, and control of robot manipulators and to robot motion planning. Specifically, forward kinematics of serial chain manipulators using Denavit-Hartenberg parameters and product of exponentials. Inverse kinematics. The manipulator Jacobian. Manipulator dynamics using the Euler-Lagrange equations and the Newton-Euler formulation. PID, computed torque, and force control. The basic motion planning problem. Configuration space. Motion planning methods such as visibility graphs, Voronoi diagrams, cell decomposition, and potential fields. Introduction to nonholonomic motion planning. Handling uncertainty through preimage backchaining. 4 cr.

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ENG AM 561 Dynamics

Prereq: ENG EK 302 or equivalent. Advanced dynamics of mechanical systems; review of Newtonian mechanics; fundamental concepts of analytical dynamics; Hamilton's principle; Lagrange's equations; kinematics and dynamics of rigid bodies in general motion; definition of stability; application to engineering problems. 4 cr.

ENG AM 562 Introduction to Non-linear Oscillations

Prereq: ENG AM 441 or AM 515. Introductory concepts of non-linear oscillations, dynamics of conservative and nonconservative systems; phase plane analysis; local and global stability; damping mechanisms; internal and external resonances; primary, secondary and combination resonances; self-excited oscillations; bifurcations; parametric excitations; Floquet theory; non-linear multi-degree-of-freedom systems; application to continuous systems, strings, beams, plates and shells; engineering applications. 4 cr.

EMG AM 570/MN 570 Robot Motion Planning

ENG AM 580 Theory of Elasticity

Prereq: ENG AM 308 or equivalent. An introduction to the general theory of solid deformation; small deformation emphasized. Topics include: Cartesian tensors, indicial notation. Introduction to continuum mechanics: deformation of continuous media, deformation gradient, strain definitions. Stress, Cauchy’s postulate, Cauchy and Piola-Kirchhoff stress tensors. Balance laws. Constitutive equations, strain energy and Green’s postulate. Linear Elasticity: Two dimensional problems, Airy stress function, in plane loading of strips, St. Venant’s principle, complex variable methods, Goursat-Muskhelishvili representation, stress concentrations around holes and cracks. Three-dimensional problems, Kelvin’s solution, the Boussinesq problem, Hertzian contact, Eshelby’s energy-momentum tensor. 4 cr.

ENG AM 581 Experimental Techniques in Solid Mechanics

Prereq: ENG AM 308 or equivalent, some computer proficiency, and consent of instructor. Theory and practice of experimental techniques used in solid mechanics. Topics include ultrasonic NDE, optical strain techniques (e.g., Moire interferometry, spectroscopy), and material strength and stiffness testing (e.g., fracture, fatigue, elastic constants). Also examines the use of computer for data acquisition and control. Some discussion of theory related to filters, sampling theory, uncertainty analysis, and spectra and correlations are incorporated. 4 cr.

ENG AM 582 Advanced Mechanical Behavior of Materials

Prereq: ENG AM 308 and AM 400 or equivalent. Fundamental concepts of modern materials behavior and materials engineering. Emphasis on analytical and numerical methods for predicting material properties and behavior, as well as some discussion of the relationships between solid structure and material properties. Topics include: constitutive relations, fracture, fatigue, plasticity, creep, damping, impact, and deformation. Elastic, plastic, and viscous behavior. Some discussion of the effects of processing—thermodynamics, kinetics—may be addressed. Specific examples from ceramics, metals, polymers, and composites is given, with the emphasis changing for each offering. 4 cr.

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ENG AM 700 Advanced Topics in Aerospace and Mechanical Engineering

Prereq: graduate standing or consent of instructor. Other specific prerequisites vary according to the research topic. 4 cr.

ENG AM 702 Computational Fluid Dynamics

Prereq: ENG AM 504, AM 542, AM 543. Numerical techniques for solving the Navier-Stokes and related equations. Topics are selected from the following list, although the emphasis may shift from year to year: boundary integral methods for potential and Stokes flows; free surface flow computations; panel methods; finite difference, finite element and finite volume methods; spectral and pseudospectral methods; vortex methods; lattice-gas and lattice-Boltzmann techniques; numerical grid generation. 4 cr.

ENG AM 704 Adaptive Control of Dynamical Systems

Prereq: ENG AM/SC 501 or equivalent. Adaptive control refers to the control of partially known systems. Discusses the analysis and design of adaptive control systems, including simple adaptive systems, adaptive observers, and the stability of adaptive controllers. Studies the issue of parameter convergence and the concomitant property of robustness. Typical applications covered include aircraft systems, flexible structures, process control, robotics, and bioengineering. 4 cr.

ENG AM 706 Acoustics and Aerodynamic Sound

Prereq: ENG AM 420, ENG AM 421, or equivalent. Theoretical foundations of fluid and structural acoustics. Solutions of the wave equation; vibrations of plates and membranes; multiple expansions, influence of source motion; reciprocity; compact Green's functions, radiation from vibrating bodies; matched expansions; acoustics energy equation; aerodynamic sound. 4 cr.

ENG AM 707 Finite Element Analysis

Prereq: ENG AM 505 and either AM 580 or AM 542. An introduction to the finite element method with emphasis on fundamental concepts. Variational equations, Galerkin's method. Finite element applications to linear elliptic boundary value problems in structures, solid and fluid mechanics, and heat transfer. Optimality, convergence, function spaces and energy norms. Isoparametric elements. Mixed methods, penalty methods, selective reduced integration; applications may include Kirchoff plate theory, incompressible elasticity, Stokes flow. Thick and thin beams, plates, and shells. Implementation: element data structures, numerical integration, assembly of equations, element routines, solvers. Advanced topics may include: dynamic analysis, stabilized methods, eigenvalue problems, hybrid analytical methods. 4 cr.

ENG AM 708 Waves in Fluids

Prereq: ENG EK 510 or equivalent. Analytical methods are developed for studying the propagation and diffraction of waves in uniform and in homogeneous fluid media. Illustrative applications are made to sound waves, gravity waves, waves in random media, evanescent waves. 4 cr.

ENG AM 709 Turbulent Flows

Prereq: ENG AM 420 or AM 421 and AM 701 or equivalent. Introduction to turbulence. Deterministic versus statistical descriptions of fluids; kinematics; correlations and spectra; closure of the fluid equations of turbulence. Reynolds stresses; spectral evolution; analysis of scales. Analysis of isotropic turbulence and modeling of turbulent flows. Current topics. 4 cr.

ENG AM 711 Multiscale Methods in Computational Mechanics

Prereq: ENG AM 707 or CAS MA 539 or CAS MA 556. This course will cover the state-of-the-art in analytical and (especially) computational techniques for solving problems with multiple spatial and temporal scales. Such problems are now at the forefront of computational mechanics with applications ranging from turbulence and its modeling to the coupling of atomistic and continuum scales in solid mechanics. We will begin with the more traditional methods including multiscale perturbation techniques and renormalization group theory. Thereafter we will focus on more recent developments with distinct computational focus including: the Optimal Prediction Method of Chorin et al., the Equation Free Method of Kevrekidis et al., the Variational Multiscale Method of Hughes et al., and the Heterogeneous Multiscale Method of Weinan et al. We will also cover an approach to determine unknown parameters in the models derived from these methods. The differences and similarities between these methods will also be discussed and highlighted. 4 cr.

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ENG AM 713 Viscous Flow

Prereq: ENG AM 542, or AM 543. Brief review of the fundamental conservation and constitutive equations, exact solutions of the viscous Navier-Stokes equations, similarity solutions, boundary layer theory; creeping flows, flow in Hele-Shaw cells, lubrication theory, thin shear layer approximations, jets and wakes, hydrodynamic instability and transition to turbulence, Reynolds-averaged Navier-Stokes equations. 4 cr.

ENG AM 718 Advanced Topics in Nanotechnology

Prereq: undergraduate solid-state physics and quantum mechanics courses or instructor’s consent. Nanotechnology is emerging as the technology of the 21st century. There is an ever-growing effort by scientists and engineers across disciplines to envision, fabricate, and integrate nanoscale devices for countless applications. This course will give a rigorous introduction to the basic concepts and experimental techniques in nanoscience and nanotechnology. The course will review relevant quantum mechanics and solid-state physics as a basis for understanding the physical phenomena at the nanoscale. Then, a selection of issues from nanoscience and nanotechnology including nanofabrication techniques, Scanning Probe Microscopy (SPM), nanomechanics, and nanoelectronics will be discussed. 4 cr.

ENG AM 720 Acoustics II

Prereq: ENG AM 520.Wave equation in cylindrical and spherical co-ordinate systems. Propagation in waveguides. Diffraction: the Rayleigh integral and the Helmholtz-Kirchhoff integral. Green’s function and angular spectrum methods. Diffraction of sound beams: Gaussian beams, unfocused and focused sources, and arrays. Diffraction by apertures, discs, and wedges. Scattering of sound; Rayleigh scattering, scattering cross-section, elastic scatterers. Propagation in inhomogeneous media: rays, the eikonal equation, the Blokhintzev invariant and the acoustic field near caustics. Absorption and dispersion of acoustic waves. Transmission and reflection at a fluid-solid interface. 4 cr.

ENG AM 722 Wave Propagation in Solids

Prereq: ENG AM 580 or AM 515. One-dimensional waves in rods and beams. Initial values problems, dispersion relations, reflection and transmission at boundaries. Two-dimensional waves in membranes, plates and shells, including the effects of fluid loading. Bulk waves in infinite and semi-infinite solids. Integral transforms and asymptotic evaluation. Rayleigh and Love waves. Scattering of elastic waves by cavities and inhomogeneities. Thermal effects and viscoelasticity. Plasticity and non-linear propagation. Applications to nondestructive evaluation, structural dynamics, and seismology. 4 cr.

ENG AM 723 Waves in Random Media

Prereq: at least one graduate level course in either acoustics or fluid dynamics. Systematic development of wave phenomena in weakly inhomogeneous and moving media. Emphasis is on acoustic waves, with selected examples from other branches of wave physics. Both ray-tracing and full-wave methods are discussed. Introduction to the statistical description of random media and of turbulent media. Formulations for relating statistical properties of wave phenomena to the statistical properties of the medium. 4 cr.

ENG AM 724 Non-linear Acoustics and Sonic Booms

Prereq: understanding of fluid mechanics at a depth consistent with what is covered in an undergraduate curriculum in aerospace or mechanical engineering. Propagation of finite amplitude sound, principles of one-dimensional unsteady compressible flow. Discussion of non-linear distortion, generation of harmonics, weak shocks, N-waves, and of shock profiles. Supersonic aerodynamics, flow around bodies in supersonic flight, generation of sonic booms, non-linear acoustics theory of boom propagation through the atmosphere. Selected additional topics in non-linear acoustics. 4 cr.

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ENG AM 725 Acoustic Bubble Dynamics

Prereq: ENG AM 520, AM 542, or equivalent. Bubbles and acoustic cavitation play an important role in many aspects of application of sonic and ultrasonic energy in fluids and biological tissue. This course will introduce the study of bubble phenomena in sound fields. The fundamental physical acoustics of bubbles (and the fundamental physics which can be illustrated by the study of bubble dynamics) will be stressed. The family of Rayleigh-Plesset equations for time-dependent bubble behavior will be derived from the Navier-Stokes equations. Analytical approximations to the Rayleigh-Plesset equations in various limiting cases will be derived and studied. Approximations to the thermodynamic behavior of oscillating bubbles will be considered in detail. Thermal, acoustic and viscous contributions to dissipation will be treated. Numerical solutions will also be studied, specifically in the context of highly nonlinear behavior during acoustically forced oscillations. Other topics covered will include scattering of sound and acoustic radiation, acoustics of bubbly liquids, bubble-mediated bioeffects, shape instabilities, acoustic levitation, sonoluminescence, heat and mass transfer during bubble oscillations, sonochemistry and cavitation detection and monitoring. 4 cr.

ENG AM 726 Special Topics in Wave Propagation

Prereq: permission of instructor. Format is similar to that of regular classroom courses, with in-depth coverage of an announced topic of current interest in wave propagation. Subject matter varies from year to year. 4 cr.

ENG AM 740/MN 740 Vision, Robotics, and Planning

Prereq: graduate standing or consent of the instructor. Methodologies required for constructing and operating intelligent mechanisms. Comprehensive introduction to robot kinematics for motion planning. Dynamics and control of mechanical systems. Formal treatment of differential relationships for understanding the control of forces and torques at the end effector. Discussion of robot vision and sensing and advanced topics in robot mechanics, including elastic effects and kinematic redundancy. Students may not receive credit for both. 4 cr.

ENG AM 741 Fluid-Structure Interaction

Prereq: understanding of fluid mechanics and dynamics at a level commensurate with an undergraduate degree in aerospace or mechanical engineering. Discussion of basic phenomena occurring when the response of a solid structure immersed in or bounding a flow has a significant influence on the flow. Methods are developed and applied to a general range of vibration problems that arise in diverse situations involving the interaction of laminar and turbulent flows with rigid and elastic structures. 4 cr.

ENG AM 742 Bio-Fluids and Structural Mechanics

Prereq: ENG AM 542 and EK 305. Mechanics of biological systems, with emphasis on biological application of fluid mechanics. Topics will be chosen from the following: cardiovascular dynamics—pulsatile flow, vessel elasticity, non-Newtonian behavior, flow in bifurcations, thermodilution; pulmonary dynamics—oscillatory flow, convection-diffusion interactions, surface tension effects, high frequency ventilation, turbulence; clinical applications—urodynamics, bone fracture, dental mechanics, male impotency; mechanics of propulsion—microorganisms in viscous liquids, swimming, flying. 4 cr.

ENG AM 743 Multiphase Flow

Prereq: ENG AM 542 and AM 713. Fluid dynamics of systems with two or more phases: particulate suspensions, emulsions, bubbly liquids, porous media; analytical approach in dilute and semidilute regimes, sedimentation and centrifugation, fibers and orientable particles, cavitation, colloidal phenomena, turbulent two-phase flows, flows with phase change (condensation and evaporation); continuum models: mixture theory, interpenetrating continua, forces on the dispersed phase, closure relationships. 4 cr.

ENG AM 744 Advanced Compressible Aerodynamics

Prereq: ENG AM 423 or AM 513. Unsteady compressible flows. Non-linear potential aerodynamics with applications to the transonic and hypersonic regimes. Compressible boundary layers. Real gas effects. Approximate and numerical techniques. 4 cr.

ENG AM 745 Computational Aeroacoustics

Prereq: ENG AM 504, at least one graduate-level course in acoustics or compressible fluid mechanics. General introduction to analytical and computational techniques relevant to the computation of sound generation by flow, sound production from fluid-structure interaction, and the interaction of sound with flow. Overview of principal methodologies of computational fluid dynamics and of principal theories of aeroacoustics. Benchmark examples of validation methodology, numerical techniques based on the acoustic analogy, direct simulation. Examples involving prediction of sound generation by turbulence and by fluid-structure interaction. 4 cr.

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ENG AM 761 Experimental Modal Analysis and System Identification

Prereq: ENG AM 515 or equivalent. Fundamental concepts of modal testing; analysis of multi-degree-of-freedom systems; viscous and hysteretic damping models; proportional and non-proportional damping; receptance, mobility and inertance frequency response functions; random and transient vibrations; practical issues concerning mobility measurement techniques; modal parameter extraction in frequency domain and time domain; structural modification; effects of non-linearities on modal analysis; engineering applications. 4 cr.

ENG AM 762 Non-linear Control of Mechanical Systems

Prereq: ENG AM/SC 501 or permission of instructor. Introduction to the theory and design methods of non-linear control systems. Application to robotics, vibration and noise control, fluid control, manufacturing processes, and biomedical systems. Mathematical methods based on the theory of differentiable manifolds; non-linear control techniques include feedback linearization, backstepping, forwarding, and sliding mode control. Additional course topics will include controllability and observability, Lyapunov stability and its applications, limit cycles, input-output stability, zero dynamics, center manifold theory, perturbation theory, and averaging. 4 cr.

ENG AM 764/SC 701 Optimal and Robust Control

Prereq: ENG AM/SC 501 or equivalent. Fundamentals of multivariable control analysis and synthesis. Control objectives include achieving robust stability and performance (robust control) and minimization of cost functions (optimal control). Topics include modeling (state space, transfer function matrix), MIMO poles and zeroes, controllability and observability, stability and robustness, structured and unstructured perturbations, the small gain theorem, optimization theory, and the Maximum Principle. Estimation and control techniques include Linear Quadratic (H2), full-state LQR, LQG, (H), and Kalman filtering. Applications and numerical examples taken from robotics, aircraft control, and vibration control. Students may not receive credit for both. 4 cr.

ENG AM 780 Perturbation Methods in Mechanics

Prereq: ENG AM 505. Regular and singular perturbation theory. Topics taught through examples related to solid mechanics, fluid mechanics, and dynamics, and include: matched asymptotic expansions, method of multiple scales, WKB, strained coordinates, asymptotic expansion of integrals, method of averaging, exponential asymptotics, asymptotic summation, perturbation of dimension. 4 cr.

ENG AM 850 Graduate Teaching Seminar

First time graduate teaching fellows are required to register for special training which will be organized and facilitated by their assigned professor in cooperation with their department. 2 cr.

ENG AM 900 Research

By petition only. Limited to MS and pre-candidate PhD students in Aerospace and Mechanical Engineering. Participation in a research project under the direction of a faculty advisor. If not leading to an MS thesis or PhD dissertation, a final report is normally required. Variable cr.

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ENG AM 901 Thesis

By petition only. Taken by students who choose to present a thesis as part of the requirements for the MS in Aerospace Engineering or Mechanical Engineering. Preparation of an original thesis under the guidance of a faculty member. Variable cr.

ENG AM 951 Independent Study

By petition only. Graduate students may study, under a faculty member's supervision, subjects not covered in a regularly offered course. Final report and/or written examination normally required. Variable cr.

ENG AM 991 Dissertation

Limited to PhD candidates in Aerospace and Mechanical Engineering. Advisor and hours arranged. Variable cr.

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Biomedical Engineering

ENG BE 500 Special Topics in Biomedical Engineering

Prereq: engineering graduate student standing. Others by permission of instructor. Specific prerequisites vary according to topic. Coverage of a specific topic in biomedical engineering. One topic covered in depth each semester offered. Subject matter varies from year to year. 4 cr.

ENG BE 505 Molecular Bioengineering I

Prereq: ENG EK 424 or equivalent, graduate standing. Undergraduates must have stamped approval. The course is an engineering science-based introduction to the building blocks of living cells and materials for biotechnology. Throughout the course, detailed structural and energetic properties of molecules are emphasized. Topics include: 1) biological pathways for synthesis of DNA, RNA, and proteins, 2) formal physical and mathematical treatment of transduction, transmission, storage, and retrieval of biological information by macromolecules, 3) polymerase chain reaction, restriction enzymes, and DNA sequencing, 4) energetics of protein folding and trafficking, 5) energetic mechanisms of enzymatic catalysis and receptor-ligand binding, 6) cooperative proteins, multi-protein complexes and the control of metabolic pathways, 7) generation, storage, transmission, and release of biomolecular energy, and 8) physical bases of methods for study and manipulation of molecules, including isolation, purification, detection, chemical characterization, and visualization of structure. 4 cr.

ENG BE 506 Physical Chemistry of Cell Structure and Machinery

Prereq: ENG BE 505. Building on the engineering perspective of molecular-cell biology presented in ENG BE 505, the objective of this course is to provide a basic understanding of the physical chemistry of molecular structures important in living cells and in technological applications. Topics include: noncovalent interactions of biomolecules in water, thermodynamics of solutions and phase mixtures; nonequilibrium kinetics; polymer physics and elasticity; lipid self-assembly and interfacial thermodynamics; biomembranes; adhesion and molecular bonding; chemical grafting; and surface analysis. 4 cr.

ENG BE 508 Quantitative Studies of Respiratory and Cardiovascular Systems

Prereq: ENG BE 401, graduate student standing or consent from instructor; Coreq: BE 436. The quantitative physiological aspects of the respiratory and cardiovascular systems are studied. Classical models of these systems are considered including lumped element models, branching tree structures, and distributed parameter models to predict wave propagation in compliant walled tubes filled with compressible or incompressible fluids. Extensive computer models are developed to simulate the behavior of these systems in the frequency and time domains. 4 cr.

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ENG BE 509 Quantitative Physiology of the Auditory System

Prereq: ENG BE 200, CAS BI 315, and ENG BE 401 or permission of the instructor. Introduction to the anatomy, acoustics, and physiology of the mammalian auditory pathways from a systems perspective including implications for hearing aid and prosthetic design. Topics include measuring sound and microscopic motion, head-related transfer function, middle ear and cochlear mechanics, hair cell transduction, binaural processing in the brainstem and midbrain, auditory thalamic and cortical structure and function. 4 cr.

ENG BE 511 Biomedical Instrumentation

Prereq: ENG SC 412, ENG BE 402. Physiological signals, origin of biopotentials (ECG, EMG, EEG), biomedical transducers and electrodes. Biomedical signal detection, amplifications and filtering. Analog front-ends of biomedical instruments. Electrical safety in medical environment. Laboratory experiments supplement lectures. 4 cr.

ENG BE 512 Biomedical Instrument Design

Prereq: ENG BE 511, ENG SC 311, and ENG SC 412 or equivalent. An introduction to techniques for the design of biomedical instrumentation including sensors and their associated electronics. Mathematical models for a wide variety of sensors ranging from resistive sensors to biosensors are reviewed along with the resulting implications for the design of signal-conditioning electronics. A case-study approach is used in which specific sensor systems are evaluated for sensitivity, selectivity, dynamic range, response time, and reproducibility. Includes lab. 4 cr.

ENG BE 515 Introduction to Medical Imaging

Prereq: ENG BE 401, ENG SC 401, or ENG EK 510 and elementary knowledge of atomic physics. Methods of obtaining useful images of the interior of the body using X-rays, ultrasound, and radionuclides. Image formation and display. Projection radiography. Radiation detectors. Conventional and computerized tomography. Nuclear imaging. Automating diagnosis and non-invasive testing. Radiation safety. Same as MN 515; students may not receive credit for both. 4 cr.

ENG BE 516 Applied Medical Imaging

Prereq: ENG EK 301, ENG BE 401. Biomedical engineering course in the format of a clinical rotation (25 hours per week); this is a six-week course offered only during the Summer II session. The program consists of separate components of approximately equal duration and emphasis. An engineering component with focus in the physics/mathematics/computer subjects most relevant to medical imaging (attended solely by engineering students) and a radiological component in lectures and review sessions with medical/clinical focus (attended together with fourth-year medical students [BUSM-IV] and first-year radiology residents). 4 cr.

ENG BE 521/AM 521 Continuum Mechanics for Biomedical Engineers/Continum Mechanics

Prereq: ENG EK 424 or ENG AM 308 and either ENG EK 304, ENG AM 420, ENG AM 422, ENG BE 420, ENG BE 436, or consent of instructor. The main goal of this course is to present a unified, mathematically rigorous approach to two classical branches of mechanics: the mechanics of fluids and the mechanics of solids. Topics will include kinematics, stress analysis, balance laws (mass, momentum, and energy), the entropy inequality, and constitutive equations in the framework of Cartesian vectors and tensors. Emphasis will be placed on mechanical principles that apply to all materials by using the unifying mathematical framework of Cartesian vectors and tensors. Illustrative examples from biology and physiology will be used to describe basic concepts in continuum mechanics. The course will end at the point from which specialized courses devoted to problems in fluid mechanics (e.g., biotransport) and solid mechanics (e.g., cellular biomechanics) could logically proceed; students may not receive credit for both. 4 cr.

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ENG BE 523/MN 523 Mechanics of Biomaterials

Prereq: ENG EK 301, ENG EK 305, or ENG BE 420; ENG EK 306 is desirable. Covers the chemical composition, physical structure, and mechanical behavior of engineering polymers. Study of types of polymers; rubber elasticity; fundamentals of viscoelastic phenomena such as creep, stress relaxation, stress rupture, mechanical damping, impact; effects of chemical composition and structure on viscoelastic and strength properties; methods of mechanical property evaluation. Fracture and fatigue of polymer materials. Influences of plastics fabrication methods on mechanical properties. Emphasis on recent research techniques and results. Same as ENG MN 523; students may not receive credit for both. 4 cr.

ENG BE 524/AM 524 Skeletal Tissue Mechanics

Prereq: ENG EK 301, ENG EK 302, ENG EK 305, ENG AM 308, CAS MA 242 or equivalent. The course is structured around classical topics in mechanics of materials and their application to study of the mechanical behavior of skeletal tissues, whole bones, bone-implant systems, and diarthroidal joints. Topics include: mechanical behavior of tissues, (anisotropy, viscoelasticity, fracture and fatigue) with emphasis on the role of the microstructure of these tissues; structural properties of whole bones and implants (composite and asymmetric bean theories); and mechanical function of joints (contact mechanics, lubrication, and wear). Emphasis is placed on using experimental data to test and to develop theoretical models, as well as on using the knowledge gained to address common health-related problems related to aging, disease, and injury. Students may not receive credit for both. 4 cr.

ENG BE 533 Biorheology

Prereq: ENG BE 420 and ENG EK 424. An introductory course emphasizing those rheological properties (such as elasticity, viscoelasticity, poroelasticity, plasticity, and viscoplasticity) that often characterize solid biological tissues. 4 cr.

ENG BE 535 Cell Mechanics

Prereq: ENG BE 209, ENG EK 424, ENG EK 305, or ENG BE 436. The physical and chemical basis for the mechanical properties and activities of living cells considered from an engineering perspective. The instructional approach emphasizes in-depth study of a limited number of cases and relies heavily on selected readings. Topics studied include cell adhesion and elasticity of red cells as well as phenomena in which active motility is involved (e.g., the first cleavage division of the sea urchin egg, the contraction of skeletal muscle, the crawling motility of fibroblastic cells, and the beating of flagella). Lectures and assignments emphasize the role of quantitative theory and mathematical models in elucidating the molecular basis of physiological observations in these diverse areas. 4 cr.

ENG BE 537 Biomedical and Biochemical Microsystems

Prereq: graduate standing or permission of instructor. Focus is on micro and nanofabrication approaches to engineer the cellular and subcellular environment. The course covers applications of these technologies in the biomedical and biochemical fields, ranging from micro-analytical systems to implantable drug delivery microsystems. 4 cr.

ENG BE 540 Bioelectric Signals: Analysis and Interpretation

Prereq: ENG BE 402 or consent of instructor. Detailed study of bioelectric signals that can be recorded from conscious humans. Alternative recording and signal processing procedures with attention to relative advantages and disadvantages, including instrumentation requirements and examples. Mathematical models that relate signal parameters to physiological events. Examples given to demonstrate the applicability of bioelectric signals to control devices external to the body. Myoelectric signals used as primary examples throughout the course. 4 cr.

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ENG BE 550 Bioelectromechanics

Prereq: ENG BE 420, ENG BE 436 or ENG SC 453. Conduction, diffusion, and convection in electrolytes. Equilibrium double layers and electrical forces in physiological systems. Applications to physiological systems including membrane/electrolyte and electrode/electrolyte interfaces, interaction of biomaterials with electric fields, electrophoresis and electroosmosis, and electromechanical coupling in charged biological structures. 4 cr.

ENG BE 560 Biomolecular Architecture

Prereq: CAS PY 212, CAS CH 131 or CH 102, and ENG BE 209. Provides an introduction to the molecular building blocks and the structure of three major components of the living cells: the nucleic acids, the phospholipids membrane, and the proteins. The nucleic acids, DNA and RNA, linear information storing structure as well as their three-dimensional structure are covered in relationship to their function. This includes an introduction to information and coding theory. The analysis tools used in pattern identification representation and functional association are introduced and used to discuss the patterns characteristic of DNA and protein structure and biochemical function. The problems and current approaches to predicting protein structure including those using homology, energy minimization, and modeling are introduced. The future implications of our expanding biomolecular knowledge and of rational drug design are also discussed. 4 cr.

ENG BE 561 DNA and Protein Sequence Analysis

Prereq: ENG BE 200, ENG BE 209, ENG EK 125, ENG EK 126, or equivalent. Fundamental concepts from molecular biology and molecular genetics are presented. Biological inferences are made from DNA and protein sequence data using mathematical and computer science techniques. Pairwise sequence comparative analyses and homolog identification are studied in detail. The dynamic programming algorithm is extended to deal with more general cases and is applied to RNA structure prediction. Additional topics include: multiple sequence alignment and conserved sequence pattern recognition methods, phylogenetic tree reconstruction to study molecular evolution, methods of identifying coding regions in genomic data, algorithms to solve the fragment assembly problem of DNA sequencing, techniques for physical mapping, and mathematical models and computations alogrithms for genetic regulation. An introduction to protein 3-dimensional structure predictions is also given. 4 cr.

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ENG BE 563 Cellular and Molecular Systems Analysis

Prereq: ENG BE 402 or equivalent. The course addresses the interface between cellular and molecular phenomena using methods of engineering system analysis. Topics include storage and processing of genetic information in the cell, the regulation and control of gene action, the analysis of cell surface receptor/ligand binding and trafficking, signal transduction, receptor-mediated cell responses, metabolic pathways and control mechanisms, cell proliferation and growth, and some analysis of the immune system. The interpretation and analysis of these systems will be based, as much as possible, on the engineering methodologies taught in traditional signals and systems courses, with some additional training in nonlinear system kinetics and dynamics. The emphasis in the course will be to expose undergraduate and graduate students to molecular/cellular phenomena for which there is sufficient experimental data and mechanistic understanding for the analysis from an engineering perspective. The aim is not just to translate the cellular and molecular systems into engineering terminology, but to attempt to be sufficiently predictive for the design of modified biological systems. 4 cr.

ENG BE 565 Molecular Biotechnology

Prereq: ENG EK 424, ENG BE 505, CAS CH 102, or consent of instructor. Covers the basic properties of biological macromolecules and assemblies including proteins, nucleic acids, and membranes. Among the topics covered are the forces that govern biological structures, how proteins act as catalysts, how membranes act to store energy, and how nucleic acids and proteins are synthesized in cells. Methods for manipulating the living cells to change their properties and to produce specific proteins or nucleic acids are detailed. 4 cr.

ENG BE 566 DNA Structure and Function

Prereq: CH 102, PY 212, EK 424. Physical structure and properties of DNA. The physical principles of the major experimental methods to study DNA are explained, among them: X-ray analysis, NMR, optical methods (absorption, circular dichroism, fluorescence), centrifugation, gel electrophoresis, chemical and enzymatic probing. Different theoretical models of DNA are presented, among them: the melting (helix-coil) model, the polyelectrolyte model, the elastic-rod model, the topological model. Theoretical approaches to treat the models, (e.g., Monte Carlo method) are covered. Special emphasis is on DNA topology and DNA unusual structures, and their biological significance. In parallel with DNA, major structural features of RNA are considered. Main principles of DNA-protein interactions are presented. The role of DNA and RNA structure in most fundamental biological processes, replication, transcription, recombination, reparation, and translation are considered. 4 cr.

ENG BE 567 Nonlinear Systems in Biomedical Engineering

Prereq: graduate standing or consent of instructor; ENG BE 505 or equivalent; ordinary differential equations. Linear dynamic systems and linear algebra are recommended. Introduction to nonlinear dynamical systems in biomedical engineering. Qualitative, analytical, and computational techniques. Stability, bifurcations, oscillations, multistability, hysteresis, multiple time-scales, chaos. Introduction to experimental data analysis and control techniques. Applications discussed include genetic circuit engineering, neural processing, cardiac control, posture control, and population dynamics. 4 cr.

ENG BE 570 Introduction to Computational Vision

Prereq: CAS MA 226; ENG BE 401 or ENG SC 401, ENG EK 510; ENG BE 200 or ENG EK 500; and working knowledge of MATLAB. Introductory course in computational visual neuroscience. Provides a survey of general neural network models for vision and the computational vision theories and survey of neuroanatomy, neurophysiology, and psychophysics underlying specific problems in vision. Topics addressed include models of visual motion analysis such as optic flow, boundary extraction, and three-dimensional structure and motion, and models of stereopsis. Briefly addresses learning mechanisms and their relationship to brain plasticity. A term project is required for graduate credit. 4 cr.

ENG BE 700 Advanced Topics in Biomedical Engineering

Prereq: graduate standing or consent of instructor. Advanced study of a specific research topic in biomedical engineering. Intended primarily for advanced graduate students. 4 cr.

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ENG BE 703 Numerical Methods and Modeling in Biomedical Engineering

Prereq: graduate standing, undergraduate degree in engineering or physics. This graduate course is an introduction to the computational tools most commonly applied in biological and physiological research, with emphasis on the art of using models, programming and simulation to reach useful conclusions and insights. The first half of the course is an introduction to the Unix operating system, the elements of programming, and basic methods of numerical analysis. Specific topics include exact and iterative methods for the solution of large systems, differentiation and interpolation, numerical integration, Monte Carlo methods and statistical bootstrap methods, Fourier transform and spectral methods, and also finite element and finite difference methods for the solution of ordinary and partial differential equations. Each weekly lecture is accompanied by a computer lab in which the students will gain experience in the use of the techniques under study. The last half of the course uses a case study approach comprised of several two-week modules designed to immerse students in a variety of specific bioengineering applications covering the range from genes and molecules to cells organs and systems. Each module will begin with lectures on the derivation and implementation of a particular model or computational algorithm and be accompanied by a related computational mini-project. 4 cr.

ENG BE 706 Quantitative Physiology for Engineers

Pre- or Coreq: CAS MA 226, ENG BE 401, graduate standing or consent of instructor. Course in human physiology for biomedical engineering students. Fundamentals of cellular and systems physiology, including the nervous, muscular, cardiovascular, respiratory, renal, gastrointestinal, endocrine, and immune systems. Quantitative and engineering approaches will be applied to understanding physiological concepts. 4 cr.

ENG BE 707 Quantitative Studies of Excitable Cells

Prereq: ENG BE 401 and graduate standing; seniors with consent of instructor. Focuses on the properties of the membranes of nerve and muscle cells. Classical models of resting potentials, action potentials, synaptic transmission, and sensory receptors are treated. The structure and function of single ionic channels are characterized in detail from patch-clamp recordings, neuropharmacological studies, and molecular studies. Mechanisms of muscle contraction and other forms of cellular motility are also covered. 4 cr.

ENG BE 710 Neural Plasticity and Perceptual Learning

Prereq: ENG BE 200 (or an introductory course in probability and statistics); GRS BI 755 (or any other introductory course in Neuroscience). Recommended: either ENG BE 570 or ENG BE 500 Physiology of the Auditory System. Graduate student standing or permission of the instructor. This course explores the capacity of cortical sensory and motor maps in the adult brain to change as a result of alterations in the effectiveness of the input, direct damage, or practice. The lectures will describe and discuss (1) the physiology and anatomy underlying adult dynamics; (2) psychophysical methods and experimental paradigms that have been used to study cortical plasticity in the early stages of the sensory and motor pathways; (3) evidence for perceptual learning; and (4) biologically plausible computational models of learning. We will discuss applications of functional neuroimaging to study perceptual learning and restorative plasticity in the human brain. 4 cr.

ENG BE 722 Advanced Continuum Biomechanics and Biofluid Dynamics

Prereq: ENG BE 521 or equivalent or permission by instructor. This is the second course in a two-semester sequence, which emphasizes the application of continuum mechanics to problems in physiology, biology, and medicine. Material will be presented through topical examples, which will employ the governing equations and field theory of continuum mechanics and illustrate how to apply these principles to formulate and solve problems in biomechanics and biofluid dynamics. Examples will be presented in the context of four three-week-long modules. Utilizing various problem-solving techniques (e.g., the finite element method, Monte Carlo simulation, perturbation methods, etc.), each module will take a multidisciplinary approach that will illustrate the necessity to incorporate concepts and tools from a variety of fields (e.g., chemistry, physical chemistry, thermodynamics, acoustics, electrostatics, molecular dynamics, etc.), and which might include non-continuum approaches (e.g., statistical physics, structural mechanics, etc.). Some modules will include wet/computer lab components. 4 cr.

ENG BE/MN 726 Biomaterials and Tissue Engineering I

Prereq: graduate student standing in BE, CH, or MFG. Provides the chemistry and engineering skills needed to solve challenges in the biomaterials and tissue engineering area, concentrating on the fundamental principles in biomedical engineering, material science, and chemistry. Covers the structure and properties of hard materials (ceramics and metals) and soft materials (polymers and hydrogels). Includes the biological response to materials such as cell-surface interactions and inflammation. Same as MN 726, students may not receive credit for both. 4 cr.

ENG BE/MN 727 Biomaterials and Tissue Engineering II

Prereq: graduate student standing in BE, CH, or MFG. Provides the chemistry and engineering skills needed to solve challenges in the biomaterials and tissue engineering area, concentrating on material properties, mechanics and specific research topics. Covers the rheological properties of polymers and gels as well as fatigue and fracture of materials.  Research topics such as tissue engineering, polymer chemistry, drug delivery, and micro-nano biosystems. Same as MN 727, students may not receive credit for both. 4 cr.

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ENG BE 740/SC 740 Parameter Estimation and Systems Identification

Prereq: ENG EK 500 or consent of instructor. Application of models with physical parameters to experimental data. Linear and non-linear systems estimation, system identifiability, time and frequency domain estimation, model sensitivity and experiment multivariate statistical analysis, and optimal design. Application predominantly to biomedical systems (e.g., cardiovascular, respiratory, and pharmokinetics). Other applications included. Same as ENG SC 740; students may not receive credit for both. 4 cr.

ENG BE 747 Advanced Signals and Systems Analysis for Biomedical Engineering

Prereq: ENG BE 200 and ENG BE 401 or equivalent, graduate standing in BME. Introduction to advanced techniques for signals and systems analysis with applications to problems in biomedical engineering research. Time-domain and frequency-domain analysis of multiple input, multiple output systems using the fundamental matrix approach. Hilbert transform relations; applications to head-related transfer functions. Second-order characterization of stochastic processes: power density spectra, cross-spectra, auto- and cross-correlation functions. Gaussian and Poisson processes. Models of neural firing patterns. Effects of linear systems on spectra and correlation functions. Applications to models of the peripheral auditory system. Optimum processing applications. Applications to psychophysical modeling. Introduction to wavelets and wavelet transforms. Wavelet filter banks and wavelet signal processing. 4 cr.

ENG BE 760 Structural Bioinformatics

Prereq: BE 561 (Protein and DNA Sequence Analysis), BE 560 (Biomolecular Architecture) or equivalent. Principles and significance of protein structure. Protein domains and folds. Functional classification of proteins. Functional and structural annotation. Molecular modeling and simulation methods. Structure validation and refinement. Assignment of structure to genome sequences by homology modeling and fold recognition. The role of structure in functional annotation. Protein families and folds in genomes. Protein–protein interactions and docking. Annotation from protein interactions. Interactions between proteins and small molecules. Structure-based drug design. Quantitative Structure–Affinity Relationships (QSAR) and the estimation of affinities. Chemoinformatics, molecular diversity, and combinatorial library design. DNA structure, protein–DNA interactions and recognition sites. Binding of small molecules to DNA. RNA structure prediction. 4 cr.

ENG BE 764 Biophysics of Large Molecules

Coreq: ENG EK 424. Prereq: CAS CH 102, ENG BE 401, graduate standing, or consent of instructor. Correlation between various physical properties of large molecules and their structure is considered in detail. Physical and mathematical description of polyatomic molecules and macromolecules is elaborated. Methods to study large molecules are described. A special emphasis is given to interaction of large molecules with electromagnetic radiation (visual light, ultraviolet and infrared radiation, X-rays, radiowaves). Physics of macromolecules (or polymers) is treated in detail. Numerous biomedical photosynthesis, DNA damage under irradiation, structure of major biological molecules (proteins and nucleic acids). 4 cr.

ENG BE 765/SC 765 Biomedical Optics and Biophotonics

This course surveys the applications of optical science and engineering to a variety of biomedical problems, with emphasis on optical and photonics technologies that enable real, minimally-invasive clinical applications. The course teaches only those aspects of biology itself that are necessary to understand the purpose of the application. The first weeks introduce the optical properties of tissue, and following lectures cover a range of topics in three general areas: 1) Optical spectroscopy applied to diagnosis of cancer and other tissue diseases; 2) Photon migration and optical imaging of subsurface structures in tissue; and 3) Laser-tissue interactions and other applications of light for therapeutic purposes. In addition to formal lectures, recent publications from the literature will be selected as illustrative of various topical areas, and for each publication one student will be assigned to prepare an informal presentation (with overhead slides or PowerPoint) reviewing for the class the underlying principles of that paper and outlining the research results. Same as ENG SC 765; students may not receive credit for both. 4 cr.

ENG BE 767 Protein and Genomic Systems Engineering

ENG BE 768 Biological Database Analysis

Prereq: CAS CS 112 or CS 113, graduate standing, or consent of instructor. Background knowledge of biochemistry and genetics. Describes relational data models and database management systems. Teaches the theories and techniques of constructing relational databases with emphasis on those aspects needed for various biological data, including sequences, structures, genetic linkages and maps, and signal pathways. Introduces relational database query language SQL. Summarizes currently existing biological databases and the Web-based programming tools for their access. Object-oriented modeling is introduced primarily as a design aid for dealing with the particular complexities of biological information in standard RDB design. Emphasis will be on those problems associated with dealing with data whose nomenclature and interrelationships are undergoing rapid change. 4 cr.

ENG BE 775 Mechanisms and Models of Cellular Regulation

Prereq: Graduate standing; MA 226 or equivalent; at least one course in computer programming. ENG BE 505 or equivalent is recommended. Regulatory and control processes in cells are presented from a genetic and biochemical network perspective. Systems analysis of networks include logical (Boolean), deterministic (ordinary differential equations), and stochastic approaches. Case studies of gene regulatory networks as well as metabolic, signaling, cell survival, proliferation, and death pathways are discussed. Existing modeling platforms of systems biology and bioinformatic pathways databases are introduced. 4 cr.

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ENG BE 777 Computational Genomics

Prereq: BE 561 or consent of instructor. A case-study approach to current topics in computational genomics. Mathematical and engineering tools for analyzing genomic data are reviewed. The relationships between sequence, structure, and function in complex biological networks are studied using quantitative modeling. Whole genome analysis is performed. Completion of a series of projects emphasizing real-life data, integrated approaches, practical applications, hands-on analysis, and collaboration. Course projects aim at improving current approaches and involve C and/or PERL programming to interface with existing software packages. The course will be offered in a computer laboratory equipped with one laptop per student. 4 cr.

ENG BE 790 Biomedical Engineering Seminar

Prereq: senior standing. Required for graduate students in biomedical engineering. Discussion of current topics in biomedical engineering. Students are expected to read assigned journal articles and to participate actively in weekly discussion meetings. Meetings organized around presentations by invited guests of their research problems, strategy, and technique. 0 cr.

ENG BE 791 PhD Biomedical Engineering Laboratory Rotation System

Prereq: PhD standing. This course allows PhD students to take part in a laboratory rotation system. During these rotations, students become familiar with research activity within departmental laboratories that are of interest to them. These rotations help students identify the laboratory in which they will perform their dissertation research. Postbachelor's PhD students must complete three rotations: one in their first semester of matriculation, and two in their second semester. Post-master's PhD students must complete a minimum of two rotations, one of which must be in their first semester of matriculation. Normally each rotation will last up to seven weeks. 1 cr per lab rotation.

ENG BE 801 Teaching Practicum

ENG BE 900 Research

Prereq: graduate standing. Participation in a research project under the direction of a faculty advisor. Includes research leading to the development of an MS thesis proposal or PhD prospectus, as well as the work necessary to generate an original MS thesis or PhD dissertation. Variable cr.

ENG BE 951 Independent Study

By petition only. A course of reading under the direction of a faculty advisor covering subject matter not available in a lecture course. Final report or examination normally required. Variable cr.

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Manufacturing Engineering

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ENG MN 500 Special Topics in Manufacturing Engineering

Prereq: engineering graduate student standing; others by permission of instructor. Specific prerequisites vary according to topic. Coverage of a specific topic in manufacturing engineering. One topic covered in depth each term. Subject matter, which varies from year to year, is generally from an area of current or emerging research. 4 cr.

ENG MN 501, 502 Manufacturing Case Studies I, II

Prereq: consent of instructor. An integrated experience in manufacturing engineering. A series of topic areas are covered using intensive weekly cases. Cases emphasize such topics as probability and statistics, mechanics and heat transfer, automation and control, materials and processes, and microcomputers as appropriate in manufacturing. One case analysis is finished and presented each week. 4 cr.

ENG MN 505 Intellectual Assets: Creation, Protection, and Commercialization

Prereq: Senior or graduate standing in an engineering or science discipline, or consent of instructor. This course provides students with the knowledge and tools necessary to create, protect, and commercialize engineering and scientific intellectual assets. Students will first make use of creativity tools to attack posed engineering problems, then turn to means for protecting their solutions. Rapidly growing areas that are affecting nearly all businesses (e.g., software and the Internet) as well as “high-tech” areas including microelectronics, communications, and bioengineering will be emphasized. Extensive patent searches and analysis will be carried out to develop skills for quickly ascertaining the protected technical content of patents, and for recognizing what intellectual property (IP) should be and can be protected. Legal aspects for protecting creative ideas will be studied at a level appropriate for engineers to interact easily and smoothly during their technical careers with IP lawyers. Various business models for the commercialization of intellectual assets will be analyzed. Extensive class exercises and projects will explore in depth all three of these important areas of IP, with emphasis on key contributions during engineering and scientific research and development activities. 4 cr.

ENG MN 507 Process Modeling and Control

Prereq: senior or graduate standing in Engineering; ENG EK 307, CAS MA 226 or equivalent coursework and permission of instructor. An introduction to modeling and control as applied to industrial unit processes providing the basis for process development and improvement. Major themes include an integrated treatment of modeling multi-domain physical systems (electrical, mechanical, fluid, thermal), application of classical control techniques, and system design. Topics include modeling techniques, analysis of linear dynamics, control fundamentals in the time and frequency domain, and actuator selection and control structure design. Examples drawn from a variety of manufacturing processes and case studies. 4 cr.

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ENG MN 510 Production Systems Analysis

Prereq: ENG MN 345 or consent of instructor. Operations research and dynamic systems methods applied in modeling, analysis, and control of production systems. Inventory analysis and control for single and multi-item systems based on deterministic and stochastic demand models. Demand forecasting. Supply chain management. Machine, flow shop and job shop scheduling, project scheduling with PERT and CPM. Production control methods: MRP, MRP-II, Just-in-Time, and Kanban. 4 cr.

ENG MN 511 Manufacturing Information Systems

Prereq: graduate status or consent of instructor. Introduction to Information Systems concepts, design and analysis techniques, and their application to Manufacturing Operations Management. The impact of contemporary Information Technology solutions on Manufacturing Operations Management is explored by focusing on Enterprise Resource Planning, Manufacturing Execution, and Advanced Planning and Scheduling systems. Trends and challenges facing Information Technology solutions to Manufacturing Operations Management are highlighted through case studies focusing on Lean and Agile manufacturing, Supply Chain Management and Electronic Procurement, six sigma, and related methodologies. 4 cr.

ENG MN 513 Product Development

Prereq: senior or graduate standing in an engineering discipline. Dynamics of converting ideas into marketable products. Choosing products and defining their specifications to achieve competitive advantage. The product development process is deconstructed and its elements are examined critically in the context of actual case studies; risk evaluation, concurrent engineering, and impact of new product decisions on the factory. A step-by-step methodology for new product development is derived. 4 cr.

ENG MN 514/SC 514 Simulation

Prereq: ENG EK 126, ENG EK 127, or knowledge of a general purpose programming language; ENG MN 308, CAS MA 381, or knowledge of probability and statistics. Modeling of discrete event systems and their analysis through simulation. Systems considered include, but are not limited to, manufacturing systems, computer-communication networks and computer systems. Simulating random environments and output analysis in such contexts. A simulation language is introduced and is the main tool for simulation experimentation. Same as ENG SC 514; students may not receive credit for both. Includes lab. 4 cr.

ENG MN 515 Diagnostic Imaging Systems

Prereq: one of ENG SC 401, ENG BE 401, or ENG EK 510, and elementary knowledge of atomic physics. Methods of obtaining useful images of the interior of the body and industrial objects using X-rays, ultrasound, and radionuclides. Image formation and display; projection radiography; radiation detectors; conventional and computerized tomography; nuclear imaging; ultra-sonic imaging; automating diagnosis and nondestructive testing; radiation safety. Same as ENG BE 515; students may not receive credit for both. 4 cr.

ENG MN 518 Product Quality

Prereq: ENG MN 308 or consent of the instructor. Introduction to statistical methods for design, control, and improvement of quality. Includes Statistical Process and Quality Control (SPC & SQC) and Acceptance Sampling. Extensive coverage of Design of Experiments (DOE) with applications to designing quality into products and to process and product performance improvement. Also covers Robust Design and Taguchi's method. Introduction to modern approaches to management of quality (TQM, Six Sigma). 4 cr.

ENG MN 522 Technology Ventures

ENG MN 523/BE 523 Mechanics of Biomaterials

ENG MN 524/SC 524 Optimization Theory and Methods

Prereq: ENG MN 409 or consent of instructor. Introduction to optimization problems and algorithms emphasizing problem formulation, basic methodologies, and the underlying mathematical structures. Covers classical optimization theory as well as recent advances in the field. Topics include modeling issues and formulations, simplex method, duality theory, sensitivity analysis, large-scale optimization, integer programming, interior-point methods, non-linear programming optimality conditions, gradient methods, and conjugate direction methods. Particular applications are considered and a few case studies covered. In addition to extensive paradigms from production planning and scheduling in manufacturing systems, other illustrative applications include fleet management, air traffic flow management, optimal routing in communication networks, and optimal portfolio selection. Meets with ENG SC 524; students may not receive credit for both. 4 cr.

ENG MN 526 Simulation of Physical Processes

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ENG MN 527 Transport Phenomena

Prereq: ENG EK 304 or equivalent or consent of instructor. Introduction to momentum, heat, and mass transport phenomena occurring in various processes. Whereas transport phenomena underlie many processes in engineering, agriculture, meteorology, physiology, biology, analytical chemistry, materials science, pharmacy and other areas, they are key to specific applications in diverse areas such as materials processing, green manufacturing of primary materials, biological membranes, fuel cell engineering, and synthesis of clean fuels. This course covers three closely related transport phenomena: momentum transfer (fluid flow), energy transfer (heat flow), and mass transfer (diffusion). The mathematical underpinnings of all three transport phenomena are closely related and the differential equations governing them are frequently quite similar. Since in many situations the three transport phenomena occur together, they are presented and studied together in this course. 4 cr.

ENG MN 529 Thermodynamics and Kinetics of Materials and Processes

Prereq: ENG EK 306. Provides a basic understanding of the laws of thermodynamics as they apply to different elements and compounds and their interactions in the solid, liquid, and gaseous forms as a function of various extensive and intensive variables. Analysis of the path to thermodynamic equilibrium or process kinetics will be covered by discussing reaction kinetics and the laws that govern mass transfer in solids and fluids. Mass transfer through membranes/cellular materials will also be covered. The course primarily covers thermodynamics and kinetics as they apply to the study of materials structure and synthesis. 4 cr.

ENG MN 530 Materials and Processes in Manufacturing

Consent of instructor. Graduate-level introduction to manufacturing processes and their relationship to the structure/properties of materials. Detail development of structure of solids, equilibrium thermodynamics, kinetics, mechanical properties, and some key processes, such as machining, consolidation, and surface modification. 4 cr.

ENG MN 531 Phase Transformations

Prereq: ENG EK 306 Material Science or graduate standing. Graduate-level introduction to phase transformations; solution thermodynamics; phase diagrams; kinetics of mass transport and chemical reactions; atomistic models of diffusion; nucleation and growth; spinodal decomposition; martensitic transformations; order-disorder reactions; point defects and their relation to transport kinetics. 4 cr.

ENG MN 532 Mechanical Behavior of Materials

Prereq: ENG EK 305, EK 306, or graduate standing. This course relates mechanical behavior of crystalline materials to processes occurring at microscopic and/or atomic levels. Topics covered include structure of materials and their determination by X-ray diffraction; dislocations and their relationship to plastic deformations and strength of materials; fracture and creep. 4 cr.

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ENG MN 534 Materials Technology for Microelectronics

Prereq: graduate status or consent of instructor. This course deals with the materials issues in microelectronics processing. Fundamental materials science concepts of bonding, electronic structure, crystal structure, defects, and phase diagrams are applied to key processing steps in microelectronics technology. Also included are single crystal growth, lithography, thermal oxidation of Si, dopant diffusion, ion implantation, thin film deposition, etching and back-end processing; as well as widely used microelectronics simulation software such as SUPREM. Materials challenges in emerging directions in micro and nanoelectronics, including silicon on insulator technology, Si-Ge strained layers, and quantum dots will also be addressed. 4 cr.

ENG MN 535 Green Manufacturing

Prereq: senior/graduate standing; Background knowledge of chemistry (e.g., CAS CH 131 or CAS CH 101); calculus through differential equations (e.g., CAS MA 226); thermodynamics (e.g., ENG EK 304 or ENG EK 424); and process kinetics (e.g., ENG MN 465 or ENG MN 529); or consent of the instructor. Provides a systems view of the manufacturing process that aims to efficiently use energy, water, and raw materials to minimize air and water pollution and generation of waste per unit of the manufactured product. Specifically, the course will discuss methods to maximize yield and minimize waste effluents in processes, ways to devise treatment strategies for handling manufacturing wastes, innovative ways to decrease energy consumption in manufacturing, by-product use and product recycling, and policies that encourage green manufacturing. 4 cr.

ENG MN 540 Design of High-Speed Automation Systems

Prereq: senior/graduate standing, ENG MN 345 or consent of instructor. This course, based on industrial best practice, teaches students to justify, design, and implement high-speed assembly automation systems in production. The course concentrates on the production of high-volume consumer products that must be manufactured in quantities ranging from 100 to 600 parts per minute to be cost-effective. Topics covered, via case studies, include financial justification, equipment specification, design of basic assembly mechanisms, feeding systems, control systems, integration, and debugging. This course is proposed as both a manufacturing and productivity elective. 4 cr.

ENG MN 544/SC 544 Networking the Physical World

Prereq: ENG SC 312, ENG SC 450 or equivalents; ENG SC 441 is desirable, C programming experience. Considers the evolution of embedded network sensing systems with the introduction of wireless network connectivity. Key themes are computing optimized for resource constrained (cost, energy, memory and storage space) applications and sensing interfaces to connect to the physical world. Studies current technology for networked embedded network sensors including protocal standards. A laboratory component of the course introduces students to the unique characteristics of distributed sensor motes including programming, reliable communication, sensing modalities, calibration, and application development. Experience with the C language is required. Students may not receive credit for both. 4 cr, 1st sem.

ENG MN 545 Electrochemistry of Fuel Cells and Batteries

Prereq: ENG MN 529. Electrochemistry of high-temperature fuel cells, batteries, and ceramic gas separation membranes. Types, advantages, and disadvantages of fuel cells currently being developed by the power generation industry, and the electrochemical underpinnings of fuel cell operation. Thermodynamics of fuel cells, electrode kinetics, and mass transport in porous electrodes. Measurements techniques (dc polarization, ac impedance spectroscopy, and blocking electrodes) used extensively in fuel cell research and development. Operation of batteries and ceramic gas separation membranes. Current manufacturing techniques used in fuel cell industry. 4 cr.

ENG MN 550 Product Supply Chain Design

Prereq: ENG MN 415 or consent of instructor. Integrated design of systems to deliver quality products to customers. Lean manufacturing with hard automation. Worker empowerment with active learning. Creation of lean supply chains with control of logistics and information. Creating customer value in a world of excess capacity. Industry project required. 4 cr.

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ENG MN 555 MEMS: Fabrication and Materials

Prereq: graduate status or consent of instructor. This course will explore the world of microelectromechanical devices and systems (MEMS). This requires an awareness of design, fabrication, and materials issues involved in MEMS. The material will be covered through a combination of lectures, case studies, and individual homework assignments. The course will cover design, fabrication technologies, material properties, structural mechanics, basic sensing and actuation principles, packaging, and MEMS markets and applications. The course will emphasize MEMS fabrication and materials. 4 cr.

ENG MN 560 Precision Machine Design and Instrumentation

ENG MN 566 Advanced Engineering Mathematics

Prereq: CAS MA 225, CAS MA 226, senior standing, and consent of instructor. Introduces students of engineering to various mathematical techniques which are necessary in order to solve practical problems. Topics covered include a review of calculus methods, elements of probability and statistics, linear algebra, transform methods, difference and differential equations, numerical techniques, and mathematical techniques in optimization theory. Examples and case studies focus on applications to several engineering disciplines. The intended audience for this course is advanced seniors and entering MS engineering students, who desire strengthening of their fundamental mathematical skills, in preparation for advanced studies and research. 4 cr.

ENG MN 567/SC 567 Electromagnetic Wave Computation

Prereq: ENG SC 453 or consent of instructor. Introduction to numerical methods for solving the three-dimensional Maxwell's equations in the frequency and time domains. Integral equations and the method of moments. Finite-element frequency-domain method. Finite-difference and finite-element time-domain methods. Numerical grid generation. Applications to scattering, antennas, waveguides, and high-speed electronic circuits. Students may not receive credit for both. 4 cr.

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ENG MN 568 Modeling of Pattern Transfer in Microlithography

Prereq: ENG AM 400 or consent of instructor. This course covers simulation methods essential for improving the manufacturability of semiconductor microchips. In particular, the simulation of microlithography processes is covered, as microlithography is the key component of semiconductor manufacturability. The following aspects are covered: optical simulation, photoresist simulation, etching, electron beam mask making simulation, and phenomenological models. Emphasis is placed on incorporating this information into current manufacturing R & D directions and on applying these simulation methods to help address key technology problem areas. 4 cr

ENG MN 570/AM 570 Robot Motion Planning

Prereq: ENG EK 102 or CAS MA 142 and CAS MA 226. Provides an overview of state-of-the-art techniques for robot motion planning. The emphasis is on the algorithms. It covers topology of configuration spaces, potential functions, roadmaps, cell decompositions, sampling-based algorithms, and model checking approaches to robot motion planning and control. Students may not receive credit for both. 4 cr.

ENG MN 579/SC 579 Microelectronic Device Manufacturing

Prereq: graduate standing plus an undergraduate course in semiconductors at the level of ENG SC 410, SC 471, SC 453, CAS PY 313, or PY 354, or consent of instructor. Physical processes and manufacturing strategies for the fabrication and manufacture of microelectronic devices. Processing and device aspects instrumental in silicon, including the fabrication of