Graduate Courses

Note: Students may also take courses from other engineering departments within Duke's Pratt School of Engineering, and courses from other graduate schools at Duke with the permission of the adviser and the Director of Graduate Studies.

510. Diffraction and Spectrometry of Materials. This course focuses on the fundamentals and applications of x-ray and electron-beam based techniques for the characterization of materials, covering a wide range of analytical tools used in both scientific research and in industry. The class will cover a broad selection of topics in diffraction for the study of the atomic structure of materials, as well as spectrometry to investigate microscopic dynamics and composition. The class will provide the students with the fundamental concepts and a comprehensive understanding for applications to many x-ray / electron / neutron scattering techniques, for the study of a wide range of materials, including: energy materials, semiconductors, polymers, biomaterials, films, nano-materials, or structural materials.

511. Computational Materials Science. Since quantum mechanics was invented, scientists have known that the properties of any material are, in principle, governed by a set of mathematical rules that we know exactly. The challenge is to use these laws that start at the smallest scale (atoms and electrons) to predict phenomena that are macroscopically important. The computers and methods that we have today are bringing us closer to this vision. This course covers modern computational techniques for the prediction of materials properties, beginning from the scale of electrons and atoms and connecting to materials challenges in experiments today. Subjects covered include Schrödinger's Equation and Density Functional Theory, Molecular Dynamics, and so-called multiscale approaches to connect quantities computed at the nanoscale to macroscopic properties. In addition to traditional classroom teaching, the class incorporates specific examples as explicit computer exercises for the participants.

512. Thermodynamics of Electronic Materials. Basic thermodynamic concepts applied to solid state materials with emphasis on technologically relevant electronic materials such as silicon and GaAs. Thermodynamic functions, phase diagrams, solubilities and thermal equilibrium concentrations of point defects; non-equilibrium processes and the kinetic phenomena of diffusion, precipitation, and growth. 3 units.

513. Nanobiomechanics. The course focuses on the development of an understanding of the mechanical properties of biopolymers such as DNA, proteins and polysaccharides by examining these properties at the nanoscale level both theoretically using polymer elasticity models and experimentally through direct mechanical manipulations of individual molecules. The course consists of didactic lectures and many laboratory demonstrations and real experiments done by the students themselves. Objectives of the course are: i) Review of single-molecule force spectroscopy (SMFS) techniques that allow mechanical stretching and relaxing of single polymer chains to determine their force-extension relationships; ii) Review of SMFS instrumentation (Scanning Tunneling Microscopy (STM), Atomic Force Microscopy and Spectroscopy (AFM/AFS)), magnetic tweezers (MT), optical tweezers (OT)) and their physical principles, resolution and resolution limitations; iii) Principles of entropic and enthalpic elasticity of biopolymers and their roles in biology such as in passive elasticity of muscle; iv) Understanding force-induced mechanical unfolding and refolding reactions of individual proteins, DNA and sugar molecules; v) Principles of computer modeling of biopolymers and their force-induced structural alterations; vi) designing novel, DNA encoded, protein-based nanostructured biomaterials with tailored viscoelastic properties. 3 units.

514. Theoretical and Applied Polymer Science (GE, BB). An intermediate course in soft condensed matter physics dealing with the structure and properties of polymers and biopolymers. Introduction to polymer syntheses based on chemical reaction kinetics, polymer characterization. Emphasizes (bio)polymers on surfaces and interfaces in aqueous environments, interactions of (bio)polymer surfaces, including wetting and adhesion phenomena. 3 units. C-L: Biomedical Engineering 529

515. Electronic Materials. An advanced course in materials science and engineering dealing with materials important for solid-state electronics and the various semiconductors. Emphasis on thermodynamic concepts and on defects in these materials. Materials preparation and modification methods for technological defects in these materials. Prerequisite: Mechanical Engineering 221L. 3 units.

516. Thin-Film Photovoltaic Technology. The earth receives approximately 120,000 terawatts (TWs) of solar energy annually (versus human consumption of ~15 TW), in a form that is renewable, reliable and geographically distributed. One particular avenue for exploiting solar energy is the direct conversion of sunlight into electricity or photovoltaics (PV). This course will focus in on a promising class of solar cells based on thin-film absorbers, some of which are already commercialized (e.g., CdTe, CIGS), while others are on the cutting edge of new photovoltaics technology (e.g., perovskites). The course will employ a combination of lecture, directed reading and hands-on approaches to get a better appreciation of the advantages and challenges of this class of PV technologies. The hands-on component of the course will involve fabricating PV devices and employing contemporary characterization and modeling tools to evaluate device performance. Both the specific techniques employed, as well as the intellectual framework used in the course are more generally applicable to other solar cell and electronic device technologies. Note: 12 student limit on class size. 3 units.

524. Introduction to the Finite Element Method. Investigation of the finite element method as a numerical technique for solving linear ordinary and partial differential equations, using rod and beam theory, heat conduction, elastostatics and dynamics, and advective/diffusive transport as sample systems. Emphasis placed on formulation and programming of finite element models, along with critical evaluation of results. Topics include: Galerkin and weighted residual approaches, virtual work principles, discretization, element design and evaluation, mixed formulations, and transient analysis. Prerequisites: a working knowledge of ordinary and partial differential equations, numerical methods, and programming in FORTRAN. 3 units. C-L: see Civil and Environmental Engineering 530

525. Nonlinear Finite Element Analysis. Formulation and solution of nonlinear initial/boundary value problems using the finite element method. Systems include nonlinear heat conduction/diffusion, geometrically nonlinear solid and structural mechanics applications, and materially nonlinear systems (for example, elastoplasticity). Emphasis on development of variational principles for nonlinear problems, finite element discretization, and equation-solving strategies for discrete nonlinear equation systems. Topics include: Newton-Raphson techniques, quasi-Newton iteration schemes, solution of nonlinear transient problems, and treatment of constraints in a nonlinear framework. An independent project, proposed by the student, is required. Prerequisite: Civil Engineering 530(254) or consent of instructor. 3 units. C-L: see Civil and Environmental Engineering 630

527. Buckling of Engineering Structures. An introduction to the underlying concepts of elastic stability and buckling, development of differential equations and energy approaches, buckling of common engineering components including link models, struts, frames, plates, and shells. Consideration will also be given to inelastic behavior, postbuckling, and design implications. Prerequisite: Civil Engineering 421L(131L) or consent of instructor. 3 units. C-L: see Civil and Environmental Engineering 647

531. Engineering Thermodynamics. Axiomatic formulations of the first and second laws. General thermodynamic relationships and properties of real substances. Energy, availability, and second law analysis of energy conversion processes. Reaction and multiphase equilibrium. Power generation. Low temperature refrigeration and the third law of thermodynamics. Thermodynamic design. 3 units.

532. Convective Heat Transfer. Models and equations for fluid motion, the general energy equation, and transport properties. Exact, approximate, and boundary layer solutions for laminar flow heat transfer problems. Use of the principle of similarity and analogy in the solution of turbulent flow heat transfer. Two-phase flow, nucleation, boiling, and condensation heat and mass transfer. 3 units.

535. Biomedical Microsystems. The objective of the course is to introduce students to the interdisciplinary field of biomedical microsystems with an emphasis on biomedical microelectromechanical systems (bioMEMS) and microtechnologies. Topics include Scaling laws, Micropatterning of substrates and cells, Microfluidics, Molecular biology on a chip, Cell-based chips for biotechnology, BioMEMS for cell biology, Tissue microengineering, and Microfabricated implants and sensors. 3 units.

536. Compressible Fluid Flow. Basic concepts of the flow of gases from the subsonic to the hypersonic regime. One-dimensional wave motion, the acoustic equations, and waves of finite amplitude. Effects of area change, friction, heat transfer, and shock on one-dimensional flow. Moving and oblique shock waves and Prandtl-Meyer expansion. Prerequisite: Mechanical Engineering 336L or equivalent. 3 units.

539. Interfacial Transport Phenomena for Energy Technologies. The main topics of the course are transport phenomena taking place on interfaces in renewable/sustainable energy technology. These transport phenomena comprise of charge transport (ions and electrons, for example), heat transfer (conduction, convection, radiation), and mass transfer (e.g. diffusion), sometimes coupled with chemical reactions (catalytic, electrochemical, photochemical, etc.). We will study these transport phenomena at interfaces, especially in the micro- and nano-scale and apply this knowledge to energy conversion and storage processes. All these interfacial transport phenomena are essential for photovoltaic cells, fuel cells, batteries, desalination, solar-thermal devices, thermoelectric devices, and many others. 3 units.

541. Intermediate Dynamics: Dynamics of Very High Dimensional Systems. Comprehensive treatment of the dynamic motion of particles and rigid bodies with an introduction to nonlinear dynamics and the vibration of continuous systems. Topics include: conservation of linear and angular momentum, superposition applied to linear systems, motion in inertial and noninertial frames of reference, Hamilton's principle and Langrange's equations, and generalized coordinates. 3 units. C-L: see Civil and Environmental Engineering 625

543. Energy Flow and Wave Propagation in Elastic Solids. Derivation of equations for wave motion in simple structural shapes: strings, longitudinal rods, beams and membranes, plates and shells. Solution techniques, analysis of systems behavior. Topics covered include: nondispersive and dispersive waves, multiple wave types (dilational, distortion), group velocity, impedance concepts including driving point impedances and moment impedances. Power and energy for different cases of wave propagation. Prerequisites: Engineering 244L(123L) and Mathematics 353(108) or consent of instructor. 3 units. C-L: see Civil and Environmental Engineering 626

544. Advanced Mechanical Vibrations. Advanced mechanical vibrations are studied primarily with emphasis on application of analytical and computational methods to machine design and vibration control problems. Equations of motion are developed using Lagrange's equations. A single degree-of-freedom system is used to determine free vibration characteristics and response to impulse, harmonic periodic excitations, and random. The study of two and three degree-of-freedom systems includes the determination of the eigenvalues and eigenvectors, and an in-depth study of modal analysis methods. The finite element method is used to conduct basic vibration analysis of systems with a large number of degrees of freedom. The student learns how to balance rotating machines, and how to design suspension systems, isolation systems, vibration sensors, and tuned vibration absorbers. 3 units.

555. Applications in AI for Materials. In this special topics course, AI principles are applied to a series of materials science example problems, each taught in a module by an expert in materials science and/or data science. Each module spans 2-3 weeks, demonstrating an array of data science/AI methods in unique materials case studies in advancing discovery or design principles. Example modules include: Boosted decision trees for discovering structural patterns controlling bandgaps in metamaterials, Machine learning to predict dynamic heterogeneities in materials, and AI assisted design of high entropy materials for catalysis. 3 units.

Details for current course located here:

555. Data Driven Dynamic Systems and Control.

555. Experiment Design and Research Methods (MS Capstone). Students define a hands-on project of their choice that would prepare them for research in their preferred master’s study concentration.  The design process is employed to identify a problem, formulate it, propose design alternatives and rank them, produce and test prototypes, refine and iterate on the selected design. The experiments that are developed are incorporated within the graduate and undergraduate curriculum.  The course is composed of equal parts design, technical content, and communication skills (including an online portfolio). Projects can be further developed during the subsequent semester to fulfill the master’s project requirement during the Poster Expo. 3 units.

Details for current course located here:

555. Fundamentals of Soft Matter. Soft matter is a subfield of science that describes properties and behavior of an important class of materials including polymers, colloids, surfactants, and liquid crystals. The course provides a unified overview of key aspects of the physics of soft condensed matter. The course introduces relevant energies, forces and time scales governing the interactions of soft materials in bulk and at surfaces. The course will touch upon concepts and phenomena including phase transitions, self-assembly, and viscoelastic behavior of these materials. The main objective of the course is to bring students to a common level of knowledge and competency in soft condensed matter that allows them to pursue more specialized directions in soft matter science. 3 units. See also PHY 590.

555. Intermediate Polymer Physics. Review of Introduction to Polymer Physics. Polyelectrolyte Solutions: counterion distribution, dilute & semidilute solutions, adsorption, grafting. Random Branching and Gelation: percolation model; gelation; mean field model; scaling picture of gelation. Networks and Gels: history of rubber; thermodynamics of rubber; rubber elasticity; swelling of polymer gels. Dynamics of Unentangled Polymers: Rouse and Zimm models, semi-dilute unentangled solutions, relaxation modes, diffusion. Dynamics of Entangled Polymers: polymer entanglements, reptation model, stress relaxation. 3 units. See also PHY 590.

555. Intro to Programming. This course builds strong programming fundamentals, so that students can use computing to solve problems in your research or other technical pursuits. Students spend half the semester learning programming fundamentals in C and are then introduced to C++ and move on to data structures and algorithms. During the last few weeks of class, you willstudents write a program in C++ that generates a finite element mesh, plans a path for a robot, or performs other functions according to the student’s choice. C and C++ are chosen for the pedagogical benefit of learning to program with “no magic,” for their applications in computer engineering, and because a compiled executable can be very fast. After this course, learning an additional programming language will be much easier. 3 units.

555. Introduction to Polymer Physics. The overarching goals of this course are to learn about the physical properties of polymers and to demonstrate how these properties can be understood from simple molecular models. The course is divided into the following units. Introduction: history; polymer configurations; homopolymers and copolymers; types of polymeric structures; molecular weight distributions. Ideal Chains: models of ideal chains; conformations; free energy; scattering. Real Chains: excluded volume interactions; deformations; temperature effects. Polyelectrolyte Chains: Electrostatic interactions, distribution of counterions, models of polyelectrolytes without and with added salt. Thermodynamics of Mixing: entropy of mixing; enthalpy of mixing; equilibrium and stability; phase diagrams; mixtures at low compositions. Polymer Solutions: theta solvent; poor solvent; good solvent; semidilute theta solutions; polymer brush; multi-chain adsorption. 3 units. See also: BME 590 and PHY 590.

555. Materials Synthesis and Processing. Materials form the basis of most modern technologies, whether referring to energy, data processing, medical/health or consumer product application. While materials properties are central to the application, the techniques used for processing functional materials into films, crystals or bulk form, with carefully tailored properties, are no less important and will form the basis of the class.  Additionally, the course will expose students to current materials processing/application research thrusts at Duke. 3 units.

555. Microfluidics. 3 units.

555. Model Predictive Control. Introduction to state-space realizations, set theory and optimization. Lyapunov stability theory. Proof of closed-loop stability and persistent feasibility. Computation of quadratic terminal costs and polyhedral constraints for linear systems. Explicit model predictive control and robust receding horizon control will be introduced, time permitting. 3 units.

555. Numerical Optimization. Optimization has widespread applications across science, engineering, economics and other fields.  For instance, optimization algorithms are commonly used in medical imaging, energy exploration, machine learning, materials design, motion planning for robots, and many other applications.​

The course covers theoretical and numerical aspects of nonlinear optimization. Topics will include optimality conditions for constrained and unconstrained optimization, line search and trust region approaches, Newton and quasi-newton methods, methods for large scale optimization, and treatment of equality and inequality constraints. The course will have a balance between theory, algorithms, and computer implementation. 3 units.

555. Physics of Colloidal Dispersion. This class will cover various physical processes relevant to particles having a size scale of less than one micrometer. The topics covered include hydrodynamics, electrostatics in salty fluids, electrokinetics, Brownian motion, rheology, phase transitions, flocculation, sedimentation, and particle capture. Students will write programs in MATLAB to predict the trajectories of multiple particles in space, and will assess various properties about ensembles of trajectories. 3 units.

555. Scientific Computing and Intro ML. This course provides an introduction to key concepts in computer simulation, scientific computing and machine learning that are of paramount importance across many engineering (and non-engineering) applications (e.g. stress analysis of prostheses, vehicle crash testing, autonomous systems, additive manufacturing, etc.). All the techniques introduced in the course will be motivated with real applications. The first part of the course will cover concepts related to numerical methods for solving linear systems, nonlinear systems, eigenvalue problems, optimization, and an introduction to methods for physics-based simulations.

The second part of the course will introduce fundamentals of machine learning tools for unsupervised and supervised learning. We will also cover practical aspects such as data acquisition, feature extraction, training, testing, and performance assessment. The machine learning part will involve a project related to sound/audio classification.

Prerequisites: Linear Algebra, Calculus, and basic programming in Python or MATLAB. 3 units.

555. Solar Thermal Energy Applications. Characteristics of solar radiation, blackbody model. Wien displacement law, greenhouse effect. Flat plate collectors and evacuated tube collectors, cosine losses, energy balance for flat plate collectors. Thermal storage by sensible heat and latent heat.  Fluid mechanics and pumping losses. Trough solar, dish solar, concentration ratio, conversion engines for dish solar. Heliostat systems for power generation, materials for primary and secondary loops, steam cycle.  Basics of passive solar architecture. 3 units.

555. Wind Turbine Design and Analysis. An introduction to the design and analysis of horizontal-axis wind turbines. Topics include wind as a resource, economics of wind power generation, aerodynamics of horizontal axis wind turbines, actuator disk, rotor disk, and rotor blade theories, performance of fixed-speed and constant tip speed ratio turbines, yaw and pitch control, breakdown of momentum theory, Prandtl tip loss factor, blade geometry, lift and drag of aerofoils, stall delay, unsteady flows, ultimate strength analysis using partial safety factors, fatigue analysis using Marin derating factors and Minor’s rule rain-flow cycle counting, and solid mechanics of composite materials.   

Use of software analysis tools including Finite Element Analysis (FEA) for component mode shape and frequency analysis, FEA generation of 6x6 Timoshenko blade element stiffness matrices, XFoil and XRotor generation of turbine blade lift-drag polars, NREL FAST v8/OpenFAST whole-turbine time-domain aeroelastic analysis of Design Load Cases. 3 units.

555/BME 590. Biomaterials. This introductory course in Biomaterials will review the major classes of materials used in medical devices. This includes issues with synthesis, processing, fabrication and sterilization. Interactions of proteins and cells with materials, and resulting complications related to biocompatibility, will be introduced. 3 units.

555/412. Modern Materials. Modern Materials examines the underlying molecular details that give commercially- and industrially-important materials their specific properties. The course will emphasize polymers, photovoltaics, magnetic materials, and biomaterials. The study of each material will begin with an overview of applications, economics, and history of the material. Starting with the standard characterization methods for each material, we will work towards an understanding of the fundamental physics and chemistry that leads to the unique properties of each material. For a final project, students will select a material that enables an artistic or athletic event and then relate the molecular structure of this material to its use. Modern Materials is open to upper-level undergraduates and graduate students. 3 units. See also CHEM 512.

555/490. Molecular Modeling of Soft Matter. Fundamentals and application of statistical mechanics and molecular simulations towards modeling biological and soft materials. Students will learn various computational methods including energy minimization, molecular dynamics simulations, Monte Carlo simulations, and stochastic dynamics simulations. Students will obtain valuable hands-on experience in using molecular simulation software, visualizing molecular systems, and analyzing simulation data for computing material properties. Prerequisites: Basic programming skills in any one of the following languages or platforms: C, MATLAB, Fortran, or Python. Basic undergraduate-level understanding of concepts in mathematics, physics, and chemistry, especially probability, algebra, geometry, calculus, Taylor’s expansion, finite differences, molecular bonding, laws of thermodynamics, ideal gases, and Newton’s laws of motion. 3 units.

571. Aerodynamics. Fundamentals of aerodynamics applied to wings and bodies in subsonic and supersonic flow. Basic principles of fluid mechanics analytical methods for aerodynamic analysis. Two-and three-dimensional wing theory, slender-body theory, lifting surface methods, vortex and wave drag. Brief introduction to vehicle design, performance and dynamics. Special topics such as unsteady aerodynamics, vortex wake behavior, and propeller and rotor aerodynamics. This course is open only to undergraduate seniors and graduate students. Prerequisites: Mechanical Engineering 336L or equivalent, and Mathematics 353 or equivalent. 3 units.

572. Engineering Acoustics. Fundamentals of acoustics including sound generation, propagation, reflection, absorption, and scattering. Emphasis on basic principles and analytical methods in the description of wave motion and the characterization of sound fields. Applications include topics from noise control, sound reproduction, architectural acoustics, and aerodynamic noise. Occasional classroom or laboratory demonstration. This course is open only to undergraduate seniors and graduate students. Prerequisites: Mathematics 353 or equivalent or consent of instructor. 3 units.

590/BME 590. Engineering Technology in Urology Applications. This course provides a unique opportunity to examine various engineering technologies and applications in urology for the treatment of kidney stone patients and other benign urinary tract diseases. Selective topics in laser lithotripsy, shock wave lithotripsy, high-intensity focused ultrasound and ultrasound neuromodulation will be discussed to highlight the key engineering principles, advances in technology and techniques associated with imaging-guided therapy. The goal is to educate engineering students and foster their research interest and development in interdisciplinary and translational biomedical research, applicable to various medical fields. The course is designed for students with diverse backgrounds and research interests, including biophotonics, solid/fluid and computational mechanics, heat transfer, materials science, acoustics, ultrasound instrumentation, and engineering design. Laboratory projects and interaction with clinical doctors will be specifically formulated to enrich the learning experience and encourage students to collaborate in a multidisciplinary team environment to create engineering solutions to address clinical challenges and unmet needs. 3 units.

627. Linear System Theory. This graduate level course focuses on linear system theory in the time domain. The course introduces the fundamental mathematics of linear spaces, linear operator theory, and then proceeds with existence and uniqueness of solutions of differential equations, structural properties of linear systems, and design of linear controllers. The focus is on linear time invariant systems in continuous and discrete time. Topics covered include: Introduction: State-space representation, linearization, existence and uniqueness of solutions of linear differential equations. Review: Linear spaces, eigenvalues, eigenvectors, change of basis, diagonalization, Jordan forms, Cayley-Hamilton theorem, matrix exponential. Stability: Uniform, asymptotic, and exponential stability, Lyapunov stability theorems. Controllability and observability: Kalman rank test, PBH test. State feedback and estimation: Canonical forms, pole placement, observer design. Optimal control: Riccati equation, Hamiltonian matrix, stability.

Prerequisites: Basic knowledge of linear algebra, differential equations, and signals and systems. Undergraduates need permission. 3 units. C-L: see Civil and Environmental Engineering 627

631. Intermediate Fluid Mechanics. A survey of the principal concepts and equations of fluid mechanics, fluid statics, surface tension, the Eulerian and Lagrangian description, kinematics, Reynolds transport theorem, the differential and integral equations of motion, constitutive equations for a Newtonian fluid, the Navier-Stokes equations, and boundary conditions on velocity and stress at material interfaces. 3 units.

632. Advanced Fluid Mechanics. Flow of a uniform incompressible viscous fluid. Exact solutions to the Navier-Stokes equation. Similarity methods. Irrotational flow theory and its applications. Elements of boundary layer theory. Prerequisite: Mechanical Engineering 631 or consent of instructor. 3 units.

639. Computational Fluid Mechanics and Heat Transfer. An exposition of numerical techniques commonly used for the solution of partial differential equations encountered in engineering physics. Finite-difference schemes (which are well-suited for fluid mechanics problems); notions of accuracy, conservation, consistency, stability, and convergence. Recent applications of weighted residuals methods (Galerkin), finite-element methods, and grid generation techniques. Through specific examples, the student is guided to construct and assess the performance of the numerical scheme selected for the particular type of transport equation (parabolic, elliptic, or hyperbolic). 3 units.

647. Buckling of Engineering Structures. An introduction to the underlying concepts of elastic stability and buckling, development of differential equation and energy approaches, buckling of common engineering components including link models, struts, frames, plates, and shells. Consideration will also be given to inelastic behavior, postbuckling, and design implications. Prerequisite: Civil Engineering 421L(131L) or consent of instructor. 3 units. C-L: see Civil and Environmental Engineering 647

671. Advanced Aerodynamics. Advanced topics in aerodynamics. Conformal transformation techniques. Three-dimensional wing theory, optimal span loading for planar and nonplanar wings. Ground effect and tunnel corrections. Propeller theory. Slender wing theory and slender body theory, transonic and supersonic area rules for minimization of wave drag. Numerical methods in aerodynamics including source panel and vortex lattice methods. Prerequisite: Mechanical Engineering 571. 3 units.

672. Unsteady Aerodynamics. Analytical and numerical methods for computing the unsteady aerodynamic behavior of airfoils and wings. Small disturbance approximation to the full potential equation. Unsteady vortex dynamics. Kelvin impulse and apparent mass concepts applied to unsteady flows. Two-dimensional unsteady thin airfoil theory. Time domain and frequency domain analyses of unsteady flows. Three-dimensional unsteady wing theory. Introduction to unsteady aerodynamic behavior of turbomachinery. Prerequisite: Mechanical Engineering 571. 3 units.

674. Fundamentals of Shock Wave Lithotripsy. Introduction to the engineering concepts and technologies used in shock wave lithotripsy - a noninvasive ultrasonic treatment modality for kidney stone disease. Shock wave generation, focusing, and propagation in water and biological tissues will be discussed, as well as measurement techniques for lithotripter field characterization and analysis of shock wave-stone-tissue interactions. Milestone studies on the mechanisms of stone fragmentation and tissue injury will be reviewed with emphasis on technology improvement. Laboratory projects are designed to enrich the learning experience of students in developing essential skills for independent research. 3 units.

676. Advanced Acoustics. Analysis methods in acoustics including wave generation, propagation, reflection, absorption, and scattering; sound propagation in a porous material; coupled structure acoustic systems; acoustic singularities: monopoles, dipoles, quadrupoles; radiation from flat surfaces; classical radiation and scattering solutions for cylinders and spheres; Green's functions, Radiation conditions, Modal analysis; sound fields in rooms and enclosures: energy methods; dissipation in fluid media; introduction to nonlinear effects. This course is open only to graduate students with some prior background in acoustics and applied mathematics. Prerequisites: Mechanical Engineering 572 or equivalent. 3 units.

711. Nanotechnology Materials Lab. This course provides an introduction to advanced methods for the characterization and fabrication of materials, nanostructures, and devices. Cleanroom methods to be covered include lithography, evaporation, and etching. Characterization methods include electron microscopy, atomic force microscopy, X-ray photoelectron spectroscopy, and optical spectroscopy. Students will receive an overview of the techniques in the Shared Materials Instrumentation Facility through lectures and demonstrations. In the lab section, each student will engage in a project that focuses on those capabilities that are needed for their research, and will receive training and certification on that equipment. 3 units. C-L: Electrical and Computer Engineering 721

742. Nonlinear Mechanical Vibration. A comprehensive treatment of the role of nonlinearities in engineering dynamics and vibration. Analytical, numerical, and experimental techniques are developed within a geometrical framework. Prerequisite: Mechanical Engineering 541 or 544 or equivalent. 3 units.

758S. Curricular Practical Training. Curricular Practical Training. Students gain practical Mechanical Engineering and Materials Science experience by taking a job in industry and writing a report about this experience. Course requires prior consent from the student's advisor and from the Director of Graduate Studies and may be repeated with consent of the advisor and the Director of Graduate Studies. Variable credit.

775. Aeroelasticity. A study of the statics and dynamics of fluid/structural interaction. Topics covered include static aeroelasticity (divergence, control surface reversal), dynamic aeroelasticity (flutter, gust response), unsteady aerodynamics (subsonic, supersonic, and transonic flow), and a review of the recent literature including nonlinear effects such as chaotic oscillations. Prerequisite: Mathematics 230 and consent of instructor. 3 units.

CEE 622. Fracture Mechanics. Theoretical concepts concerning the fracture and failure of brittle and ductile materials. Orowan and Griffith approaches to strength. Determination of stress intensity factors using compliance method, weight function method, and numerical methods with conservation laws. Cohesive zone models, fracture toughness, crack growth stability, and plasticity. Prerequisites: CE 520(201) or instructor consent. 3 units.

CHEM 548. Solid State Materials Chemistry. 3 units.

CHEM 590. Polymer Chemistry. 3 units.