Graduate Study Tracks

Choose Your Path — 5 Study Tracks

Students in our doctoral (PhD) and Master of Science (MS) programs may choose from five engineering study tracks.

Tracks are designed to be both preparation for the needs of their specific research and also as a foundation for their further professional growth in the years to come. The combination of departmental courses and track-specific core courses will greatly enhance that growth.

Students must satisfy the course requirements for their chosen study track, listed below, in addition to the other requirements for the Master of Science(MS) or doctoral (PhD) degree. A course waiver may be granted – documentation of previous knowledge and written permission of the Director of Graduate Studies (DGS) are required.

Each study track encompasses a core set of courses which parallel research interests of our faculty:

Computational Mechanics and Scientific Computing

Computational mechanics 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 University has unique facilities and world-renowned 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.

  • 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:

Courses

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 Structues, 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

 

Engineering Environmental Geomechanics and Geophysics

The Engineering and Environmental Geomechanics and Geophysics (EEGG) focus mirrors modern developments in Geomechanics and Geophysics, which address applications to new technologies in contemporary energy, global health issues related to the geo-environment and environmental protection industry: conventional and unconventional fossil fuel exploration and exploitation, including shale gas and oil, nuclear, industrial and municipal waste disposal, CO2 sequestration, geothermal energy production, storage, procurement of clean water in arid areas, to mention only a few.

The core area of interest encompasses multi-physics and multi-scale problems for studying problems related to mechanics and a variety of physical and chemical processes of geomaterials.

The Pratt School of Engineering has world-renowned faculty in this area and offers possibilities for intense international collaboration and engagement. Students of EEGG at Duke receive premier training in the core disciplines of applied mechanics of geo-materials and non-invasive geophysical methods in characterizing geomaterials for engineering and environmental purposes and involves laboratory and field testing.

  • 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.

Courses

Mathematics

  • Math 551. Applied Partial Differential Equations and Complex Variables
  • Math 557. Introduction to Partial Differential Equations
  • Math 561. 
 Scientific Computing I
  • Math 557. 
 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

 

Systems, Risk and Decision

The study track in Systems, Risk, and Decisions 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.

  • 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.

Courses

Mathematical Modelling and Optimization

  • CEE 627: Linear Systems Theory – each Fall Semester
  • 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 –each Fall
  • 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

  • ENVIRON 590. Economic Input-Output Life Cycle Analysis each Spring
  • PUBPOL 607. Cost-Benefit Analysis for Health and Environ. Policy each Spring
  • ECON 530. Resource & Environmental Economics each Fall
  • ECON 620. Game Theory with Applications Fall or 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 Water-Energy 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

First Fall

First Spring

Second Fall

Second Spring

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. Cost-Benefit 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. Cost-Benefit 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 Input-Output Life Cycle Analysis (VAD)

Elective (e.g., ENVIRON 717: Markets for Electric Power)

Elective

Elective (e.g., ENERGY 729. The Water-Energy 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

 

Hydrology and Fluid Dynamics

Graduate study in environmental engineering is highly interdisciplinary and 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, land-atmosphere interaction, remote sensing), eco-hydrology (impact of hydroclimatic variability on ecosystems and feedbacks on the hydrologic cycle and local climate), contaminant transport hydrology (surface-subsurface 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.

Within the MS/PhD course and research opportunities offered for Duke graduate environmental engineering students, there are two tracks of study encompassing water resource engineering, hydrology, environmental fluid dynamics, and chemical and biological aspects of pollution ofwater, atmosphere, and soil, among others.

  • Students must take at least a total of five (5) courses from the lists below, with at least one (1) course in each of four principal areas.

Courses

Applied Math/Statistics

  • CEE 501(202): Applied Mathematics for Engineers
  • CEE 502(200): Engineering Data Analysis
  • STA 611(213): Introduction to Statistical Methods
  • MATH 561(224): Scientific Computing
  • MATH 577(229): Mathematical Modeling 

Environmental Fluid Dynamics

  • ME 631(226): Intermediate Fluid Mechanics
  • ME 632(227): Advanced Fluid Mechanics
  • CEE 690(265): Introduction to Turbulence
  • ENVIRON 856(356): Environmental Fluid Mechanics 

Hydrometeorology and Ecohydrology

  • CEE 684(224): Physical Hydrology and Hydrometeorology
  • CEE 686(220): Ecohydrology 
  • CEE 690(265): Vegetation and Hydrology
  • ENVIRON 564(282): Biogeochemistry 

Contaminant Transport Hydrology

  • CEE 581(245): Pollutant Transport Systems
  • CEE 585(260): Vadose Zone Hydrology
  • CEE 683(227): Groundwater Hydrology and Contaminant Transport

 

Environmental Process Engineering 

Graduate study in environmental engineering is highly interdisciplinary and offers students tremendous flexibility in crafting a graduate program that suits individual interests. Research focuses on phenomena that govern the origin, transport, transformation and impacts of contaminants on our environment and technologies for reducing the associated risks to human health and the environment. Research includes chemical processes that affect the fate of trace metals in the environment, transport and impacts of nanomaterials, molecular biological methods to monitor and improve performance of engineered microbial systems; biodegradation of organic contaminants, development of advanced membrane processes for water treatment and reuse, energy technologies and their impacts, and the properties, measurement and effects of ambient aerosols.

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.

Within the MS/PhD course and research opportunities offered for Duke graduate environmental engineering students, there are two tracks of study encompassing water resource engineering, hydrology, environmental fluid dynamics, and chemical and biological aspects of pollution ofwater, atmosphere, and soil, among others.

  • Students must take at least a total of five (5) courses from the lists below, with at least one (1) course in each of four principal areas
  • A course marked with an asterisk (*) is important for the Preliminary Examination

Courses

Applied Math/Statistics

  • CEE 501(202): Applied Mathematics for Engineers
  • CEE 502(200): Engineering Data Analysis
  • ENVIRON 710(210): Applied Data Analysis in Environmental Sciences
  • ENVIRON 764: Applied Differential Equations in Environmental Sciences
  • MATH 541(216): Applied Stochastic Processes
  • MATH 551(211): Applied Partial Differential Equations and Complex Variables

Transport Phenomena

  • CEE 307(207): Transport Phenomena in Biological Systems 
  • CEE 560(208): Environmental Transport Phenomena*
  • CEE 581(245): Pollutant Transport Systems 

Environmental Science

  • CEE 561(242): Aquatic Chemistry*
  • CEE 563(240): Chemical Fate of Organic Compounds
  • CEE 566(250): Environmental Microbiology*
  • CEE 569(229): Introduction to Atmospheric Particles

Environmental Design

  • CEE 562(244): Biological Processes in Environmental Engineering*
  • CEE 564(241): Physical and Chemical Treatment Processes in Environmental Engineering*
  • CEE 571(249): Control of Hazardous and Toxic Waste
  • CEE 575(247): Air Pollution*
  • CEE 576L(230L): Aerosol Measurements