Choose Your Path
Students in Duke CEE's doctoral (PhD) and Master of Science (MS) degree programs may choose from five engineering study tracks—each one aligned with faculty research interests:
 Computational Mechanics and Scientific Computing
 Environmental Health Engineering
 Geomechanics and Geophysics for Energy & the Environment
 Hydrology and Fluid Dynamics
 Systems, Risk and Decision
Note: Course waivers require documentation of previous knowledge and written permission of the CEE Director of Graduate Studies (DGS).
Computational Mechanics & Scientific Computing
Encompasses the development and use of computational methods for studying problems governed by the laws of mechanics. Modern computational mechanics is embodied in the broad field of computational science and engineering.
This discipline plays a fundamental role in a vast number of many important problems in science and engineering. Duke has unique facilities and worldrenowned faculty in this area.
Students of computational mechanics at Duke receive premier training in the core disciplines of applied mathematics, numerical methods, computer science, and mechanics.
 Courses

Students must take a total of at least five (5) courses from the set listed below, with at least one (1) course in each of the four principal areas:
Mathematics
 Math 531. Basic Analysis I
 Math 541. Applied Stochastic Processes
 Math 551. Applied Partial Differential Equations and Complex Variables
 Math 561. Scientific Computing I
 Math 635. Functional Analysis
 CEE 690. Mathematical Analysis of the Finite Element Method
Numerical Methods
 CEE 530. Introduction to the Finite Element Method
 CEE 531. Finite Element Methods for Problems in Fluid Mechanics
 CEE 630. Nonlinear Finite Element Method
 CEE 690. Numerical Optimization
Computer Science
 CS 201. Data Structures and Algorithms
 CS 308. Software Design
 ECE 551D. Programming, Data Structures, and Algorithms in C++
Engineering Sciences and Mechanics
 CEE 520. Continuum Mechanics
 ME 531. Thermodynamics
 ME 555. Computational Materials Science
 ME 631. Intermediate Fluid Dynamics
 ME 632. Advanced Fluid Dynamics
ENVIRONMENTAL HEALTH ENGINEERING
Duke's research in environmental health engineering addresses the consequences of society’s production and use of energy and materials, emphasizing approaches to protecting the health of human populations and predicting, monitoring and managing impacts on air, water and other global cycles.
Duke CEE faculty members work closely with Duke's Nicholas School of Environment in many research and educational efforts.
Master of Science (MS)
MS students may substitute a core area course with another course in that area and should obtain permission from the Director or Assistant Director of Master’s Studies prior to enrollment.
Doctoral (PhD)
PhD students can modify their course plan from these guidelines and should consult with their PhD exam committee chair (i.e., advisor). Note that PhD students will be tested on their proficiency in the core areas during their PhD exams.
 Courses

Students should take at least a total of five (5) courses from the lists below, with at least one (1) course in the core areas of chemical principles, physical processes, and microbiological processes.
CHEMICAL PRINCIPLES CORE AREA
 CEE 561L: Environmental Aquatic Chemistry – Fall
 CEE 563: Chemical Fate of Organic Compounds – Fall
PHYSICAL PROCESSES CORE AREA
 CEE 560: Environmental Transport Phenomena – Fall
 CEE 5XX/690. Hydrology  Spring
MICROBIOLOGICAL PRINCIPLES CORE AREA
 CEE 566: Environmental Microbiology – Fall
 CEE 562L: Biological Processes in Environmental Engineering – Spring
ADDITIONAL ELECTIVES
 CEE 501: Applied Mathematics for Engineers – Occasional
 CEE 502: Engineering Data Analysis – Occasional
 CEE 530: Finite Elements Methods
 CEE 564: Physical and Chemical Treatment Processes in Environmental Engineering – Spring
 CEE 565: Environmental Analytical Chemistry – alt. Spring
 CEE 574: Remote Sensing – odd Fall semesters
 CEE 575/690: Air Pollution Engineering – Fall
 CEE 581: Numerical Methods in Environmental Transport  Spring
 CEE 627: Linear Systems Theory – each Fall Semester
 CEE 643: Engineering and Environmental Geophysics – Fall/Spring
 CEE 661L: Environmental Molecular Biotechnology – Spring
 CEE 666: Aquatic Geochemistry – Spring
 CEE 667: Chemical Transformations of Environmental Contaminants – alt. Spring
 CEE 683: Groundwater and Vadose Zone Hydrology – alt. Fall
 CEE 684: Hydrometeorology and LandAtmosphere Interactions – even Fall
 CEE 686: Ecohydrology – occasional
 CEE 690: Introduction to Turbulence – Fall
 CEE 690: Numerical Optimization – odd Spring Semesters
 CEE 690: Modeling of Environ., Chem., and Biol. Processes – Fall
 CEE 690. Risk and Resilience in Engineering – odd Fall & odd Spring
 CEE 690: Data Science and Machine Learning in Applied Science and Engineering – Fall
 CEE 690: Introduction to Deep Learning – Fall
 CEE 690: Environmental Cheminformatics – alt. Fall
 ENVIRON 501: Environmental Toxicology – Fall
 ENVIRON 710: Applied Data Analysis in Environmental Sciences – Fall (limited enrollment)
 CEE 761: Environmental Spatial Data Analysis  Fall
 EOS 520: Introduction to Fluid Dynamics – Fall
 BIOL 665: Bayesian Inference for Environmental Models – Spring
 ME 631(226): Intermediate Fluid Mechanics  Fall
 ME 632(227): Advanced Fluid Mechanics  Spring
 PHARM 733: Experimental Design and Biostatistics for Basic Biomedical Scientists – Fall & Spring (limited enrollment)
Geomechanics and Geophysics for energy & environment
The Geomechanics and Geophysics for Energy & the Environment (GGEE) study track mirrors modern developments in geomechanics and geophysics, which address applications to new technologies in contemporary energy, global health issues related to the geoenvironment and environmental protection industry: conventional and unconventional fossil fuel exploration and exploitation, including shale gas and oil, nuclear, industrial and municipal waste disposal, CO_{2} sequestration, geothermal energy production, storage, procurement of clean water in arid areas, to mention only a few.
The core area of interest encompasses multiphysics and multiscale problems for studying problems related to mechanics and a variety of physical and chemical processes of geomaterials.
Duke CEE has worldrenowned faculty in this area. You will receive premier training in the core disciplines of applied mechanics of geomaterials and noninvasive geophysical methods in characterizing geomaterials for engineering and environmental purposes and involves laboratory and field testing.
 Courses

Students must take a total of at least five (5) courses from the lists below, with at least one (1) course in each of four principal areas.
Mathematics
 Math 551. Applied Partial Differential Equations and Complex Variables
 Math 557. Introduction to Partial Differential Equations
 Math 561. Scientific Computing I
 Math 577. Mathematical Modeling
Numerical Methods
 CEE 530. Introduction to the Finite Element Method
 CEE 630. Nonlinear Finite Element Method
 CEE 635. Computational Methods for Evolving Discontinuities and Interfaces
Geomechanics and Geophysics
 CEE 525. Wave Propagation in Elastic and Poroelastic Media
 CEE 560. Environmental Transport Phenomena
 CEE 621. Plasticity
 CEE 642. Environmental Geomechanics
 CEE 686. Ecohydrology
Engineering Sciences and Mechanics
 CEE 520. Continuum Mechanics
 CEE 541. Structural Dynamics
 ME 531. Thermodynamics
 ME 631. Intermediate Fluid Mechanics
 ME 632. Advanced Fluid Mechanics
HYDROLOGY AND FLUID DYNAMICS
Offers students tremendous flexibility in crafting a graduate program that suits individual interests. Research focuses on some of the most modern open problems in environmental fluid dynamics, hydrology and water resources. Ongoing research topics include hydrometeorology (rainfall dynamics, landatmosphere interaction, remote sensing), ecohydrology (impact of hydroclimatic variability on ecosystems and feedbacks on the hydrologic cycle and local climate), contaminant transport hydrology (surfacesubsurface interactions), water cycle dynamics and human health, and stochastic hydrology.
In addition to courses offered within the Pratt School of Engineering, students may take courses from Duke's professional schools and institutes including the Nicholas School for the Environment and Earth Sciences, the Nicholas Institute for Environmental Policy Solutions, and the Sanford Institute of Public Policy.
Course and research opportunities include two tracks of study encompassing water resource engineering, hydrology, environmental fluid dynamics, and chemical and biological aspects of pollution of water, atmosphere, and soil, among others.
 Courses

PhD Students must take a total of at least six (6) courses from the lists below, with at least one (1) CEE course in each of five principal areas (except for Applied Math/Statistics).
Applied Math/Statistics
 CEE 501: Applied Mathematics for Engineers
 STA 601(L): Bayesian and Modern Statistics
 STA 611: Introduction to Statistical Methods – Fall
 MATH 551: Applied Differential Equations and Complex variables
 MATH 561: Scientific Computing  Fall
 MATH 577: Mathematical Modeling – alt. Fall
 MATH 660: Introduction to Numerical PDES
 ENVIRON 764: Applied Differential Equations in Environmental Science
Data Science
 CEE 502: Engineering Data Analysis
 CEE 690: Data Science and Machine Learning in Applied Science and Engineering – Fall
 CEE 690: Uncertainty Quantification
 CEE 690: Environmental Spatial Data Analysis – Fall
 CEE 675: Introduction to the Physical Principles of Remote Sensing of the Environment – odd Fall
Environmental Fluid Dynamics
 CEE 690: Environmental Fluid Mechanics and Sediment Transport  Spring
 ME 631: Intermediate Fluid Mechanics  Fall
 ME 632: Advanced Fluid Mechanics  Spring
 CEE 690: Introduction to Turbulence – even Fall
 CEE 690: Advanced Turbulence – odd Fall
Hydrology
 CEE 684: Physical Hydrology and Hydrometeorology – even Fall
 CEE 690: Hydrology  Spring
 CEE 683: Groundwater Hydrology and Vadose Zone Hydrology
 EOS 511: The Climate System
Contaminant Transport Hydrology
 CEE 531: Finite Elements for Fluids
 CEE560: Environmental Transport Phenomena  Fall
 CEE 581: Numerical Methods in Env Transport – Spring
 CEE 683: Groundwater and Vadose Zone Hydrology – even Fall
Systems, Risk and Decision
Emphasizes a systems approach, the use of statistical decision theory, and the leveraging of large data sets to assess the potential for extreme events and their consequences.
The curriculum provides students with specialized training in risk assessment, the analysis of hazard mitigation technologies, and the design of resilient systems while deepening a student's expertise in one or more engineering disciplines.
The track includes courses in mathematical modeling, optimization, risk assessment, and decision theory, as well as courses that more explicitly integrate methods and applications.
 Courses

Students must take a total of at least five (5) courses from the set listed below, with at least one (1) course in each of the first three areas and two (2) courses in any one area of application.
Mathematical Modeling and Optimization
 CEE 627: Linear Systems Theory – each Fall Semester
 CEE 629: System Identification
 CEE 690: Numerical Optimization –odd Spring Semesters
 CEE 690: Modeling of Environ., Chem., and Biol. Processes –alt. Falls
 MATH 551: Applied Partial Differential Equations –each Fall
 MATH 555. Ordinary Differential Equations –each Fall
 MATH 561. Numerical Lin. Algebra, Opt. and Monte Carlo Simul. –each Fall
Uncertainty Quantification and Statistical Modeling
 CEE 644. Inverse Problems in Geosciences and Engineering –alt. years
 CEE 690. Risk and Resilience in Engineering –odd Fall & odd Spring
 CEE 690. Uncertainty Quantification –alt. years
 ECE 555. Probability for Electrical and Computer Engineers –each Fall
 STA 502. Bayesian Inference & Decision –Fall & Spring
 STA 561D. Probabilistic Machine Learning –Fall & Spring
 BIOL 665: Bayesian Inference for Environmental Models –each Spring
Valuation, Assessment, and Decision Making
 ECON 620. Game Theory with Applications –Fall or Spring
 ENVIRON 520/521. Resource and Environmental Economics –each Fall
 ENVIRON 590. Economic InputOutput Life Cycle Analysis –each Spring
 PUBPOL 607. CostBenefit Analysis for Health and Environ. Policy –each Spring
Application Area: Water and Environment
 CEE 560: Environmental Transport Phenomena –each Fall
 CEE 561: Environmental Aquatic Chemistry –each Fall
 CEE 683: Groundwater Hydrology and Contaminant Transport –even Falls
 CEE 686: Ecohydrology –odd Falls
 CEE 684: Physical Hydrology and Hydrometeorology –odd Falls
Application Area: Environmental Engineering
 CEE 562. Biological Processes in Environmental Engineering –each Spring
 CEE 563: Fate and Behavior of Organic Contaminants – each Fall
 CEE 564: Physical Chemical Processes in Environ. Engineering – each Spring
 CEE 581: Pollutant Transport Systems – occasional
 CEE 566: Environmental Microbiology – each Fall
Application Area: Materials and Structures
 CEE 525. Wave Propagation in Elastic and Poroelastic Media – odd Springs
 CEE 520. Continuum Mechanics – even Falls
 CEE 530. Finite Element Analysis – each Fall
 CEE 541. Structural Dynamics – even Falls
Application Area: Energy Systems
 ENVIRON 711 Energy and the Environment – each Fall
 ENERGY 630: Transportation and Energy – each Fall
 ENERGY 631: Energy Technology and Impact on the Environment – each Spring
 ENERGY 716: Modeling for Energy Systems – each Fall
 ENERGY 729. The WaterEnergy Nexus – alt. Springs
 Sample Course Sequences

Program Requirement Designations
 MMO = Mathematical Modelling and Optimization
 UQS = Uncertainty Quantification and Statistical Modeling
 VAD = Valuation, Assessment, and Decision Making
 AA = Application Area
 ELE = Elective
Water and Environment
Fall 1
Spring 1
Fall 2
Spring 2
CEE 690: Modeling of Environ., Chem., and Biol. Processes (MMO)
CEE 644. Inverse Problems in Geosciences & Engineer’g (UQS)
CEE 684: Physical Hydrology and Hydrometeorology (AA)
Elective
ECON 530. Resource & Environmental Economics (VAD)
Elective (e.g., LAW 320: Water Resources Law)
CEE 683: Groundwater Hydrology & Contaminant Transport (AA)
Elective
Elective (e.g., CEE 675: Remote Sensing of the Environment)
Elective (e.g., CEE 686: Ecohydrology)
Elective
Elective
Environmental Engineering
First Fall
First Spring
Second Fall
Second Spring
CEE 561: Environmental Aquatic Chemistry (AA)
CEE 690. Numerical Optimization (MMO)
CEE 560: Environmental Transport Phenomena (AA)
Elective
CEE 690: Risk and Resilience in Engineering (UQS)
PUBPOL 607. CostBenefit Analysis for Health & Environ. Policy (VAD)
Elective (e.g., CEE 563 Fate and Behavior or Organic Contaminants)
Elective
Elective (e.g., CEE 564: Physical Chemical Processes in Environ. Eng.)
Elective (e.g., CEE 566: Environmental Microbiology)
Elective (e.g., CEE 571: Control of Hazardous and Toxic Waste)
Elective
Materials and Structures
First Fall
First Spring
Second Fall
Second Spring
CEE 530. Finite Element Analysis (AA) or
CEE 520. Continuum Mechanics (AA)
PUBPOL 607. CostBenefit Analysis for Health and Environ. Policy (VAD)
CEE 541. Structural Dynamics (AA)
Elective
MATH 551: Applied Partial Differential Equations (MMO)
Elective (e.g., ME 742. Nonlinear Mechanical Vibration)
CEE 690. Risk and Resilience in Engineering (UQS)
Elective
Elective (e.g., ME 527. Buckling of Engineering Structures)
Elective
Elective (e.g., Math 541. Applied Stochastic Processes)
Elective
Energy Systems
First Fall
First Spring
Second Fall
Second Spring
CEE 690. Risk and Resilience in Engineering (UQS)
CEE 690. Numerical Optimization (MMO)
Elective (e.g., ECON 527. Regulation and Deregulation in Public Utilities)
Elective
ENERGY 716: Modeling for Energy Systems (AA)
ENVIRON 590. Economic InputOutput Life Cycle Analysis (VAD)
Elective (e.g., ENVIRON 717: Markets for Electric Power)
Elective
Elective (e.g., ENERGY 729. The WaterEnergy Nexus)
ENERGY 631: Energy Technology and Impact on the Environment (AA)
Elective
Elective
 Additional Relevant Courses at Duke

 CEE 629: System Identification
 CEE 571: Control of Hazardous and Toxic Waste
 COMPSCI 571: Machine Learning
 COMPSCI 579: Statistical Data Mining
 DECISION 614. Forecasting
 DECISION 611. Decision Models
 ECON 527. Regulation and Deregulation in Public Utilities
 ECON 753. Natural Resource Economics
 ECE 581: Random Signals and Noise
 ECE 585: Signal Detection and Extraction Theory
 ENRGYENV 625. Energy, Markets & Innovation
 ENVIRON 531: Economic Valuation of the Environment
 ENVIRON 539. Human Health & Ecological Risk Assessment
 ENVIRON 640: Climate Change Economic
 ENVIRON 717: Markets for Electric Power
 LAW 590: Risk Regulation
 MATH 541: Applied Stochastic Processes
 MATH 577: Mathematical Modeling
 PUBPOL 504: Counterterrorism Law and Policy
 PUBPOL 505S: National Security Decision Making
 PUBPOL 580S: Water Cooperation and Conflict
 PUBPOL 582: Global Environmental Health: Economics and Policy
 PUBPOL 583S: Energy and U.S. National Security
 PUBPOL 585: Climate Change Economics and Policy
 STA 601: Bayesian and Modern Statistics
 STA 611: Introduction to Modern Statistics
 STA 623: Statistical Decision Theory