Recent developments in engineering. The students report on assigned subjects.
Departmental approval.
The fundamentals of topics from algebra that are important in system theory, control theory, network theory and computer science. The topics include set theory, rings, groups, finite-dimensional vector spaces, matrices, Boolean algebra and linear graphs.
3 hr./wk.
Extensive physical background; introduction to basic theorems and concepts. Application of vector calculus and tensor analysis to inviscid and viscous steady and unsteady flow. Navier-Stokes equations and Prandtl boundary layer theory; application to in-compressible fluid motions.
3 hr./wk.
General theory of compressible, steady and unsteady flows, theory of characteristics. Linear and nonlinear wave propagation. Hypersonic flow.
3 hr./wk.
Function of matrices, application to systems of ordinary differential and difference equations. Definitions and basic properties of Legendre, Bessel, and other special functions. Common problems in partial differential equations and solution by separation of variables. Eigenfunction expansions. Fourier integral. Applications of Laplace and Fourier transforms.
3 hr./wk.
The elementary functions and their geometric representation. Cauchy integral theorems, Taylor and Laurent series. Classification of singularities. Analytic continuation, multivalued functions and their Riemann surfaces. Conformal mapping, Laplace and Fourier transforms and their inversion. Causality conditions, Nyquist criterion, Wiener-Hopf problems.
3 hr./wk.
Elements of analytic function theory: contour integration, residue theorem. Laplace, Fourier, Mellin, Hankel, Hilbert and other common transforms. Properties, inversion formulas. Applications to the solution of ordinary differential equations, integral and dual integral equations and various problems in elasticity, vibrations, and fluid mechanics.
3 hr./wk.
Inhomogeneous boundary value problems and solution by separation of variables. First order equations and their solution by characteristics. Higher order equations and systems, classification by characteristics. Hyperbolic equations and systems. The Riemann function, propagation of discontinuities and shocks. Boundary value problem for elliptic equations, maximum principle, Green's function. Potential theory, reduction of boundary value problem to an integral equation. Introduction to regular and singular perturbation solutions of non-linear equations.
3 hr./wk.
Computation of roots of algebraic and transcendental equations. Solution of simultaneous equations. Determinations of eigenvalues. Interpolation. Approximation of functions by polynomials. Integration. Solution of ordinary differential equations.
3 hr./wk.
Numerical solutions of problem in science and engineering. Linear and nonlinear systems of algebraic equations. Sparse matrix techniques. Eigenvalue-eigenvector problems. Error analysis. Nonlinear initial value problems and two-point boundary value problems for ordinary differential equations. Analysis of stability and accuracy. Least squares problems, approximation with sine functions, function minimization. Students are expected to use available work stations.
3 hr./wk.
Equilibrium and variational formulations of finite element methods. Plane, axisymmetric, and shell elements. Isoparametric elements. Static and transient response of structures. Applications in potential flow, electrostatic, thermal conduction field problems, and diffusion equations. Students are expected to use available work stations.
3 hr./wk.
Introduction to probability theory. Random processes: ergodic, stationary and non-stationary processes. Autocorrelation and cross-correlation functions, power and cross spectra, correlation coefficients. Input-output relationships for linear and nonlinear oscillators. Discrete and continuous systems. Zero-crossing and up-crossing problem. Stochastic characteristics of maximum response. Applications to vibrations, earthquake and wind engineering.
3 hr./wk.
Origins of turbulence and the qualitative features of turbulent flow. Prandtl's mixing length theory, von Karman's similarity hypothesis, and entrainment theories. Calculations of the behavior of free turbulent flows, including jets, wakes and plumes. Calculations of bounded turbulent flows, including pipe flow and boundary layers. Turbulent dispersion and diffusion.
3 hr./wk.
An introduction to equilibrium statistical mechanics; ensembles, partition function, relation to classical thermodynamics. Evaluation of thermodynamic and transport properties of dense gases and liquids from molecular theory.
3 hr./wk.
Continuum kinematics, formulation of physical principles in the continuum context, the formulation of constitutive equations, the theories of elastic solids, viscous fluids and viscoelastic solids. At the end of the course there will be an emphasis on either deformable porous media or finite deformation elasticity, depending on student interest.
Basic undergraduate courses in Mechanics of Materials, Fluid Mechanics and Linear Algebra (including vector field theory).
3 hr./wk.
Linear theory of viscoelasticity with applications to vibrations and buckling. Introduction to the theory of plasticity. Physical basis, yield conditions. Perfectly plastic and strain hardening materials. Drucker's postulates, flow rule. Upper and lower bound theorems. Applications to torsion, indentation and plate theory. Numerical solutions.
3 hr./wk.
Hyperbolic and dispersive, linear and non-linear waves. Hyperbolic waves: the wave equation, stationary waves, breaking waves, shock waves. Dispersive waves: dispersion relations, group and phase velocities. Non-linear waves and chaos in wave fields. Application to (1) water waves, (2) stress waves in solids (dilation and distortion waves, Rayleigh waves).
3 hr./wk.
Incorporating elastic solid properties and Darcy's law, Biot poroelasticity is a model for interaction of stress and fluid flow in a porous medium. The Biot Model is used to solve quasistatic problems containing creep, stress relaxation and consolidation as well as wave propagation problems, including the "second sound" prediction and verification. The Biot model is then extended as a continuum mixture model suitable for a description of the mechano-electro-chemical behaviors associated with deformation and fluid flow in charged-hydrated porous materials. This mixture model provides a flexible and general basis that permits the development of a unified viewpoint for many diverse and perhaps simultaneously occurring phenomena.
ENGR I1400: Applied partial differential equations and
ENGR I4200: Continuum mechanics (or a course in elasticity and fluid mechanics that included viscous fluid theory).
3 hr./wk.
Definitions of concentrations, velocities and mass fluxes. Conservation of species equation; multicomponent diffusion; Stefan-Maxwell equations. Transient diffusion in semi-infinite media. Definition of transfer coefficients with mass addition. Application of film, penetration and boundary layer theory. Diffusion with homogeneous and heterogeneous chemical reaction. Interphase transport.
3 hr./wk.
The Professional Seminar,which will be taught by a diverse group of faculty members, partners and other experts, will serve as a unifying foundation for the program by offering students a global perspective on environmental issues,introducing internship and research opportunities, and providing training in professional and personal skills.
Graduate student standing in ESEE. Permission of instructor
3 hr./wk.
The final project will consist of a research project with a faculty member. ESEE students will have the opportunity to work on real environmental science and engineering projects to gain practical experience and, in some cases, hands-on experience in the field or research lab. The faculty member will work with the student to prepare a research proposal and conduct a 3-credit research project. Research proposals and final projects will be presented orally.
3 hr./wk.