Engineering & Applied Science Graduate Courses

Core Course Requirements for the Ph.D. Degree

Each department and program may have identified math courses that will meet the math requirement:

Applied Physics: ENAS 500 or PHYS 506
Biomedical Engineering: ENAS 500 or ENAS 505
Chemical Engineering: ENAS 500 or ENAS 505
Electrical Engineering: No math requirement
Environmental Engineering: ENAS 500 or ENAS 505 or STAT 660 or F&ES 77113 or F&ES 77107
Mechanical Engineering: ENAS 500 or PHYS 506 or ENAS 902

The core courses for each department and program are as follows:

Applied Physics: Solid State Physics I (ENAS 850) and II (ENAS 851), Quantum Mechanics I (PHYS 508) and II (PHYS 608), Electromagnetic Theory I (PHYS 502), Statistical Phyics I (PHYS 512). Two of these courses may be taken in the second year.

Biomedical Engineering: Physiological Systems (ENAS 550), Physical and Chemical Basis of Biosensing (ENAS 510). One of these courses may be taken in the second year.

Chemical Engineering: Classical and Statistical Thermodynamics (ENAS 521), Energy, Mass, and Momentum Processes (ENAS 603), Chemical Reaction Engineering (ENAS 602).

Electrical Engineering (Microelectronics track): Solid State Physics I (ENAS 850), Semiconductor Silicon Devices and Technology (ENAS 986).

Electrical Engineering (System and Signals track): Linear Systems (ENAS 902), Stochastic Processes (ENAS 502).

Electrical Engineering (Computer Engineering track): Introduction to VLSI System Design (ENAS 875) and Advanced Topics in Computer Engineering (ENAS 921).

Environmental Engineering: Aquatic Chemistry (ENAS 640), Biological Processes in Environmental Engineering (ENAS 641), Environmental Physicochemical Processes (ENAS 642).

Mechanical Engineering: Please refer to the Mechanical Engineering section in the 2009-2010 Qualification Procedure.

Below are the frequently offered Engineering & Applied Science graduate courses. For the most up-to-date course offerings and lecturer information, visit Yale University’s Online Course Information site.

ENAS 500, Mathematical Methods I 
Vector analysis in three dimensions (2 weeks), linear algebra (4 weeks), functions of a complex variable (4 weeks), topics at the discretion of the instructor (3 weeks), e.g., (1) specific examples to reinforce the material already presented and (2) new topics (to choose among: Fourier series in one and more dimensions, Laplace transformations, Fourier integrals in one and more dimensions, optimization, elements of ODE).

ENAS 501, Mathematical Methods II
Special functions, the Laplace transformations, Fourier series, Fourier integrals, and partial differential equations including separation of variables, methods of characteristics, variational techniques, and the brief discussion of numerical methods.

ENAS 502, Stochastic Processes
Elements of set and measure theory. Probability distributions, moments, characteristic functions. The central limit theorem. Basic properties of random processes. Stationarity and ergodicity. Correlation functions and power spectra. Linear and nonlinear operations on random processes.

ENAS 503, Probabilistic Networks, Algorithms, and Applications
Examines probabilistic and computational methods for the statistical modeling of complex data. The emphasis is on the unifying framework provided by graphical models, a formalism that merges aspects of graph theory and probability theory. Graphical models: Markov random fields, Bayesian networks, and factor graphs. Algorithms: filtering, smoothing, belief-propagation, sum-product, and junction tree. Variational techniques: mean-field and convex relaxations. Markov processes on graphs: MCMC, factored HMMs, and Glauber dynamics. Some statistical physics techniques: cavity and replica methods. Applications to error-correcting codes, computer vision, bio-informatics, and combinatorial optimization.

ENAS 505, Advanced Engineering Mathematics
A beginning graduate-level introduction is given to ordinary and partial differential equations, vector and tensor analysis, and linear algebra. Laplace transform, series expansion, Fourier transform, and matrix methods are given particular attention. Applications to problems frequently encountered by chemical, biomedical, and environmental engineers are stressed throughout.

ENAS 506, Basic Quantum Mechanics
Basic concepts and techniques of quantum mechanics essential for solid state physics and quantum electronics. Topics include the Schrödinger treatment of the harmonic oscillator, atoms and molecules and tunneling, matrix methods and perturbation theory.

ENAS 509, Electronic Materials: Fundamentals and Applications
Survey and review of fundamental issues associated with modern microelectronic and optoelectronic materials. Topics include band theory, electronic transport, surface kinetics, diffusion, materials defects, elasticity in thin films, epitaxy, and Si integrated circuits.

ENAS 510, Physical and Chemical Basis of Bioimaging and Biosensing
Basic principles and technologies for imaging and sensing the chemical, electrical, and structural properties of living tissues and biological macromolecules. Topics include magnetic resonance spectroscopy, MRI, positron emission tomography and flourescent probes.

ENAS 511, Physics and Devices of Optical Communication
A survey of the enabling components and devices that constitute modern optical communication systems. Focus on the physics and principles of each functional unit, its current technological status, design issues relevant to overall performance, and future directions.  

ENAS 513, Introduction to Analysis
Foundations of real analysis, including metric spaces and point set topology, infinite series, and function spaces.

ENAS 514, Real Analysis
The Lebesgue integral, Fourier series, applications to differential equations.

ENAS 521, Classical and Statistical Thermodynamics
A unified approach to bulk-phase equilibrium thermodynamics, bulk-phase irreversible thermodynamics, and interfacial thermodynamics in the framework of classical thermodynamics, and an introduction to statistical thermodynamics. Both the activity coefficient and the equations of state are used in the description of bulk phases. Emphasis on classical thermodynamics of multicomponents, including concepts of stability and criticality, curvature effect, and gravity effect. The choice of Gibbs free energy function covers applications to a broad range of problems in chemical, environmental, biomedical, and petroleum engineering. The introduction includes theory of Gibbs canonical ensembles and the partition functions, fluctuations, and Boltzmann’s statistics, Fermi-Dirac and Bose-Einstein statistics. Application to ideal monatomic and diatomic gases is covered.

ENAS 525, Optimization I
Focus on linear programming, a resource-allocation method widely used by engineers, managers, economists, and social scientists. The theory of linear programming (the simplex method, sensitivity analysis, prices, duality, and geometry) is coupled with a survey of its principal uses.

ENAS 530, Optimization Techniques
Fundamental theory and algorithms of optimization, emphasizing convex optimization. The geometry of convex sets, basic convex analysis, the principal of optimality, duality. Numerical algorithms: steepest descent, Newton’s method, interior point methods, dynamic programming, unimodal search.

ENAS 534, Biomaterials
Introduction to materials, classes of materials from atomic structure to physical properties. Major classes of materials: metals, ceramics and glasses, and polymers, addressing their specific characteristics, properties, and biological applications. Throughout the presentation of the synthesis, characterization, and properties of the classes of materials, a connection is made to the selection of materials for use in specific biological applications by matching the material’s properties to those necessary for success in the application. Case studies address the successes and failures of particular materials from each of the classes in biological applications.

ENAS 535, Tissue/Biomaterial Interactions
The course addresses the interactions between tissues and biomaterials, with an emphasis on the importance of molecular- and cellular-level events in dictating the performance and longevity of clinically relevant devices. In addition, specific areas such as biomaterials for tissue engineering and the importance of stem/progenitor cells, and biomaterial-mediated gene and drug delivery are addressed.

ENAS 550/C&MP 550/MCDB 550, Physiological Systems
Regulation and control in biological systems, emphasizing human physiology and principles of feedback. The physiology of membranes and membrane transport systems is discussed. The cellular and molecular principles of organ and tissue physiology are explained by coverage of major human physiological systems including renal, cardiovascular, respiratory, endocrine, digestive, and nervous systems.

ENAS 549, Biomedical Data Analysis
This course focuses on the analysis of biological and medical data associated with applications of biomedical engineering. It provides basics of probability and statistics, and analytical approaches for determination of quantitative biological parameters from noisy, experimental data. Programming in Matlab to achieve these goals is a major portion of the course. Applications include Michaelis-Menten enzyme kinetics, Hodgkin Huxley, neuroreceptor assays, receptor occupancy, MR spectroscopy, PET neuroimaging, brain image segmentation and reconstruction, and molecular diffusion.

ENAS 551, Biomedical Engineering I: Quantitative Physiology
Demonstration of the use of engineering analysis and synthesis in problems in the life sciences and medicine; focus on modeling of molecular physiological processes and design of artificial organs. The lectures in the course are coordinated with the sequence of lectures in ENAS 550a to illustrate how engineering analysis can be used to understand physiological processes. In addition, the course presents elements of pharmacokinetics, heat and mass transfer in physiological systems, hemodialysis, drug delivery, and tissue engineering.

ENAS 553, Immuno-Engineering
This course focuses on the applications of engineering techniques and methods to the study of immunology and immunological problems. The course introduces the fundamentals of immunity, followed by examples of how quantitative analysis and biomaterial intervention have helped us shape our understanding of how the immune system works and how to repair its defects. The course is a mixture of lectures and weekly readings.

ENAS 554, Biochemical Engineering: Biotechnology 
Biotechnology treated from the point of view of chemical engineering. Basics of microbiology, microbial genetics and control, and genetic engineering, followed by enzyme kinetics and biochemical reactors. Fermentation technologies: biochemical separation processes with emphasis on chromatography. Field trips to fermentation facilities.

ENAS 557, Biomechanics
An introduction to the application of mechanical engineering principles to biological materials and systems. Topics include ligaments, tendons, bones, muscles; joints, gait analysis; exercise physiology. The basic concepts are directed toward an understanding of the science of orthopaedic surgery and sports medicine.

ENAS 560, Measurement and Noise
Noise is a fundamental part of every movement. A well-designed experiment seeks to reduce the magnitude of the noise to fundamental limits while preserving the intended signal. This course introduces students to this process from both a theoretical and an experimental perspective, using MATLAB as a modeling and visualization tool.

ENAS 562, Digital Systems Testing and Design for Testability  
Introduction to the fundamental concepts, algorithms, and design techniques for testing digital systems. Covered topics include test issues and economics, fault modeling, logic and fault simulation, test generation algorithms for combinational and sequential circuits, testability analysis, design for testability, built-in self-test, delay fault test, functional test, case studies (memory test, FPGA test, system-on-chip test, etc.). Lab work consists of projects employing logic and fault simulation, automatic test pattern generation, and design for testability software tools.

ENAS 563, Fault Tolerant Computer Systems
This course provides an in-depth overview of the theory and practice of fault tolerant systems. Sources of defects as well as hardware and software fault tolerance techniques to mititgate their effects are reviewed. Case studies are used to demonstrate the practical applications of the theory presented in the lectures.

ENAS 564, Tissue Engineering
Introduction to the major aspects of tissue engineering, including materials selection, scaffold fabrication, cell sources, cell seeding, bioreactor design, drug delivery, and tissue characterization. Class sessions include lectures and hands-on laboratory work.

ENAS 570/C&MP 560/MCDB 560, Cellular and Molecular Physiology: Molecular Machines in Human Disease 
This course focuses on understanding the processes that transfer molecules across membranes at the cellular, molecular, biophysical, and physiological levels. Students learn about the different classes of molecular machines that mediate membrane transport, generate electrical currents, or perform mechanical displacement. Emphasis is placed upon the relationship between the molecular structures of membrane proteins and their individual functions. The interactions among transport proteins in determining the physiological behaviors of cells and tissues are also stressed. Molecular motors are introduced and their mechanical relationship to cell function is explored. Students read papers from the scientific literature that establish the connections between mutations in genes encoding membrane proteins and a wide variety of human genetic diseases.

ENAS 575/CPSC 575, Computational Vision and Biological Perception
An overview of computational vision with a biological emphasis. Suitable as an introduction to biological perception for computer science and engineering students, as well as an introduction to computational vision for mathematics, psychology, and physiology students. After MATH 120 and CPSC 112, or with permission of instructor.

ENAS 580,Seminars in Biomedical Engineering
Tutorial seminars illustrating applications of physics and engineering to biomedical problems. Students are required to attend the seminars, to do the readings assigned after each seminar, to ask questions, and to participate in the discussions. Four to five short papers are required on issues arising from selected topics. The final papers may be presented to the rest of the class.

ENAS 585, Fundamentals of Neuroimaging
To understand the neuroenergetic and neurochemical basis of several dominant neuroimaging methods, including fMRI. Topics range from technical aspects of different methods to interpretation of the neuroimaging results. Controversies and/or challenges for application of fMRI and related methods in medicine are identified.

ENAS 600, Computer-Aided Engineering
Aspects of computer-aided design and manufacture including reasons for increased use of CAD/CAM, the computer’s role in the mechanical engineering design and its manufacturing process, hardware and software elements of typical commercial systems, and computer graphics and drafting.

ENAS 602, Chemical Reaction Engineering
Applications of physical-chemical and chemical-engineering principles to the design of chemical process reactors. Ideal reactors treated in detail in the first half of the course, practical homogeneous and catalytic reactors in the second.

ENAS 603, Energy, Mass, and Momentum Processes
Application of continuum mechanics approach to the understanding and prediction of fluid flow systems that may be chemically reactive, turbulent, or multiphase.

ENAS 605, Colloidal Chemical Engineering
A graduate-level introduction is given to modern colloid science as practiced by engineers. Topics include self-assembly in solution and at surfaces, surface chemistry, the electric double layer, colloidal forces, and polymers. Applications to problems frequently encountered by chemical, biomedical, and environmental engineers are stressed throughout.

ENAS 606, Polymer Physics
A graduate-level introduction to the physics and physical chemistry of macromolecules. This course covers the static and dynamic properties of polymers in solution, melt and surface adsorbed states and their relevance in industrial polymer processing, nanotechnology, materials science, and biophysics. Starting from basic considerations of polymerization mechanisms, control of chain architecture, and a survey of polymer morphology, the course also extensively addresses experimental methods for the study of structure and dynamics via various scattering (light, x-ray, neutron) and spectroscopic methods (rheology, photon correlation spectroscopy) as integral components of polymer physics.

ENAS 608, Surface and Surface Processes
The chemistry and physics of solid surfaces. Emphasis on fundamental aspects of the following areas of surface science: surface crystallography and reconstruction; kinetics of gas-solid interactions; adsorption; heterogeneous catalysis by transition metal surfaces; oxidation and corrosion; and nucleation and growth of thin film by physical and chemical vapor deposition.

ENAS 611, Separation Processes
Theory and design of separation processes for multicomputer and/or multiphase mixtures via equilibrium and rate phenomena. Included are single-stage and cascaded absorption, adsorption, extraction, distillation, filtration, and crystallization processes.

ENAS 614, Surface and Thin-Film Characterization
Fundamental and practical aspects of spectroscopy, diffraction, and microscopy related to the structural and chemical characterization of surfaces and thin films. Emphasis on identification of adsorbed species by vibrational spectroscopy, determination of the chemical state of the surface by photoelectron spectroscopy, quantitative methods in surface analysis, determination of surface structure by scanned per microscopy techniques and diffraction methods, and recent advances in surface characterization.

ENAS 615, Synthesis of Nanomaterials
This course focuses on the synthesis and engineering of nanomaterials, a primary frontier for the development of new and improved materials with new properties. We also introduce different types of nanomaterials, unique properties at the nanoscale, measurement and important applications of nanomaterials (including biomedical, electronic, and energy applications). Synthesis methods covered include gas phase and high vacuum techniques (CVD, MOCVD) as well as wet chemistry techniques such as reduction of metal salts, sonochemistry, and sol gel methods. Taking sample applications, we discuss the properties necessary for each, and how to control these properties through synthesis control, such as by using templating methods. This course is directed to chemistry, biology and engineering students.

ENAS 616, Multiscale Modeling and Design in Biology
A survey of the physicochemical properties that dictate a broad range of biological phenomena, in the context of a wide range of physical / mathematical models and computational algorithms. In addition, this course presents several concepts in macromolecular design and synthetic biology, including pioneering literature and current states.

ENAS 618, Principles and Practice of Heterogeneous Catalysis
Emphasis on heterogeneous characterization by spectroscopic techniques. Following the introduction of principles we review several large-scale industrial applications, which include catalytic reforming of naphtha (metal and bimetallic catalysts), catalytic cracking (zeolite catalysts), catalytic hydrotreating, automobile pollution catalysts, and chemical productions, e.g., ethylene oxide, methanol, etc.

ENAS 622, Topics in Multiphase Chemical Reaction Engineering
A series of lectures dealing with fundamental aspects of the thermochemistry, phase/chemical equilibria, chemical kinetics and transport phenomena underlying the use of homogeneous and/or heterogeneous chemical reactions (often-combustion-related) to economically synthesize materials at high production rates, including valuable vapors, particulate matter (ultrafine powders), dense- and granular- coatings, and monoliths. Included are scale-up, purity, safety, and environmental issues associated with the economics/choice of synthesis reactors, along with a summary of R&D trends and associated research needs.

ENAS 626, Chemical Engineering Process Control
Transient regime modeling and simulations of chemical processes. Conventional and state-space methods of analysis and control design. Applications of modern control methods in chemical engineering. Course work includes a design project.

ENAS 627, Advanced Integrated Circuits
Neuromorphic analog integrated circuit design, fabrication processes, fundamentals of devices, circuits, and basic topologies. Analog and mixed-signal VLSI and SOC for biomedical instrumentation and bio-inspired circuits. System-level design, simulation, layout and tapeout. Examples of VLSI systems for biomedical applications: models of biological systems and circuit implementation. Biomedical sensors, SNR, and electronic circuit noise. Sensor arrays, communication and analog-digital circuit interaction and co-design. Signal conversion, conditioning, compression, and reconstruction.

ENAS 628, Sensors and Biosensors
This course provides students with the knowledge of basic integrated analog blocks and how to combine these circuits into sensory systems for biomedical applications. Target areas are in physiology, brain-machine interfaces, neural recording and stimulation, imaging and bioimaging. Lecture includes details on operation amplifiers, voltage amplifiers, current mode circuits, analog-to-digital converters, photo-transduction circuits, layout, simulation, and design of VLSI circuits and systems.

ENAS 639, Management of Water Resources and Environmental Systems.
The general purpose of the course is to allow the participants to have an integrative view and to consider broad aspects of analyzing problems related to water resources and environmental issues. The integrative approach is based on management modeling, considering simultaneously engineering aspects, water quality, environmental characteristics, economic aspects, and community welfare facets. The purpose is to incorporate all effective factors into a quantitative optimal situation, allowing all participating partners in the analyzed enterprise to gain their share and satisfaction. The presented approach is a decision-supporting tool toward reaching an optimal situation, subject to a series of given limitations.

ENAS 640/F&ES 60109, Aquatic Chemistry
A detailed examination of the principles governing chemical reactions in water. Emphasis is on developing the ability to predict the aqueous chemistry of natural and perturbed systems based on a knowledge of their biogeochemical setting. Focus is on inorganic chemistry, and topics include elementary thermodynamics, acid-base equilibria, alkalinity, speciation, solubility, mineral stability, redox chemistry, and surface complexation reactions. Illustrative examples are taken from the aquatic chemistry of estuaries, lakes, rivers, wetlands, soils, aquifers, and the atmosphere. A standard software package used to predict chemical equilibria may also be presented.

ENAS 641, Biological Processes in Environmental Engineering
Fundamental aspects of microbiology and biochemistry, including stoichiometry, kinetics, and energetics of biochemical reactions, microbial growth, and microbial ecology, as they pertain to biological processes for the transformation of environmental contaminants; principles for analysis and design of aerobic and anaerobic processes including suspended- and attached-growth systems, for treatment of conventional and hazardous pollutants in municipal and industrial wastewaters and in groundwater.

ENAS 642, Environmental Physicochemical Processes
Fundamental and applied concepts of physical and chemical (“physicochemical”) processes relevant to water quality control. Topics include chemical reaction engineering, overview of water and wastewater treatment plants, colloid chemistry for solid-liquid separation processes, physical and chemical aspects of coagulation, coagulation in natural waters, filtration in engineered and natural systems, adsorption, membrane processes, disinfection and oxidation, disinfection by-products.

ENAS 643, Transport and Fate of Organic Chemicals in the Environment
Fundamental chemical and physical processes controlling the distribution, transport, and transformation of anthropogenic organic chemicals in aqueous environments including soils, sediments, and groundwater. It provides basic knowledge about the following: (a) the use of chemical and physical principles to quantify the thermodynamics and kinetics of individual processes, (b) the use of chemical structure to understand these processes at the molecular level, and (c) a framework for evaluating the relative importance of these processes so that the fate of a particular chemical in a particular environment may be predicted.

ENAS 644, Environmental Organic Chemistry
Because equilibrium is rarely achieved in environmental systems, a fundamental understanding of the kinetics of environmentally relevant chemical reactions is necessary for the prediction of the fate of contaminants in the environment. After a brief review of chemical speciation and linear free-energy relationships that govern the equilibrium behavior of chemicals in the environment, the course covers the theory underlying the use of similar free-energy relationships for the prediction of chemical reaction rates. The course then discusses the following environmentally relevant reactions: complexations, substitutions (e.g., hydrolysis), natural oxidation reductions, biotransformations, engineered oxidation reductions, photochemical reactions, and a brief introduction to surface reactions.

ENAS 645/F&ES 96007, Industrial Ecology
Industrial ecology is an organizing concept that is increasingly applied to define various interactions of today’s technological society with both natural and altered environments. Technology and its potential for modification and change are central to this topic, as are implications for government policy and corporate response. The course discusses how industrial ecology is being applied in corporations to minimize the environmental impacts of products, processes, and services, and shows how industrial ecology serves as a technological framework for science, policy, and management in government and society.

ENAS 646/F&ES 61021, Hydrology and Water Resources
An introduction to the essential elements of hydrogeologic processes. Course topics include groundwater flow, occurrence and movement of water in the vadose zone, streamflow generation, groundwater contamination, and transport of chemicals in groundwater. Computer software packages are used to reinforce concepts presented in class. A modest background in general physics and calculus is required.

ENAS 647, Hydrologic Modeling
Application of computer models to solve problems related to water movement and chemical migration in subsurface environments. Unsaturated and saturated flow phenomena are considered, and the role of geochemical and microbiological processes in chemical fate and transport are examined.

ENAS 648, Environmental Transport Processes
Analysis of transport phenomena governing the fate of chemical and biological contaminants in environmental systems. Emphasis on quantifying contaminant transport rates and distributions in natural and engineered environments. Topics include distribution of chemicals between phases; diffusive and convective transport; interfacial mass transfer; contaminant transport in groundwater, lakes, and rivers; analysis of transport phenomena involving particulate and microbial contaminants.

ENAS 649/MGT 611, Policy Modeling
Building on earlier course work in quantitative analysis and statistics, Policy Modeling provides an operational framework for exploring the costs and benefits of public policy decisions. The techniques employed include “back of the envelope” probabilistic models, Markov processes, queuing theory, and linear/integer programming. With an eye toward making better decisions, these techniques are applied to a number of important policy problems. In addition to lectures, assigned articles and text readings, and short problem sets, students are responsible for completing a take-home midterm exam and a number of cases. In some instances, it is possible to take a real problem from formulation to solution, and compare the student’s own analysis to what actually happened. Prerequisites: Decision Analysis and Game Theory, Data Analysis and Statistics, or a demonstrated proficiency in quantitative methods.

ENAS 650, Instrumentation and Product Design
Survey of broadly applicable design methods with initial emphasis on analog electronics: review of op amps and other integrated circuits and their specifications, data conversion fundamentals, the use of simulation and an online engineering database, exposure to such broader issues as user-interface design, user participation in design, and the transforming role of products at work and in the home.

ENAS 658, MEMS Design
Topics to include material properties, microfabrication technologies, structural behavior, sensing techniques, actuation schemes, fluid behavior, simple electronic circuits, and feedback systems. Student teams design a complete microsystem in line with their interests to meet a set of specifications based on realistic microfabrication processes. Modeling and simulation in the design process are emphasized.  

ENAS 704,Theoretical Fluid Dynamics
Derivation of the equations of fluid motion from basic principles. Potential theory, viscous flow, flow with vorticity. Topics in hydrodynamics, gas dynamics, stability, and turbulence.

ENAS 705, Numerical Simulations of Liquids
Review of equilibrium Molecular Dynamics and Monte Carlo simulation methods in various thermodynamic ensembles. Introduction to non-equilibrium molecular dynamics techniques especially to study shear flow and heat transport in liquids. The application of novel nonequilibrium Molecular Dynamics and Monte Carlo methods to the study of supercooled liquids and glasses and sheared granular materials and foams. 

ENAS 708, Fundamentals of Combustion
Review of relevant aspects of chemical thermodynamics and chemical kinetics. Explosion and oxidation of fuels. Laminar premixed fuels. Detonations. Diffusion flame and droplet burning.

ENAS 718, Heterojunction Devices
Survey of the physics, technology, and fabrication of semiconductor heterojunction materials and devices. Topics include contemporary compound semiconductor material properties and epitaxial growth techniques; high-speed analog and digital devices; microwave and millimeter wave devices for radar and wireless communications; the physics and device properties of quantum wells and superlattices; HEMTs and modulation-doped structures; resonant tunneling physics and devices; and device modeling using computer simulation tools. Lab includes fabrication of GAAs FETs and HBTs; fabrication and measurement of quantum Hall effect standards; LEDs; and resonant tunneling devices.

ENAS 747, Applied Numerical Methods I
A variety of numerical methods applied to problems in engineering and applied science. Topics include root-finding methods, numerical solution of systems of linear and nonlinear equations, eigenvalue/eigenvector approximation, polynomial-based interpolation, and numerical integration.

ENAS 748, Applied Numerical Methods II
An introduction to numerical methods for solution of ordinary and partial differential equations, both linear and nonlinear. One-step, multistep, and Runge-Kutta methods for initial value problems. Finite difference methods for the solution of parabolic, elliptic, and hyperbolic partial differential equations.

ENAS 750, Mechanics of Deformable Solids
Unified presentation of the equilibrium behavior of structural and machine elements, including the solution of a variety of representative engineering problems. Tensorial description of stress and strain. Elementary introduction to elastic, plastic, and viscoelastic behavior of solids. Failure theories. Two-dimensional boundary value problems in elasticity. Energy methods in solid mechanics. Stability problems.

ENAS 761/G&G 525, Introduction to Continuum Mechanics
Introduction to the physics of continuous media, with applications to physical, natural, and biological sciences and engineering. Topics include tensor analysis; analysis of stress, motion, and strain; conservation of mass, momentum, and energy; rheology; examples in fluid dynamics, elasticity theory, and other topics at the discretion of instructor.

ENAS 785, Microstructural Development of Materials
An advanced course in the development of microstructure in a material. Topics include the nature of solids; thermodynamics of solids; atomic diffusion; solidification; the structure of internal interfaces; and diffusive and nondiffusive phase transformations.

ENAS 787, Intermolecular and Surface Forces
Modern materials science often exploits that atoms located at surfaces or in thin layers behave differently from bulk atoms to achieve new or greatly altered material properties. This course provides an in-depth discussion of intermolecular and surface forces, which determine the mechanical and chemical properties of surfaces. In a first part, we will discuss the fundamental principles and concepts of forces between atoms and molecules. Part two will generalize these concepts to surface forces. Part three will then give a variety of examples. The course will be of interest to students studying thin film growth, surface coatings, mechanical and chemical properties of surfaces, soft matter including biomembranes, and colloidal suspensions.

ENAS 802, Nano and Microsystem Technology
Cross-disciplinary laboratory experiments covering microfabrication, silicon micromachining, MEMS device fabrication and characterization, scanned probe microscopy, electron microscopy, microfluidics, lab-on-a-chip system. Students will fabricate MEMS, BioMEMS and microfluidic devices in a cleanroom environment.

ENAS 806, Photovoltaic Energy
Survey of photovoltaic energy devices, systems, and applications, including review of optical and electrical properties of semiconductors. Topics include solar radiation, solar cell design, performance analysis, solar cell materials, device processing, photovoltaic systems and economic analysis.

ENAS 810, Nonlinear Optics
Fundamental aspects of laser interaction with matter, including both linear and nonlinear optical responses. This course introduces and analyzes actual electro-optical and magneto-optical devices (such as harmonic doublers, parametric oscillators, modulators, and isolators).

ENAS 811, Stem Cells and Approaches to Repair in the Nervous System
A seminar in the isolation, differentiation, and therapeutic potential of neural stem cells. The seminar begins by focusing on the isolation of neural stem cells using a variety of techniques including FACS sorting, preferential passaging, and cloning. It then covers the development of techniques to control the differentiation of NSCs as well as identify their potential using gene and drug delivery approaches as well as novel high throughput assays. Comparisons are made between the in vitro and in vivo data across stem cell lines and models. The ultimate therapeutic potential of NSCs is then addressed and current results along these lines are compared with other stem cell populations as well as fetal tissue. Weekly readings are drawn from the current literature and are used to guide discussion. Experts in the field are also invited to lead sessions.

ENAS 812/NSCI 612, Molecular Transport and Intervention in the Brain
This course is a graduate-level seminar on mechanisms and rates of movement of molecules in the brain and the design of novel drug delivery systems. Topics include mathematical methods for modeling diffusion and flow processes, diffusion in the brain interstitium, fluid flows in the brain and spinal cord, the blood-brain barrier, microdialysis measurements, controlled release systems, microfluidic approaches for drug delivery. Weekly readings are assigned from neuroscience and engineering texts; current papers from the literature are used to guide discussion each week.

ENAS 816, Techniques of Microwave Measurements and RF Design
An advanced course covering the concepts and techniques of radio-frequency design, and their application in making microwave measurements. The course begins with a review of lumped element and transmission line circuits, network analysis, and design of passive elements, including filters and impedance transformers. We continue with a treatment of passive and active components such as couplers, circulators, amplifiers, and modulators. Finally, we employ this understanding for the design of microwave measurement systems, techniques for modulation and signal recovery, to analyze the performance of heterodyne/homodyne receivers and radiometers.

ENAS 817/PHYS 677, Noise, Dissipation, Amplification, and Information
Graduate-level equilibrium and non-equilibrium statistical physics applied to quantum electronics/optics phenomena. The aim is to explain the fundamental link between the random fluctuations of a physical system in equilibrium and the response of the same system to an external perturbation. Several key examples in which noise appears as a resource rather than a limitation are treated: spin relaxation in nuclear magnetic resonance (motional narrowing), Johnson-Nyquist noise in solid state transport physics (noise thermometry), photon correlation measurements in quantum optics (Hanbury Brown-Twiss experiment), and so on. The course explores both passive and active systems. It discusses in particular the ultimate limits of amplifier sensitivity and speed in physics measurements.

ENAS 818/PHYS 634, Mesoscopic Physics
Introduction to the physics of nanoscale solid-state systems that are large and disordered enough to be described in terms of simple macroscopic parameters like resistance, capacitance, and inductance, but small and cold enough that effects usually associated with microscopic particles, like quantum-mechanical coherence and/or charge quantization, dominate. Emphasis is placed on transport and noise phenomena in the normal and superconducting regimes.

ENAS 821, Physics of Medical Imaging
The physics of image formation with special emphasis on techniques with medical applications. Concepts that are common to different types of imaging are emphasized, along with an understanding of how information is limited by the basic physical phenomena involved. Mathematical concepts of image analysis, the formation of images by ionizing radiation, ultrasound, NMR, and other energy forms, and methods of evaluating image quality.

ENAS 825, Physics of Magnetic Resonance Spectroscopy in Vivo
The physics of chemical measurements performed with nuclear magnetic resonance spectroscopy, with special emphasis on applications to measurements studies in living tissue. Concepts that are common to magnetic resonance imaging are introduced. Topics include safety, equipment design, techniques of spectroscopic data analysis, and metabolic modeling of dynamic spectroscopic measurements.

ENAS 836, Biophotonics and Optical Microscopy
A review of linear and nonlinear optical microscopies and other biophotonics applications. Topics include wide-field techniques, linear and nonlinear laser scanning microscopy, fundamentals of geometrical and physical optics, optical image formation, laser physics, single molecule techniques, fluorescence correlation spectroscopy, and light scattering. Discussion of fluorescence and the underlying physics of light-matter interactions that provide biologically relevant signals.

ENAS 849, Statistical Physics II
An advanced course in statistical mechanics. Topics to be covered include a statistical formulation of thermodynamics, review of the canonical and grand canonical ensembles, theories for simple gases, treatment of interacting systems using cluster expansions, review of phase transitions and critical phenomena, introduction to the renormalization group, and discussion of the approach to equilibrium and the fluctuation-dissipation theorem.

ENAS 850 and 851/PHYS 548 and 549, Solid State Physics I and II
A two-term sequence covering the principles underlying the electrical, thermal, magnetic, and optical properties of solids, including crystal structures, phonon, energy bands, semiconductors, Fermi surfaces, magnetic resonance, phase transitions, and superconductivity.

ENAS 852/PHYS 610, Quantum Many-Body Theory
Second quantization, quantum statistical mechanics, Hartree-Fock approximation, linear response theory, random phase approximation, perturbation theory and Feynman diagrams, Landau theory of Fermi liquids, BCS theory, Hartree-Fock-Bogoliubov method. Applications to solids and finite-size systems such as quantum dots, nuclei, and nanoparticles.

ENAS 853/PHYS 691, Atom-Photon Interactions
This atomic physics introductory graduate course aims at providing the students with the basic notions of matter-light interactions, including both theoretical understandings and major applications. This course will be useful to those directly involved in atomic and molecular physics research projects, as well as those investigating the physics of quantum mesoscopic systems with few degrees of freedom in contact with a radiation bath.

ENAS 856, Theory of Solids I
Theoretical techniques for the study of the structural and electronic properties of solids, with applications. Topics include bandstructure, phonons, defects, transport, magnetism and superconductivity.

ENAS 857, Theory of Solids II
Theoretical techniques for the study of the structural and electronic properties of solids, with applications. Topics include bandstructure, phonons, defects, transport, magnetism and superconductivity.

ENAS 859/PHYS 675/APHY 458, Principles of Optics with Application
Introduction to the principles of optics and electromagnetic wave phenomena with applications to microscopy, optical fibers, laser spectroscopy, and nanostructure physics. Topics include propagation of light, reflection and refraction, guiding light, polarization, interference, diffraction, scattering, Fourier optics, and optical coherence. 

ENAS 860/PHYS 667, Special Topics in Condensed Matter Physics: Quantum Hall Effect and Conformal Field Theory
Aspects of the quantum Hall effect, particularly the fractional effect, and conformal field theory, plus the connections between the two. Quantum Hall states, composite particles, quasiparticles, fractional charge and statistics. Future applications to rotating trapped atoms. Conformal symmetry in two dimensions, applications to classical critical phenomena, [+] quamtum field theory. Nonabelian quantum Hall states and the relation with conformal field theory and Chern-Simons gauge theory. Background required: statistical mechanics, and either many-body theory or quantum field theory.

ENAS 863/PHYS 633, Introduction to Superconductivity
The fundamentals of superconductivity, including both theoretical understandings of basic mechanisms and description of major applications. Topics include historical overview, Ginzburg-Landau (mean field) theory, critical currents and fields of type II superconductors, BCS theory, Josephson junctions and microelectronic and quantum-bit devices, and high Tc oxide superconductors.

ENAS 864, Current Topics in Nanoelectronics, Nanomechanics, and Nanophotonics
An introduction to nanoscale science and engineering, including frontier topics in nanoelectronics, nanomechanics and nanophotonics. Discussion on quantum phenomena that become important at nanoscale dimensions, and the ultimate limit they impose on the performance of nano devices. Prerequisite: Quantum Mechanics, Semiconductor Physics.

ENAS 866, MOS Device Physics and Technology
Topics include basic MOS device physics, science and technology of thermal SiO2, interface properties of MOS structures, experimental techniques to probe MOS parameters, hot-carrier effects, radiation effects, channel mobility and carrier transport in MOS inversion layers, scaling of MOS devices, low-temperature properties of MOS devices, SOI device physics and technology, advanced gate dielectrics, MOS devices with wide-bandgap semiconductors, nonvolatile memory devices, ferroelectric memory devices, single-electron MOS transistors, and other MOS topics of current interest.

ENAS 875, Introduction to VLSI System Design
Chip design. Provides background in integrated devices, circuits, and digital subsystems needed for design and implementation of silicon logic chips. Historical context, scaling, technology projections, physical limits. CMOS fabrication overview, complementary logical circuits, design methodology, computer-aided design techniques, timing, and area estimation. Case studies of recent research and commercial chips. Objectives of the course are (1) to give students the ability to complete the course project (design of a digital CMOS subsystem chip through layout), and (2) to understand the directions that future chip technologies may take. Selected projects are fabricated and packaged for testing by students. Prerequisite: circuits at the level of introductory physics and computer programming.

ENAS 887, Dynamic Programming and Reinforcement Learning
Sequential decision-making via dynamic programming. Unified approach to optimal control of stochastic dynamic systems and Markovian decision problems. Applications in communications, control, and networking. Infinite horizon problems. Value and policy iteration. Approximations and reinforcement learning.

ENAS 902, Linear Systems
Background linear algebra; finite-dimensional, linear-continuous, and discrete dynamical systems; state equations, pulse and impulse response matrices, weighting patterns, transfer matrices. Stability, Lyapunov’s equation, controllability, observability, system reduction, minimal realizations, equivalent systems, McMillan degree, Markov matrices. Recommended for all students interested in robotics, systems, and information sciences.

ENAS 907, Computers for Cognition
Introduction to the development of computer architectures specialized for cognitive processing, including both offline “thinking machines” and embedded devices. The history of machines, from early conceptions in defense systems to contemporary initiatives. Instruction sets, memory systems, parallel processing, analog architectures, probabilistic architectures. Application and algorithm characteristics.

ENAS 912, Biomedical Image Processing and Analysis.  
A study of the basic computational principles related to processing an analysis of biomedical images (e.g., magnetic resonance, computed X-ray tomography, fluorescence microscopy). Basic concepts and techniques related to discrete image representation, multidimensional frequency transforms, image enhancement/restoration, image segmentation, and image registration.

ENAS 917, Optical Properties of Semiconductors
Comprehensive treatment of the optical and electronic properties of semiconductor alloys and quantum structures. Physical models of blackbody radiation, spontaneous emission, stimulated emission, absorption, and polarization. Quantitative analysis of the effects of temperature, pressure, stress fields, and electric and magnetic fields. 

ENAS 920, Programming for Image Analysis
Topics include using scripting languages for visualization, introduction to scripting languages, in particular Tcl, introduction to the Visualization Toolkit (Tcl) and local extensions, designing graphical user interfaces using Tk, introduction to Object Oriented programming (using [Incr Tcl]), using compiled languages to implement additional algorithms, intoduction to C++ programming, extending VTK by implementing additional image processing algorithms, an overview of the Insight Toolkit (ITK), and advanced software engineering techniques. Prerequisites: ENAS 912, or permission of the instructor.

ENAS 921, Advanced Topics in Computer Engineering
Concepts from compiler design, reconfigurable architectures, in-network computing and VLSI testing. The reading material for the course comes from research papers and other sources.  Laboratory work for the course consists of the completion of a project using simulation and programming tools. Prerequisites: Graduate student standing or permission of the instructor.

ENAS 936, Systems and Control
State-variable representation of linear time-invariant dynamical systems in both continuous and discrete time. Topics include model building, stability, controllability, observability, observers, optimal control, and an introduction to adaptive control. Students also work on individual projects throughout the term.

ENAS 944, Digital Communications Systems
An introduction to the rapidly expanding field of mobile and fixed, voice and data communications systems. A review of analog and digital signals and their time and frequency domain representations. Topics include modulation methods, including amplitude; frequency and time division multiplexing for continuous and discrete/digital signals; an overview of modern voice and data communications networks; and an overview of information theory, including entropy, the quantification of information, data rates, coding, and compression. Examples and demonstrations are drawn from radio, telephone, television, computer, cellular, and satellite communications networks.

ENAS 954/STAT 664 Information Theory
Foundations of information theory in communications, statistical inference, statistical mechanics, probability, and algorithmic complexity. Quantities of information and their properties: entropy, conditional entropy, divergence, mutual information, channel capacity. Basic theorems of data compression and coding for noisy channels. Applications in statistics, communication networks, and finance.

ENAS 960/CPSC 536, Networked Embedded Systems and Sensor Networks  
Introduction to the fundamental concepts of networked embedded systems and wireless sensor networks, presenting a cross-disciplinary approach to the design and implementation of smart wireless embedded systems. Topics include embedded systems programming concepts, low-power and power-aware design, radio technologies, communication protocols for ubiquitous computing systems, and mathematical foundations of sensor behavior. Laboratory work includes programming assignments on low-power wireless devices.

ENAS 964, Communication Networks
Introduction to analytical approaches to the study of communication networks. Topics include delay models, buffer overflow, multiaccess communication, routing, and congestion control. Analytical techniques include basic queueing theory, queueing networks, large deviations, optimization, and distributed algorithms. Basic knowledge of probability is required.

ENAS 986, Semiconductor Silicon Devices and Technology
Introduction to integrated circuit technology, theory of solid-state devices, and principles of device design and fabrication. Laboratory involves the fabrication and analysis of semiconductor devices, including Ohmic contacts, Schottky diodes, p-n junctions, MOS capacitors, MOSFETS, and integrated circuits.

ENAS 990, Special Investigation
Faculty-supervised individual projects with emphasis on research, laboratory, or theory. Students must define the scope of the proposed project with the faculty member who has agreed to act as supervisor, and submit a brief abstract to the director of graduate studies for approval.