Doctoral Program

Our students seek solutions to some of the world’s most complex problems, from finding ways to more efficiently produce fuels and chemicals to improving human health through better drug delivery and new biomaterials. 

Ph.D. students typically take about eight courses in their first two years and also become involved as teaching assistants during their second and third years in the program. All of our graduate students are supported financially as they work toward their Ph.D. degree.

Program Requirements

Our Ph.D. students must complete the required coursework, write a thesis, and perform satisfactorily on their examinations to earn their doctorate in chemical engineering. We do not admit students into the program with the intention of earning a terminal master’s degree; however, students who have met the requirements may obtain a master’s degree as a milestone on the path to completing their Ph.D. degree. Students typically graduate within five years.

If you are interested in pursuing a terminal master’s degree, please see to learn about the Master of Engineering in Chemical Engineering Leadership program requirements. This master’s degree is not a prerequisite to earning a Ph.D. degree.

Course Work

Course work for our Ph.D. students includes a minimum of four 500-level courses in chemical engineering and a minimum of four courses (including at least one 500-level course) in one or two other departments. Students who enter the graduate program with a B.S. in a subject other than chemical engineering typically take additional courses before the qualifying exam.

Course Reference Numbers (CRNs) for CHBE 598 (Research Seminar) and CHBE 599 (Thesis Research) are available here: CHBE 598/599 CRNs

Qualifying Exam

The Ph.D. qualifying examination, taken at the beginning of the second year, comprises an oral presentation of the proposed research including a literature review and a 6- to 12-month research plan. Please note that our qualifying exam does not include a traditional written examination. 

Preliminary Exam

The preliminary examination, typically taken before the end of the third year, includes a written research proposal and oral presentation to the examination committee describing preliminary data, a detailed research plan, and a timeline for completion of the dissertation.

Final Exam

The final examination, or the dissertation defense, is a significant milestone in a graduate student’s career. This stage involves the student presenting their work to their doctoral committee and disseminating their work to the public. More information about the final exam/dissertation defense, including deadlines, thesis writing guidelines, and assembling a committee for the final defense is provided by the Graduate College Thesis Office.

Questions about the program and its requirements may be directed to our Graduate Program Office

Coursework Options

Coursework for our Ph.D. students includes a minimum of four 500-level courses in chemical engineering and a minimum of four courses (including at least one 500-level course) in one or two other departments. Below are some of the classes that our students have selected; however, the course listings may change over time. Please refer to the course catalog for current courses of instruction.

Course Catalog


Course Reference Numbers

Current students can find Course Reference Numbers (CRNs) for CHBE 598 (Research Seminar) and CHBE 599 (Thesis Research) here:

CHBE 598/599 CRNs

CHBE 521   Applied Mathematics in CHBE Development of mathematical models and a survey of modern mathematical methods currently used in the solution of chemical and biomolecular engineering problems; topics include the application of vectors and matrices, partial differential equations, numerical analysis, and methods of optimization in Chemical and Biomolecular Engineering. Prerequisite: Consent of instructor.

CHBE 522   Fluid Dynamics   Basic concepts in fluid dynamics with special emphasis on topics of interest to chemical and biomolecular engineers. Derivation of the Navier-Stokes equations; solutions for creeping flow, perfect fluids, and boundary layers; non-Newtonian fluids; turbulence. Prerequisite: Consent of instructor.

CHBE 523   Heat and Mass Transfer  Principles of transfer operations developed in terms of physical rate processes; boundary layer heat and mass transfer, phase changes, and separation processes. Prerequisite: Consent of instructor.

CHBE 525   Statistical Thermodynamics for Chemical Engineers Fundamentals and applications of both macroscopic thermodynamics and statistical mechanics. The formalism of statistical mechanics is introduced, in particular the development and calculation of partition functions, as well as its connections to thermodynamic equations of state and material properties. These concepts will be applied to problems relevant to chemical engineering, such as solution theory, electrolytes, adsorption, non-equilibrium thermodynamics, chemical reactions, molecular simulation, and dispersive interactions. 3 graduate hours. No professional credit. Prerequisite: CHBE 321. Graduate standing required.

CHBE 551   Chemical Kinetics & Catalysis   Rates and mechanisms of chemical reactions, treatment of data, steady state and unsteady behavior predictions of mechanisms, prediction of rate constants and activation barriers. Introduction to catalysis. Catalysis by solvents, metals, organometallics, acids, enzymes, semiconductors. Same as CHEM 582. Prerequisite: An undergraduate course in chemical kinetics.

CHBE 553   Surface Chemistry   Introduction to the behavior of molecules adsorbed on solid surfaces; the structure of surfaces and adsorbate layers. The bonding of molecules to surfaces; adsorbate phase transitions; trapping and sticking of molecules on surfaces. An introduction to surface reactions; kinetics of surface reactions. A review of principles of chemical reactivity; reactivity trends on surfaces; prediction of rates and mechanisms of reactions on metals, semiconductors, and insulators. Same as CHEM 586. Prerequisite: CHEM 444.

CHBE 565   CHBE Seminar   Required of all graduate students whose major is Chemical and Biomolecular Engineering. 1 graduate hour. No professional credit. Approved for S/U grading only. May be repeated. Prerequisite: CHBE 422.

CHBE 571   Bioinformatics   Same as ANSC 543MCB 571, and STAT 530. Prerequisite: MATH 225MATH 241 and MATH 461.

CHBE 572   Metabolic Systems Engineering Prerequisite: MATH 225MATH 241, and 285; or consent of instructor.

CHBE 580   Lab Techs in Bioinformatics Prerequisite: MCB 150 and MCB 151; or consent of instructor.

CHBE 593   Individual Study   Study under the supervision of a staff member in areas not covered in established course offerings. Approved for both letter and S/U grading. Prerequisite: Consent of the staff member under whom the study is to be made.

CHBE 594   Special Topics   Various advanced topics; generally taken during the second year of graduate study. Typical topics include turbulence, hydrodynamic instability, process dynamics, interfacial phenomena, reactor design, cellular bioengineering, properties of matter at high pressure, and phase transitions. May be repeated. Prerequisite: Consent of instructor.

CHBE 597   Special Problems   Individual work on problem-oriented projects not included in theses. This could be research, engineering design, or professional work in chemical and biomolecular engineering which has educational values. The work must be done under the supervision of a staff member with the approval of the department head. Research topics will vary semester to semester and instructor to instructor. 2 to 16 graduate hours. No professional credit. May be repeated.

CHBE 598   Research Seminar   Discussion of recent developments of importance to different areas of chemical and biomolecular engineering research. The course is divided into a number of sections, and subject matter differs from section to section and from time to time. Approved for S/U grading only. May be repeated. Prerequisite: Consent of instructor.

CHBE 599   Thesis Research   Candidates for the master's degree who elect research are required to write a thesis. A thesis is always required for the Doctor of Philosophy. Not all candidates for thesis work necessarily are accepted. Any student whose major is in another department must receive permission from the head of the Department of Chemical and Biomolecular Engineering to register in this course. Approved for S/U grading only.

CHEM 442: Physical Chemistry I   Lectures and problems focusing on microscopic properties. CHEM 442 and CHEM 444 constitute a year-long study of chemical principles. CHEM 442 focuses on quantum chemistry, atomic and molecular structure, spectroscopy and dynamics. 4 undergraduate hours. 4 graduate hours. Credit is not given for both CHEM 442 and PHYS 485. Prerequisite: CHEM 204 or CHEM 222MATH 225257, or 415, and a minimal knowledge of differential equations, or equivalent; and PHYS 211PHYS 212, and PHYS 214 or equivalent.

CHEM 516: Physical Inorganic Chemistry  Includes group theory and use of physical methods to provide information about the geometry, electronic structures, and reactivity of inorganic compounds in solution; emphasizes NMR and ESR. Prerequisite: CHEM 444.

CHEM 518: Special Topics in Inorganic Chemistry   Advanced course dealing with a subject not ordinarily covered by regularly scheduled courses, such as organometallic chemistry, advanced ligand field theory and molecular orbital theory of inorganic compounds, kinetics and mechanisms of inorganic reactions, etc. May be repeated. Prerequisite: CHEM 516 or consent of instructor.

CHEM 522: Experimental Spectroscopy   Principles and applications of spectroscopic measurements and instrumentation. Atomic and molecular absorption, emission, fluorescence, and scattering, emphasizing physical interpretation of experimental data. Prerequisite: General physics and chemistry equivalent to a major in physical sciences for a bachelor's degree.

CHEM 524: Electrochemical Methods
   Structure of the metal solution interface. Electrochemical and physical methods for probing metal/solution interface. Electroanalysis. Principles of electrochemical instrumentation for electroanalysis. Electrode materials. Electrochemical surface science and electrocatalysis. Prerequisite: General physics and chemistry equivalent to a major for a bachelor's degree.

CHEM 544: Statistical Thermodynamics   Fundamentals of thermodynamics and statistical mechanics, covering equilibria, thermodynamic transforms, phase transitions, ensembles and non-equilibrium statistical mechanics, from single molecules to complex biological systems. Prerequisite: CHEM 442 and CHEM 444, or equivalent.

CHEM 546   Advanced Statistical Mechanics   Fundamentals of equilibrium statistical mechanics with selected applications to interacting classical fluids: dense gases, solutions, liquids, plasmas, and ionic solutions; introduction to nonequilibrium statistical mechanics and linear response theory. Prerequisite: CHEM 540 and CHEM 544, or equivalent, or consent of instructor.


CS 400   Accelerated Fundamentals of Computing I   The first class in a sequence of two classes that introduces students to the basic concepts in computing with an emphasis on the fundamental techniques for solving computational problems. Topics include: core programming concepts (variables, data types, conditional expressions, loops, functions), basic data structures, searching and sorting algorithms, and data exploration and visualization. No prior programming experience is required. No undergraduate credit. 3 graduate hours. Prerequisite: Current enrollment in the Illinois Computing Accelerator for Non-specialists (iCAN) program or consent of instructor. Restricted to post-baccalaureate students with a non-computing background.

CS 457   Numerical Methods II   Continuation of CS 357. Orthogonalization methods for least squares, Krylov subspace methods, non-linear equations and optimization in multiple dimensions, initial and boundary value problems for ordinary and partial differential equations. 3 undergraduate hours. No graduate credit. Credit is not given for both CS 457 and CS 450. Prerequisite: CS 357.

CS 533   Parallel Computer Architecture    Theoretical aspects of parallel and pipeline computation; time and processor bounds on classes of computations; data alignment network speed and cost bounds; conflict-free access memories; overall computer system ideas. Same as CSE 522. Prerequisite: CS 433.

CS 558   Topics in Numerical Analysis   Advanced topics in numerical analysis selected from areas of current research. Same as CSE 513. May be repeated. Prerequisite: As specified for each topic offering, see Schedule or departmental course description.

ECE 455   Optical Electronics   Optical beams and cavities; semiclassical theory of gain; characteristics of typical lasers (gas, solid state, and semiconductor); application of optical devices. 3 undergraduate hours. 4 graduate hours. Prerequisite: ECE 350 or PHYS 436.

ECE 441   Physcs & Modeling Semicond Dev   Advanced concepts including generation-recombination, hot electron effects, and breakdown mechanisms; essential features of small ac characteristics, switching and transient behavior of p-n junctions, and bipolar and MOS transistors; fundamental issues for device modeling; perspective and limitations of Si-devices. 3 undergraduate hours. 3 graduate hours. Prerequisite: ECE 340.

ECE 444   IC Device Theory & Fabrication   Fabrication lab emphasizing physical theory and design of devices suitable for integrated circuitry; electrical properties of semiconductors and techniques (epitaxial growth, oxidation, photolithography diffusion, ion implantation, metallization, and characterization) for fabricating integrated circuit devices such as p-n junction diodes, bipolar transistors, and field effect transistors. 4 undergraduate hours. 4 graduate hours. Prerequisite: ECE 340.

ECE 455   Optical Electronics   Optical beams and cavities; semiclassical theory of gain; characteristics of typical lasers (gas, solid state, and semiconductor); application of optical devices. 3 undergraduate hours. 4 graduate hours. Prerequisite: ECE 350 or PHYS 436.

ECE 488   Compound Semicond & Devices   Advanced semiconductor materials and devices; elementary band theory; heterostructures; transport issues; three-terminal devices; two-terminal devices; including lasers and light modulators. 3 undergraduate hours. 3 graduate hours. Prerequisite: ECE 340 and ECE 350.

ECE 532   Compnd Semicond & Diode Lasers   Compound semiconductor materials and their optical properties. Diode lasers including quantum well heterostructure lasers, strained layer lasers, and quantum wire and quantum dot lasers. Current topics in diode laser development. Prerequisite: ECE 340 and PHYS 486. Recommended: ECE 455; credit or concurrent registration in ECE 536.

ECE 545   Advanced Physical Acoustics   Advanced topics in acoustics including physical properties of a fluid; linear propagation phenomena; nonlinear phenomena such as radiation force, streaming, and harmonic generation; cavitation; absorption and dispersion. Prerequisite: One of ECE 473ECE 520TAM 518.

MSE 455   Macromolecular Solids   Mechanical behavior of amorphous and semi-crystalline polymers; overview of polymer structure and characterization; polymer morphology; orientation effects, rubber elasticity, polymer linear viscoelasticity using Boltzmann superposition and mechanical models; measurement of viscoelastic properties; relaxation and transitions; polymeric yield phenomena and plastic flow; deformation mechanisms; fracture and craze formation; impact and fatigue. 3 undergraduate hours. 3 graduate hours. Prerequisite: MSE 206 or TAM 251.

MSE 460   Electronic Materials I   Materials science, engineering, and processing of semiconductors. Semiconductor structure and chemistry relationships to electronic and optical properties. Control of processing to achieve desired properties; design and production of novel materials. 3 undergraduate hours. 3 graduate hours. Prerequisite: ECE 340MSE 304 or PHYS 460.

MSE 481   Electron Microscopy   Theory and application of transmission electron microscopy and diffraction with emphasis on thin crystals; electron optics, interference phenomena, interpretation of images and diffraction patterns, specimen preparation. 3 undergraduate hours. 4 graduate hours. Prerequisite: MSE 405.

MSE 500   Statistical Thermodyn of Matls   Atomistic concepts of statistical thermodynamics and their relationship to classical phenomenological thermodynamics. Application of the methods of statistical thermodynamics and statistical mechanics to describe the structure, phase behavior, and properties of both hard and soft materials. Prerequisite: MSE 401.

MSE 582   Surface Physics   Theory and experiment describing atomic behavior on crystal surfaces; thermodynamics of surfaces; surface energy; diffraction and structure; gas-solid collisions; Brownian motion, diffusion, and evaporation; electron and ion emission, tunneling; Van der Waals forces; theory of chemical interactions; kinetics and statistics of adsorption. Prerequisite: MSE 501 or PHYS 560.

MSE 598   Special Topics   Subject offerings of new and developing areas of knowledge in materials science and engineering intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. May be repeated in the same or separate terms if topics vary.

MATH 446   Applied Complex Variables   For students who desire a working knowledge of complex variables; covers the standard topics and gives an introduction to integration by residues, the argument principle, conformal maps, and potential fields. Students desiring a systematic development of the foundations of the subject should take MATH 448. 3 or 4 undergraduate hours. 3 or 4 graduate hours. Credit is not given for both MATH 446 and MATH 448. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance. Prerequisite: MATH 241.

MATH 482   Linear Programming   Rigorous introduction to a wide range of topics in optimization, including a thorough treatment of basic ideas of linear programming, with additional topics drawn from numerical considerations, linear complementarity, integer programming and networks, polyhedral methods. 3 or 4 undergraduate hours. 3 or 4 graduate hours. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance. Prerequisite: ASRM 406MATH 415, or MATH 416.

MATH 484   Nonlinear Programming   Iterative and analytical solutions of constrained and unconstrained problems of optimization; gradient and conjugate gradient solution methods; Newton's method, Lagrange multipliers, duality and the Kuhn-Tucker theorem; and quadratic, convex, and geometric programming. 3 or 4 undergraduate hours. 3 or 4 graduate hours. 4 hours of credit requires approval of the instructor and department with completion of additional work of substance. Prerequisite: MATH 241MATH 347 or MATH 348; or equivalent; MATH 415 or equivalent; or consent of instructor.

MATH 489   Dynamics & Differential Eqns   Studies mathematical theory of dynamical systems, emphasizing both discrete-time dynamics and nonlinear systems of differential equations. Topics include: chaos, fractals, attractors, bifurcations, with application to areas such as population biology, fluid dynamics and classical physics. Basic knowledge of matrix theory will be assumed. 3 or 4 undergraduate hours. 3 or 4 graduate hours. 4 hours of credit requires approval of the instructor and completion of additional work of substance. Prerequisite: One of MATH 284MATH 285MATH 286MATH 441.

MATH 540   Real Analysis   Lebesgue measure on the real line; integration and differentiation of real valued functions of a real variable; and additional topics at discretion of instructor. Prerequisite: MATH 447 or equivalent.

MATH 541   Functional Analysis   Fundamental results in functional analysis; spectral theory of compact operators; further topics chosen by the instructor. Prerequisite: MATH 540.

MATH 553   Partial Differential Equations   Basic introduction to the study of partial differential equations; topics include: the Cauchy problem, power-series methods, characteristics, classification, canonical forms, well-posed problems, Riemann's method for hyperbolic equations, the Goursat problem, the wave equation, Sturm-Liouville problems and separation of variables, Fourier series, the heat equation, integral transforms, Laplace's equation, harmonic functions, potential theory, the Dirichlet and Neumann problems, and Green's functions. Prerequisite: Consent of instructor.

MATH 558   Methods of Applied Mathematics   Introduction to modern methods of applied mathematics, including nondimensionalization and scaling analysis, regular and singular asymptotics, analysis of multiscale systems, and analysis of complex systems. Each technique is illustrated with applications from science and engineering. The mathematical frameworks will include ordinary, partial and stochastic differential equations, point processes, and Markov chains. Prerequisite: Undergraduate background in ODEs, PDEs, and probability theory (MATH 441MATH 442, and MATH 461, or equivalents), or consent of instructor.

MCB 421   Microbial Genetics   Prokaryotic microbial genetic systems; emphasis on typical data analyses, together with the basic classes of genetic phenomena. 3 undergraduate hours. 3 graduate hours. Prerequisite: MCB 300 or consent of instructor.

MCB 424   Microbial Biochemistry   Examines the biochemical ecology of diverse microbial groups with emphasis on anaerobic systems. 3 undergraduate hours. 3 graduate hours. Prerequisite: MCB 250 and MCB 354 or MCB 450, or consent of instructor.

MCB 426   Bacterial Pathogenesis   Emphasizes prokaryotes that cause important diseases in humans and other animals; host-parasite bacteriology; and chemistry and genetics of mechanisms of pathogenesis. 3 undergraduate hours. 3 graduate hours. Prerequisite: MCB 300 and MCB 354, or consent of instructor.

MCB 430   Molecular Microbiology   Modern contributions to the science of microbiology; emphasizes the structure, function, and synthesis of informational macromolecules and on the role microorganisms have played in molecular biology. 3 undergraduate hours. 3 graduate hours. Prerequisite: MCB 300 and credit or concurrent registration in MCB 354, or consent of instructor.

PHYS 402   Light   Wave kinematics; geometrical optics: basic concepts, ray-tracing and matrix formalism, Gaussian imaging by thick lenses, stops, apertures, and intensity relations; interference; interference spectroscopy and coherence; diffraction: Fresnel-Kirchhoff formulation, Fraunhofer case, Fresnel case, and holography; polarized light. 4 undergraduate hours. 3 or 4 graduate hours. (3 hours without lab). Prerequisite: PHYS 214 and PHYS 435 or ECE 329.

PHYS 404   Electronic Circuits  Physics of semiconductor devices; theory and application of discrete and integrated devices in linear circuits; use of operational amplifiers and feedback; regulation, oscillators, and modulation; emphasizes practical experience. 5 undergraduate hours. 4 graduate hours. Prerequisite: PHYS 325.

PHYS 460   Condensed Matter Physics   Bonding and structure of crystals; energy bands in insulators, semiconductors, and metals; electrical conductivity; optical properties; lattice vibrations; elasticity; point defects; dislocations. 4 undergraduate hours. 4 graduate hours. Credit is not given for both PHYS 460 and MSE 304. Prerequisite: PHYS 435PHYS 485 or PHYS 486.

PHYS 485   Atomic Phys & Quantum Theory   Basic concepts of quantum theory which underlie modern theories of the properties of materials; elements of atomic and nuclear theory; kinetic theory and statistical mechanics; quantum theory and simple applications; atomic spectra and atomic structure; molecular structure and chemical binding. 3 undergraduate hours. 3 graduate hours. Credit is not given for both PHYS 485 and CHEM 442. Prerequisite: MATH 285 or MATH 286 and PHYS 214.

PHYS 504   Statistical Physics   Single-particle distribution functions; classical and quantum mechanical systems, Boltzmann equation, virial theorem, and equations of state for gases; formal theory: ensembles, identical particles, thermodynamics of simple systems, and distribution functions; nonequilibrium problems; conservation laws and hydrodynamic equations, sound waves, and transport coefficients; plasmas, normal Fermi fluid, superfluids, and systems with internal degrees of freedom. Prerequisite: PHYS 427 and PHYS 486.

PHYS 550   Biomolecular Physics   Physical concepts governing the structure and function of biological macromolecules; general properties, spatial structure, energy levels, dynamics and functions, and relation to other complex physical systems such as glasses; recent research in biomolecular physics; physical techniques and concepts from theoretical physics emphasized. Same as BIOP 550 and MCB 550. Prerequisite: CHEM 104PHYS 485 or PHYS 487.

PHYS 560   Condensed Matter Physics I   Crystalline perfection, free-electron gas, screening, plasma oscillations, and dielectric response; Bloch electrons, Brillouin zones, and band structure; semiconductors, intrinsic and extrinsic, with applications; phonons, elasticity, and anharmonicity; ferromagnetism and second-order phase transitions; superconductivity. Prerequisite: PHYS 427 and PHYS 580.

PHYS 563   Phase Transitions   Phenomenology of phase transitions, scaling, critical behavior, and multi-criticality; Landau theory of phase transitions; renormalization group methods, including lattice models and epsilon-expansion; numerical methods; critical dynamics; selected additional topics. Prerequisite: PHYS 504.

PHYS 598   Special Topics in Physics   Subject offerings of new and developing areas of knowledge in physics intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. May be repeated in the same or separate terms if topics vary.

ATMS 420   Atmospheric Chemistry   Biochemical cycles of atmospheric trace gases, their interactions on global and regional scales, and their significance for the chemistry in the atmosphere. Important fundamental concepts central to understanding air pollutants, e.g., the formation of aerosols and the transformation and removal of species in the atmosphere. Same as CEE 447. 4 undergraduate hours. 4 graduate hours. Prerequisite: CHEM 102PHYS 211, and MATH 241.

ATMS 502: Numerical Methods in Fluid Dynamics Addresses numerical techniques for solving linear and nonlinear differential equations in initial value fluid flow problems. Students receive a thorough background in the principles used to evaluate numerical methods, the ability to critically interpret these methods as presented in the literature, and in particular, the practical application of these techniques in modeling multi-dimensional flow on high-performance computers. Temporal and directional splitting, finite differencing/volume methods, and adaptive nesting will be discussed. Same as CSE 566. 4 graduate hours. No professional credit. Prerequisite: MATH 285 or equivalent. Graduate Standing or Consent of Instructor.

BIOE 498: Special Topics in Bioengineering   Subject offerings of new and developing areas of knowledge in bioengineering intended to augment the existing curriculum. See Class Schedule or departmental course information for topics and prerequisites. 1 to 4 undergraduate hours. 1 to 4 graduate hours. May be repeated in the same or separate terms if topics vary to a maximum of 12 hours, but no more than 8 in any one term.

ME 471   Finite Element Analysis   The finite element method and its application to engineering problems: truss and frame structures, heat conduction, and linear elasticity; use of application software; overview of advanced topics such as structural dynamics, fluid flow, and nonlinear structural analysis. Same as AE 420 and CSE 451. 3 or 4 undergraduate hours. 3 or 4 graduate hours. Credit is not given for both ME 471 and CEE 470. Prerequisite: CS 101 and ME 371 or TAM 470. Alternatively, AE 370 for AE students.


TAM 538   Turbulence   Instability and origins of chaotic motion in fluid flow; Reynolds averaging and statistical description of turbulence, correlations and spectral dynamics of homogeneous turbulence, anisotropic flows, coherent structures, inhomogeneous turbulence, transport models, and large-eddy simulations. Prerequisite: TAM 532.

TAM 574   Adv Finite Element Methods   Advanced theory and applications of the finite-element method, as needed for research in computational science and engineering: applications to mechanics of solids and fluids, thermal problems, etc.; variational foundations of the finite-element method, error estimates, and adaptive analysis; finite-element methods for parabolic and hyperbolic problems; mixed finite-element methods; applications to systems of equations. Same as CSE 517. Prerequisite: One of TAM 470CEE 570CS 555ME 471.

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