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 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.

- 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 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 Land-Atmosphere 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)*

- CEE 561L: Environmental Aquatic Chemistry –

## 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 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, 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 multi-physics and multi-scale problems for studying problems related to mechanics and a variety of physical and chemical processes of geomaterials.

Duke CEE has world-renowned faculty in this area. You will 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.

- 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
- 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, 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.

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 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 Input-Output Life Cycle Analysis
*–each Spring* - PUBPOL 607. Cost-Benefit 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*

#### 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*

- CEE 690: Numerical Optimization
- 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. 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)***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 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