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Rensselaer Catalog 2018-2019 [Archived Catalog]
Courses
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MANE 6280 - Nuclear Reactor Analysis II
Reactor kinetics, stability, and control. Perturbation methods, reactivity coefficients; feedback mechanisms, long-term reactivity changes. Fission product effects on reactor startup and spatial stability. Fuel depletion. Theory of control and burnable poisons.
Prerequisites/Corequisites: Prerequisite: MANE 4480 Physics of Nuclear Reactors.
When Offered: Spring term annually.
Credit Hours: 3
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MANE 6290 - Radiation Transport Methods
Linear and nonlinear Boltzmann equations. Analytical solutions. Computer solution by P-N, S-N, diffusion, moments, integral, and Monte Carlo methods. Energy group averaging, scattering angle representation, and transport approximations. Perturbation and adjoint applications. Heavy ion and electron transport. Transport in interacting particle and photon systems.
Prerequisites/Corequisites: Prerequisite: MANE 4480 Physics of Nuclear Reactors.
When Offered: Spring term odd-numbered years.
Credit Hours: 3
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MANE 6300 - Numerical Methods in Reactor Analysis
Difference equations; matrix operation, linear systems, matrix eigenvalue problems, multi-group diffusion, and transport theory methods. Sn calculations, Monte Carlo methods. Application to nuclear engineering calculations, such as flux and power distributions, heat conduction, programming reactor problems for digital computers, codes, etc.
Prerequisites/Corequisites: Prerequisites: MANE 4480 Physics of Nuclear Reactors. MATH 4600 Advanced Calculus is recommended.
When Offered: On sufficient demand.
Credit Hours: 3
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MANE 6310 - Reactor Design
The reactor design problem is studied using current methods. Emphasis is placed on thermal and hydraulic analyses of power reactors, neutronics, fuel cycles, economics, nuclear analysis, control, siting, and safety. Complete reactor systems are analyzed. Standard reactor design codes are utilized.
Prerequisites/Corequisites: Prerequisite: MANE 2400 Fundamentals of Nuclear Engineering.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6320 - Radioactive Waste Management
Fundamental knowledge with a broad view on radioactive waste. Generation or sources, classification, management including treatment, conditioning, storage, transportation, and disposal. Environmental impact of nuclear waste management activities, risk and safety assessment, and regulatory aspects. Use of modern software (such as GoldSim) for risk and safety assessment through homework, project, and/or exams.
Prerequisites/Corequisites: Prerequisites: MATH 2400 Introduction to Differential Equations, MANE 2400 Fundamentals of Nuclear Engineering, and MANE 4400 Nuclear Power Systems Engineering.
When Offered: Spring term odd-numbered years.
Credit Hours: 3
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MANE 6350 - Radiation Shielding
Design, analysis, and confirmation of radiation shields. Point kernel, removal-diffusion, P-N, discrete ordinates, and Monte Carlo computation method. Photon, neutron, and charged particle transport data, applications, and tests. Shield materials and behavior. Dosimetry in shield confirmation.
Prerequisites/Corequisites: Prerequisite: MANE 4480.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6360 - Reactor Reliability and Safety
Theory and applications of reliability and risk assessment. Boolean algebra, logic diagrams, redundancy, and majority-vote configurations. System synthesis by reliability and fault tree techniques, quantitative evaluation, uncertainty analysis. Common cause events, failure data, and failure models. Allocation of risk to subsystems. Availability, repair policies, renewal theory. Operational reliability methods.
Prerequisites/Corequisites: Prerequisites: MANE 4050 Modeling and Control of Dynamic Systems. MATH 4600 Advanced Calculus is recommended.
When Offered: Fall term even-numbered years.
Credit Hours: 3
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MANE 6370 - Thermal-Hydraulic Design of Nuclear Reactors
An introduction to the principles underlying the thermal-hydraulic design of nuclear power reactors. Topics include plant thermal limits, sub-channel analysis, thermal-hydraulic stability analysis, and reactor system response during both normal and postulated accident conditions.
Prerequisites/Corequisites: Prerequisite: MANE 6840 or equivalent.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6380 - Nuclear Reactor Materials
The physical metallurgy and associated physical chemistry of problems encountered in the application of materials in nuclear reactors is discussed. Specifically, the metallurgy and physical chemistry of ceramic fuels (e.g., oxygen potentials), the primary fuel densification and pellet-clad interaction mechanisms, irradiation-induced creep, hardening, and embrittlement mechanisms, and the properties of zircalloy are covered.
Prerequisites/Corequisites: Prerequisite: MANE 4480 Physics of Nuclear Reactors.
When Offered: Spring term annually.
Cross Listed: Cross Listed: MANE 4460. Students cannot obtain credit for both this course and the cross listed course.
Credit Hours: 3
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MANE 6390 - Atomic and Nuclear Physics Applications
Principles and design of spectrometers and accelerators; NMR, ESR, Mossbauer methods, lasers, microwave devices, and combinations of these; sources, beam transport and focusing; targets and effects.
Prerequisites/Corequisites: Prerequisite: MANE 2830 Nuclear Phenomena for Engineering Applications.
When Offered: Fall term annually.
Cross Listed: MANE 4410; students cannot obtain credit for both this course and the cross listed course.
Credit Hours: 3
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MANE 6400 - Analytical Dynamics
A fundamental course in dynamics of rigid and flexible bodies. Review of kinematics and Newtonian dynamics; virtual variations and fundamentals of calculus of variations; generalized coordinates, velocities and momenta; constraints; generalized Hamilton’s principle and Lagrangean dynamics; rotational dynamics, orientation angles and Euler parameters; brief introduction to the analysis of nonlinear systems and stability of motion. Applications to the motion of rigid and flexible bodies. The role of symbolic manipulation in dynamics is introduced.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6420 - Multibody Dynamics
Analytical and numerical analysis of dynamic behavior of multibody mechanical systems. Emphasis on understanding all aspects of modeling and analysis process associated with real (spacecraft, automotive, biomechanical, etc.) systems. Review of traditional dynamic analysis methods (Newtonian-Euler, Lagrange, etc.), presentation of more efficient, powerful, recently developed methods (including Kane’s method). Comparison of the different formulations and their applicability to computer simulation. Treatment of constraints, extraction of data from equations of motion, and computational issues.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6430 - Nonlinear Vibrations
A fundamental course in nonlinear vibrations and stability. Basic concepts about linear and nonlinear systems; Routh-Hurwitz and Liapunov’s stability criteria; systems with periodic coefficients and Floquet theory; effects of nonlinearities; limit cycles, jump, saturation, nonlinear resonances, modal energy exchange, etc.; perturbation methods: straightforward perturbations, Lindstedt-Poincare, harmonic balancing, multiple time scales; steady-state and transient responses of nonlinear systems. Applications to discrete and structural systems. Use of symbolic manipulation to analyze problems.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6450 - Mechanics of Materials Processing
Modeling and analysis of common manufacturing processes. Topics include bulk-forming, sheet-forming, and casting processes. Classical analysis techniques, upper bound analysis, slip-line field theory, asymptotic methods, and the finite element method are investigated.
Prerequisites/Corequisites: Prerequisite: MANE 6170 or equivalent.
When Offered: Upon sufficient demand.
Credit Hours: 3
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MANE 6460 - Fracture Mechanics and Fatigue of Materials
Fracture mechanics: linear elastic fracture, elastic crack boundary value problems, path independent integrals, stress concentration and crack nucleation, statistical approach to brittle fracture, toughening mechanisms, elastic-plastic fracture mechanics, elements of dynamic fracture. Fatigue of materials: response of materials under cyclic stress, micromechanical aspects of fatigue, phenomenological approach to fatigue life prediction, fracture mechanics approaches, fatigue crack initiation and propagation, variable amplitude, and overstress effects.
Prerequisites/Corequisites: Prerequisites: MANE 4670 Mechanical Behavior of Material.
When Offered: Spring term even-numbered years.
Credit Hours: 3
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MANE 6480 - Health Physics and Medical Aspects of Radiation
Use of radioisotopes and radiation in nuclear medicine, radiation chemistry, basis of dosimetry, ionizing and nonionizing energy transfer processes in living tissue and cells. Radiation effects on the structure of nucleic acids, proteins, and cell membranes with emphasis on mechanisms by which cell viability is lost. Background in radiation chemistry is developed in particular for engineering majors. Applications are given in nuclear medicine, cancer therapy, and radiation in the environment.
When Offered: Spring term annually.
Credit Hours: 3
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MANE 6490 - Plasticity
Stress invariants. Polyaxial stress-strain relation for strain-hardening materials. Ideal plasticity, various yield conditions, and associated flow rules. Variational principles. Limit analysis. Applications in elastic-plastic stress analysis, metal forming, plastic collapse, and plastic instability.
When Offered: Spring term even-numbered years.
Credit Hours: 3
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MANE 6500 - Non-Newtonian Fluid Mechanics
Flow of non-Newtonian fluids such as polymeric liquids, granular mixtures, etc. Flow phenomena and material functions. Integral and differential constitutive equations for generalized Newtonian, linear viscoelastic, and ordered fluids.
When Offered: Upon sufficient demand.
Credit Hours: 3
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MANE 6520 - Fluid Mechanics
An introductory graduate course in fluid mechanics. Topics include: continuum hypothesis; perfect gas and departures from perfect gas; vectors and tensors; conservation laws for a continuum: mass momentum and energy; constitutive theory for fluids; viscosity and molecular transport; compressible Navier-Stokes equations; kinematics of the flow field: vorticity, streamlines; incompressible Navier-Stokes equations and their applications: Poiseuille flow, low Reynolds number flows, flows at large Reynolds number, boundary layers, external flows: flow stability and introduction to the theory of turbulence.
Prerequisites/Corequisites: Prerequisites: MATH 2010 Multivariable Calculus and Matrix Algebra and MANE 4800 Boundary Layers and Heat Transfer or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 3
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MANE 6530 - Turbulence
Navier-Stokes equations, linear stability, vorticity and its origin, transition in wall-bounded and free-shear flows, statistics and Reynolds averaging, homogeneous turbulence, coherent structures, laboratory methods for study of turbulence, including turbulence measurements and turbulence modeling.
Prerequisites/Corequisites: Prerequisite: MANE 4800 Boundary Layers and Heat Transfer. MANE 6520 Fluid Mechanics is recommended.
When Offered: Spring term odd-numbered years.
Credit Hours: 3
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MANE 6540 - Advanced Thermodynamics
General principles and applications of equilibrium thermodynamics. Second law analysis of energy systems. Thermodynamic relations, equations of state, properties of single and multiphase systems. Elementary statistical thermodynamics. Fundamentals of nonequilibrium thermodynamics.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6550 - Theory of Compressible Flow
General equations of compressible flow. Specialization to inviscid flows in two space dimensions. Linearized solutions in subsonic and supersonic flow. Characteristic equations for supersonic flow with applications in external and internal flow. One-dimensional nonsteady compressible flow. Introduction to transonic flow.
Prerequisites/Corequisites: Prerequisite: MANE 4070 Aerodynamics I.
When Offered: Spring term odd-numbered years.
Credit Hours: 3
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MANE 6560 - Incompressible Flow
Graduate fluid mechanics course on classical and modern approaches to hydrodynamics. Topics cover three areas, (1) surface waves, (2) flow instability, and (3) vortex dynamics. Wave topics include linear dispersive and nondispersive waves, weakly nonlinear waves, and viscous effects, with special attention to surface tension phenomena. Flow instabilities include gravitational, capillary, thermal, centrifugal, and viscous instabilities. Topics in vortex dynamics include vortex laws and flow invariants, generation and decay of vorticity, and vortex-boundary interaction.
When Offered: Spring term even-numbered years.
Credit Hours: 3
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MANE 6570 - Aerodynamic Flow Control
This is a graduate level course. It aims to provide students with the familiarity of traditional and modern flow control techniques. It also introduces the students to the subject of laminar-to-turbulent transition and flow separation using hydrodynamic stability analysis, which is a crucial component in design and implementation of intelligent flow control strategies.
Prerequisites/Corequisites: Prerequisite: MANE 4010 Thermal and Fluids Engineering II or MANE 4070 Aerodynamics I. The course is offered only to graduate students. Senior undergraduate students who wish to take this course must discuss it in person with the instructor.
When Offered: Fall term odd-numbered years.
Credit Hours: 3
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MANE 6600 - Systems Analysis Techniques
Methods of analysis for continuous and discrete-time linear systems. Convolution, classical solution of dynamic equations, transforms and matrices are reviewed. Emphasis is on the concept of state space. Linear spaces, concept of state, modes, controllability, observability, state transition matrix. State variable feedback, compensation, decoupling.
Prerequisites/Corequisites: Prerequisite: MANE 4050 Modeling and Control of Dynamic Systems or ECSE 2410 Signals and Systems.
When Offered: Fall term annually.
Credit Hours: 3
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MANE 6610 - Nonlinear Control Systems
Phenomena peculiar to nonlinear systems. Linearization, iteration, and perturbation procedures. Describing function stability analysis. Phase plane methods. Relaxation oscillations and limit cycles. Stability analysis by Lyapunov’s method. Popov’s theorem. Adaptive control systems. Sensitivity analysis.
Prerequisites/Corequisites: Prerequisite: ECSE 6400 or MANE 6600 Systems Analysis Techniques.
When Offered: Spring term odd-numbered years.
Cross Listed: ECSE 6420 Nonlinear Control Systems; students cannot receive credit for both this course and ECSE 6420.
Credit Hours: 3
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MANE 6620 - Optimal Control Theory
The concepts, techniques, and tools related to optimal control for dynamical systems. Major topics include calculus of variation, minimum principle, dynamic programming, optimal estimation, and differential games. Both discrete time systems and continuous times are addressed. Particular consideration is given to linear time invariant systems in terms of linear quadratic regulator and Kalman filter.
Prerequisites/Corequisites: Prerequisite: ECSE 6400 or MANE 6600 Systems Analysis Techniques.
When Offered: Spring term even-numbered years.
Cross Listed: ECSE 6440 Optimal Control Theory; students cannot receive credit for both this course and ECSE 6440.
Credit Hours: 3
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MANE 6630 - Conduction Heat Transfer
An introduction to the mathematics of conduction heat transfer. Applications of results illustrated by examples from furnace design, cooling of electric components, building design, heat exchanger design.
When Offered: Fall term odd-numbered years.
Credit Hours: 3
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MANE 6640 - Radiation Heat Transfer
An introduction to radiation heat transfer in diathermanous media and participating media. Selected applications from spacecraft design, furnace design, meteorology, temperature measurement, environmental control.
When Offered: Upon sufficient demand.
Credit Hours: 3
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MANE 6650 - Convective Heat Transfer
Fundamental study of convection heat transfer in laminar and turbulent internal and external flows. Unsteady flows, combined heat and mass transfer, conjugated unsteady heat transfer, and buoyancy induced convection. Selected applications from aeronautics and heat exchanger design.
Prerequisites/Corequisites: Prerequisite: MANE 4800 Boundary Layers and Heat Transfer. MANE 6520 Fluid Mechanics is recommended.
When Offered: Spring term even-numbered years.
Credit Hours: 3
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MANE 6660 - Fundamentals of Finite Elements
Graduate-level course on the fundamental concepts and technologies underlying finite element methods for the numerical solution of continuum problems. The course emphasizes the construction of integral weak forms for elliptic partial differential equations and the construction of the elemental level matrices using multi-dimensional shape functions, element level mappings, and numerical integration. The basic convergence properties of the finite element method will be given. This course serves as preparation for students working on finite element methods.
Prerequisites/Corequisites: Prerequisite: MATH 2400 Introduction to Differential Equations.
When Offered: Fall term annually.
Cross Listed: Cross listed: CIVL 6660. Students cannot obtain credit for both this course and CIVL 6660.
Credit Hours: 3
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MANE 6670 - Nonlinear Finite Element Methods
The formulations and solution strategies for finite element analysis of nonlinear problems are developed. Topics include the sources of nonlinear behavior (geometric, constitutive, boundary condition), derivation of the governing discrete equations for nonlinear systems such as large displacement, nonlinear elasticity, rate independent and dependent plasticity and other nonlinear constitutive laws, solution strategies for nonlinear problems (e.g., incrementation, iteration), and computational procedures for large systems of nonlinear algebraic equations.
Prerequisites/Corequisites: Prerequisites: MANE 6660 CIVL 6660 or equivalent.
When Offered: Upon sufficient demand.
Cross Listed: Cross listed as CIVL 6700. Students cannot obtain credit for both this course and CIVL 6700.
Credit Hours: 3
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MANE 6680 - Finite Element Programming
Examines the implementation of finite element methods. Consideration is first given to the techniques used in classic finite element programs. Attention then focuses on development of a general geometry-based code which effectively supports higher order adaptive technique. Technical areas covered include: effective construction of element matrices for p-version finite elements, ordering of unknowns, automatic mesh generation, adaptive mesh improvement, program and database structures. Implementation of automated adaptive techniques on parallel computers is also covered.
Prerequisites/Corequisites: Prerequisite: MANE 6660/CIVL 6660 Fundamentals of Finite Elements or MATH 6860/CSCI 6860 Finite Element Analysis.
When Offered: Spring term odd-numbered years.
Cross Listed: Cross listed: CIVL 6680. Students cannot obtain credit for both this course and CIVL 6680.
Credit Hours: 3
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MANE 6700 - Finite Element Methods in Structural Dynamics
Solutions to the free vibration and transient dynamic responses of two-and three-dimensional structures by the finite element method are considered. The governing finite element matrix equations are derived and numerical aspects of solving these time-dependent equations considered. Topics include the formulation of the eigenvalue problem, algorithms for eigenvalue extraction, time integration methods including stability and accuracy analysis, and finite elements in time. Modal analysis and direct time integration techniques are compared for a variety of two-and three-dimensional problems.
Prerequisites/Corequisites: Prerequisite: CIVL 6660 or MANE 6660 or equivalent.
When Offered: Upon sufficient demand.
Cross Listed: CIVL 6700. Students cannot obtain credit for both this course and CIVL 6700.
Credit Hours: 3
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MANE 6710 - Numerical Design Optimization
This course introduces the theory and practical use of numerical design optimization methods. Topics include: gradient-based methods for unconstrained and constrained nonlinear optimization; numerical evaluation of derivatives; polynomialand- and kriging-based surrogate models; gradient-free optimization methods; optimization under uncertainty; multi-objective and multi-disciplinary optimization. Projects require the use of computer programs to generate numerical results; therefore, experience with programming is highly recommended.
Prerequisites/Corequisites: Prerequisites: MATH 2010 AND CSCI 1190.
When Offered: Fall term annually.
Cross Listed: With MANE 4280.
Credit Hours: 3
Contact, Lecture or Lab Hours: Lecture.
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MANE 6720 - Computational Fluid Dynamics
Course focuses on computational approaches to solve the Navier-Stokes equations. Course assumes knowledge of numerical methods and therefore directly attacks the obstacles to applying these methods to the Navier-Stokes equations. Issues concerning implementation of finite difference methods (FDM), finite volume methods (FVM) and finite element methods (FEM) will be discussed. These issues include: the discrete formulation, nonlinear equation iterator (steady)/marcher (time-accurate), linear equation formation, boundary condition prescription, and linear equation solution.
Prerequisites/Corequisites: Prerequisite: MANE 6660/CIVL 6660 or equivalent.
When Offered: Spring term odd-numbered years.
Credit Hours: 3
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MANE 6730 - Tribology
A basic course in tribology that covers both the fundamental and applied aspects of the subject. Content includes viscometry, the Reynolds equation, thrust and journal bearings (including design), thermal effects, dynamic loading and instability of bearings, rolling contact bearings, dry bearings, and theories of wear. This course includes design principles and data and is basic to other courses offered in tribology.
When Offered: Fall term even-numbered years.
Credit Hours: 3
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MANE 6750 - Generalized Finite Element Methods
Fundamentals of modern numerical techniques (e.g., partition of unity methods) which overcome longstanding difficulties associated with traditional FEM (e.g., mesh generation and resolution of singularities). Topics include scattered data interpolation, weighted residual methods, integral equation methods for exterior problems (applications to MEMS modeling), multiscale solution techniques using wavelets.
Prerequisites/Corequisites: Prerequisite: MANE 4240 or CIVL 4240 or equivalent.
When Offered: Upon sufficient demand.
Credit Hours: 3
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MANE 6760 - Finite Element Methods for Fluid Dynamics
Analysis of finite element methods for basic classes of problems in fluid mechanics. Starting with scalar transport equations and building to compressible and incompressible Navier-Stokes equations. Emphasis on developing and analyzing formulations that are stable and higher-order accurate such as Galerkin/least-squares methods and SUPG methods. Unsteady formulations are proposed using space-time methods and semi-discrete methods.
Prerequisites/Corequisites: Prerequisite: MANE 6660/CIVL 6660, or equivalent.
When Offered: Upon sufficient demand.
Credit Hours: 3
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MANE 6770 - Multiscale Computational Modeling
This course will introduce a unified approach of modeling in science and engineering across spatial and temporal scales using particles as well as continuum fields, specifically focusing on methods and algorithms that will facilitate this bridging. Topics include two categories of multiscale approaches: information-passing and concurrent-bridging approaches. The goal is to algorithmically develop these methods, and in the process teach the underlying simulation techniques. Applications to realistic problems will highlight the strengths of these approaches, while stressing the challenges that still need to be surmounted.
Prerequisites/Corequisites: Prerequisite: MANE 4240/CIVL 4240, or equivalent.
When Offered: Upon sufficient demand.
Credit Hours: 3
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MANE 6780 - Numerical Modeling of Failure Processes in Materials
State of the art in computational modeling of failure processes in materials. Topics include numerical modeling of discrete defects, distributed damage and multiscale computational techniques including multiple scale perturbation techniques, boundary layer techniques, and various global-local approaches.
Prerequisites/Corequisites: Prerequisite: MANE 6660/CIVL 6660, or equivalent.
When Offered: Upon availability of instructor.
Cross Listed: Cross listed as CIVL 6780. Students cannot obtain credit for both this course and CIVL 6780.
Credit Hours: 3
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MANE 6800 - Manufacturing Systems Integration
Examination of the basic elements that are used to integrate the design and manufacture of capital and consumer products; manufacturing information systems, CAD/CAM systems, and manufacturability considerations when integrating unit process operations.
When Offered: Spring term annually.
Credit Hours: 3
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MANE 6820 - Finite Deformation Plasticity: Theory and Applications Kinematics of Finite Deformation
Elastic-plastic and elasto-viscoplastic constitutive behavior for isotropic and strain-induced anisotropic materials. Integration algorithms and finite element formulations for solving practical problems.
Prerequisites/Corequisites: Prerequisite: MANE 6170.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6830 - Combustion
Review of fundamentals of thermodynamics, chemical kinetics, fluid mechanics, and modern diagnostics. Discussion of flame propagation, thermal and chain explosions, stirred reactors, detonations, droplet combustion, and turbulent jet flames. Introduction to computational tools for complex equilibrium and kinetic calculations. Application to problems such as pollutant formation.
Prerequisites/Corequisites: Prerequisite: MANE 4010 or MANE 4080.
When Offered: Upon sufficient demand.
Cross Listed: MANE 4750 and CHME 6830; students cannot obtain credit for both this course and any of the cross listed courses.
Credit Hours: 3
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MANE 6840 - An Introduction to Multiphase Flow and Heat Transfer I
This course is intended to give students a state-of-the-art understanding about single and multicomponent boiling and condensation heat transfer phenomena. Applications include the analysis of nuclear reactors, oil wells, and chemical process equipment. Students satisfactorily completing this course are expected to thoroughly understand the current thermal-hydraulics literature on multiphase heat and mass transfer and be able to conduct independent research in this field.
Prerequisites/Corequisites: Prerequisite: a working knowledge of fluid mechanics and heat transfer.
When Offered: Upon availability of instructor.
Cross Listed: CHME 6840; students cannot obtain credit for both this course and CHME 6840.
Credit Hours: 3
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MANE 6850 - An Introduction to Multiphase Flow and Heat Transfer II
This course is intended to give students a state-of-the-art understanding in multicomponent flow phenomena. Applications in the chemical process, petroleum recovery, and fossil/nuclear power industries are given. Specific areas of coverage include two-phase: fluid mechanics, pressure drop, modeling and analysis, stability analysis, critical flow and dynamic waves, flow regime analysis, and phase separation and distribution phenomena.
Prerequisites/Corequisites: Prerequisite: MANE 6840/CHME 6840 An Introduction to Multiphase Flow and Heat Transfer I.
When Offered: Upon availability of instructor.
Cross Listed: Cross listed as CHME 6850. Students cannot obtain credit for both this course and CHME 6850.
Credit Hours: 3
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MANE 6880 - Product Realization
Concepts and tools that enable engineers and business leaders to jointly make sound business/technology decisions in moving from ideas and designs to real products will be taught using lectures, cases, and a major project that will enhance the change of success of a new venture business. Topics: disciplined toll-gate processes, customer contract, technical risk management, design decisions, quality management, sourcing, product launch.
Prerequisites/Corequisites: Prerequisites: engineering B.S. or MGMT 6620 Principles of Technological Entrepreneurship.
When Offered: Upon availability of instructor.
Credit Hours: 3
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MANE 6900 - Seminar
When Offered: Fall and spring terms annually.
Credit Hours: 0
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MANE 6940 - Individual Projects in Mechanical Engineering, Aeronautical Engineering, Nuclear Engineering, or Engineering Physics
Prerequisites/Corequisites: Permission of instructor.
When Offered: Fall and spring terms annually.
Credit Hours: 3 to 6
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MANE 6960 - Topics in Mechanical Engineering, Aeronautical Engineering, Nuclear Engineering, or Engineering Physics
When Offered: Fall and spring terms annually.
Credit Hours: 3
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MANE 6970 - Professional Project
Active participation in a semester-long project, under the supervision of a faculty adviser. A Professional Project often serves as a culminating experience for a Professional Master’s program but, with departmental or school approval, can be used to fulfill other program requirements. With approval, students may register for more than one Professional Project. Professional Projects must result in documentation established by each department or school, but are not submitted to the Office of Graduate Education and are not archived in the library. Grades of A,B,C, or F are assigned by the faculty adviser at the end of the semester. If not completed on time, a formal Incomplete grade may be assigned by the faculty adviser, listing the work remaining to be completed and the time limit for completing this work.
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MANE 6980 - Master’s Project
Active participation in a master’s-level project, under the supervision of a faculty adviser, leading to a master’s project report. Grades S or U are assigned at the end of the semester. If recommended by the adviser, the master’s project may be accepted by the Office of Graduate Education to be archived in the library.
Credit Hours: 1 to 9
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MANE 6990 - Master’s Thesis
Active participation in research, under the supervision of a faculty adviser, leading to a master’s thesis. Grades of S or U are assigned by the adviser each term to reflect the student’s research progress for the given semester. Once the thesis has been presented, approved by the adviser, and accepted by the Office of Graduate Education, it will be archived in a standard format in the library.
Credit Hours: 1 to 9
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MANE 7000 - Advanced Engineering Mathematics II
A continuation of the advanced presentation of mathematical methods useful in engineering practice. The course covers the Frobenius method for the solution of boundary value problems; the representation of arbitrary functions by characteristic functions; calculus of functions of more than one variable including the study of extreme; overview of calculus of variations; principles of vector and tensor analysis; analytical and numerical techniques for the solution of initial and boundary value problems in partial differential equations. Symbolic manipulation and scientific computation software used extensively. Emphasis on reliable computing is made throughout.
Credit Hours: 3
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MANE 7100 - Mechanical Engineering Foundations II
A presentation of the most common physical and mathematical modes used in the description of the mechanical behavior of materials. The course covers the microstructural and thermodynamic foundations of constitutive material behavior of interest in mechanical engineering applications; overview of elasticity and plasticity and their relationship to microstructural features; principles of rheology; viscoelasticity and creep; failure mechanisms including fracture crack propagation and fatigue crack growth. Particular attention throughout is given to the development of the ability to utilize the mathematical models to assess the reliability and life of mechanical engineering components at the design state.
Credit Hours: 3
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MANE 9990 - Dissertation
Active participation in research, under the supervision of a faculty adviser, leading to a doctoral dissertation. Grades of IP are assigned until the dissertation has been publicly defended, approved by the doctoral committee, and accepted by the Office of Graduate Education to be archived in a standard format in the library. Grades will then be listed as S.
Credit Hours: 1 to 15
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MATH 1010 - Calculus I
Functions, limits, continuity, derivatives, implicit differentiation, related rates, maxima and minima, elementary transcendental functions, introduction to definite integral with applications to area and volumes of revolution.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 1020 - Calculus II
Techniques and applications of integration, polar coordinates, parametric equations, infinite sequences and series, vector functions and curves in space, functions of several variables, and partial derivatives.
Prerequisites/Corequisites: Prerequisite: MATH 1010.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 1500 - Calculus for Architecture, Management, and HASS
Basic concepts in differential and integral calculus for functions of one variable. Topics will include functions, limits, continuity, derivatives, integration, exponential and logarithmic functions, and techniques of integration. Application areas will include topics in Management, Architecture, and Social Sciences with special emphasis on the role of calculus in introductory probability.
Prerequisites/Corequisites: Prerequisite: major in management, architecture, or HASS.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 1520 - Mathematical Methods in Management and Economics
Functions of several variables, introductory linear algebra, and other analytical techniques needed for further study in probability, statistics, and operations research. Topics covered include improper integrals, probability density functions, partial derivatives and optimization techniques for functions of several variables, matrix algebra, linear systems, lines and planes in 3-space, linear inequalities, introductory linear programming, introductory combinatorics, and some probability.
Prerequisites/Corequisites: Prerequisites: MATH 1010 or MATH 1500 and major in management or economics, or permission of instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 1620 - Contemporary Mathematical Ideas in Society
An application-oriented course introducing contemporary mathematical concepts that pertain to areas of Architecture and Humanities, Arts, and Social Sciences. The course will cover growth and form, symmetry, patterns, tilings, linear programming, information coding, voting systems, game theory, logic, probability, and statistics.
Prerequisites/Corequisites: Prerequisites: major in architecture or HASS and MATH 1010 or MATH 1500 or permission of instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 1900 - Art and Science of Mathematics I
A seminar for first-year math majors. The weekly student-faculty discussions will vary but examples of topics are: unsolved math problems, countability and the arithmetic of the infinite, topology and the concept of dimension, geometry and one-sided surfaces, and the theory underlying topics currently covered in calculus.
Prerequisites/Corequisites: Prerequisite: first-year math majors.
When Offered: Fall term annually.
Credit Hours: 1
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MATH 1910 - Art and Science of Mathematics II
A seminar for first-year math majors. The weekly student-faculty discussions will vary but examples of topics are: unsolved math problems, countability and the arithmetic of the infinite, topology and the concept of dimension, geometry and one-sided surfaces, and the theory underlying topics currently covered in calculus.
Prerequisites/Corequisites: Prerequisite: first-year math majors.
When Offered: Spring term annually.
Credit Hours: 1
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MATH 2010 - Multivariable Calculus and Matrix Algebra
Directional derivatives, maxima and minima, double integrals, line integrals, div and curl, and Green’s Theorem; matrix algebra and systems of linear equations, vectors and linear transformations in R^n, eigenvectors and eigenvalues, applications in engineering and science.
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 2400 - Introduction to Differential Equations
First-order differential equations, second-order linear equations, eigenvalues and eigenvectors of matrices, systems of first-order equations, stability and qualitative properties of nonlinear autonomous systems in the plane, Fourier series, separation of variables for partial differential equations.
Prerequisites/Corequisites: Prerequisites: MATH 1020 and some knowledge of matrices.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 2940 - Readings in Mathematics
Credit Hours: 1 to 4
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MATH 2960 - Topics in Mathematics
Credit Hours: 1 to 4
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MATH 4010 - Abstract Algebra
Groups, rings, polynomial rings, fields, integral domains, with emphasis on group theory; homomorphisms and isomorphisms; normal subgroups, cosets, ideals, modules; quotient groups and quotient rings; other topics chosen from number theory, polynomials and Galois Theory.
Prerequisites/Corequisites: Prerequisite: familiarity with mathematical proofs. MATH 4090 and MATH 4100 are recommended.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4020 - Introduction to Number Theory
Topics include the history of number representation systems, divisibility, greatest common divisor and prime factorization, linear Diophantine equations, congruences, and condition congruences. Additional topics may be chosen from cryptology, the perpetual calendar, hashing functions, computer operations and complexity, continued fractions, multiplicative functions, primitive roots, pseudo-random numbers, nonlinear Diophantine equations, Fermat’s last theorem, algebraic numbers, and approximation of numbers by rationals.
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 4030 - Computability and Logic
This course covers basic concepts and results in mathematical logic and computability theory, including decision procedures, automated theorem proving techniques for truth-functional and first-order logic, axiomatizations of set theory and arithmetic, Turing Machines, Abacus Machines, recursive functions, the Church-Turing Thesis, the halting problem, undecidability of first-order logic, undecidability of arithmetic, and Godel’s incompleteness results.
Prerequisites/Corequisites: Prerequisite: PHIL 2140 or CSCI 2200.
When Offered: Spring term odd-numbered years.
Cross Listed: Cross listed as PHIL 4420. Students cannot obtain credit for both this course and PHIL 4420.
Credit Hours: 4
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MATH 4040 - Introduction to Topology
Topics include general topological spaces, connectedness, compactness, continuity, and product spaces. Additional topics may be chosen from identification spaces, homotopy, the fundamental group, covering maps, lifts, classification of surfaces, Baire category, dimension, and the Jordan curve theorem.
Prerequisites/Corequisites: Prerequisite: MATH 4090 or graduate standing or permission of the instructor.
When Offered: Fall term even-numbered years.
Credit Hours: 4
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MATH 4090 - Foundation of Analysis
The course provides an opportunity for the development of theorem-proving skills in the field of mathematical analysis. Expansion of a knowledge base comes as a by-product of energy expended in theorem proving and subsequent exposition. Analysis topics included are: sets, functions, the real numbers, cardinality, induction, decimal representations of real numbers, Euclidean spaces, abstract vector spaces, and metric spaces. This is a communication-intensive course.
Prerequisites/Corequisites: Prerequisites: mathematics major and MATH 2010.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 4100 - Linear Algebra
The theory underlying vector spaces, algebra of subspaces, bases; linear transformations, dual spaces; eigenvectors, eigenvalues, minimal polynomials, canonical forms of linear transformations; inner products, adjoints, orthogonal projections, and complements.
Prerequisites/Corequisites: Prerequisite: MATH 2010.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4120 - Fundamentals of Geometry
Topics may be chosen from differential geometry of curves and surfaces, involutes and evolutes, order of contact, developable surfaces, Euler’s and Meusnier’s Theorem, mean and Gaussian curvatures, geodesics and parallel transport, The Theorem Egregium of Gauss, Gauss-Bonnet Theorem, computer-aided geometric design, computational geometry, tessellations, tiling and patterns, projective and non-Euclidean geometries, postulates and axiomatic systems, advanced Euclidean geometry, and the history of geometry.
Prerequisites/Corequisites: Prerequisites: MATH 2010.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 4150 - Graph Theory
Fundamental concepts and methods of graph theory and its applications to various areas of computing and the social and natural sciences. Topics include graphs as models, representation of graphs, trees, distances, matchings, connectivity, flows in networks, graph colorings, Hamiltonian cycles, traveling salesman problem, planarity. All concepts, methods, and applications are presented through a sequence of exercises and problems, many of which are done with the help of novel software systems for combinatorial computing.
Prerequisites/Corequisites: Prerequisites: CSCI 1100 and either CSCI 2200 or MATH 4090.
When Offered: Spring term annually.
Cross Listed: Cross listed as CSCI 4260. Students cannot obtain credit for both this course and CSCI 4260.
Credit Hours: 4
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MATH 4200 - Mathematical Analysis I
Fundamental concepts of mathematical analysis. This is the first course in a two-term sequence covering such topics as the real number system, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity, differentiability, Riemann integration, Stone-Weierstrass Theorem, functions of several variables, trigonometric series, differential forms on manifolds, and the higher dimensional Stokes Theorem.
Prerequisites/Corequisites: Prerequisites: MATH 1020 and MATH 4090 or graduate standing or permission of the instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4210 - Mathematical Analysis II
Fundamental concepts of mathematical analysis. This is the second course in a two-term sequence covering such topics as the real number system, limits, sequences, series, convergence, uniform convergence, functions of one variable, continuity, differentiability, Riemann integration, Stone-Weierstrass Theorem, functions of several variables, trigonometric series, differential forms on manifolds, and the higher dimensional Stokes Theorem.
Prerequisites/Corequisites: Prerequisite: MATH 4200 or graduate standing or permission of the instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4300 - Introduction to Complex Variables: Theory and Applications
An introduction to the theory and applications of complex variables. Topics include analytic functions, Riemann surfaces, complex integration, Taylor and Laurent series, residues, conformal mapping, harmonic functions, and Laplace transforms. Applications will be to problems in science and engineering such as fluid and heat flow, dynamical systems, and electrostatics.
Prerequisites/Corequisites: Prerequisite: MATH 2010 or equivalent.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4400 - Ordinary Differential Equations and Dynamical Systems
An intermediate course emphasizing a modern geometric approach and applications in science and engineering. Topics include first-order equations, linear systems, phase plane, linearization and stability, calculus of variations, Lagrangian and Hamiltonian mechanics, oscillations, basic bifurcation theory, chaotic dynamics, and existence and uniqueness.
Prerequisites/Corequisites: Prerequisites: MATH 2010 and MATH 2400 or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4500 - Methods of Partial Differential Equations of Mathematical Physics
An intermediate course serving to introduce both the qualitative properties of solutions of partial differential equations and methods of solution, including separation of variables. Topics include first-order equations, derivation of the classical equations of mathematical physics (wave, potential, and heat equations), method of characteristics, construction and behavior of solutions, maximum principles, energy integrals.
Prerequisites/Corequisites: Prerequisite: MATH 2010 and MATH 2400 or permission of instructor.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 4600 - Advanced Calculus
A course emphasizing advanced concepts and methods from calculus. Topics include: multivariable integral theorems (Green’s, divergence, Stokes’, Reynolds transport), extrema of multivariable functions (including Taylor’s theorem and Lagrange multipliers), the calculus of variations (Euler–Lagrange equations, constraints, principle of least action), and Cartesian tensors (calculus, invariants, representations).
Prerequisites/Corequisites: Prerequisites: MATH 2010.
When Offered: Fall and spring terms annually.
Credit Hours: 4
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MATH 4700 - Foundations of Applied Mathematics
Mathematical formulation of models for various processes. Derivation of relevant differential equations from conservation laws and constitutive relations. Use of dimensional analysis, scaling, and elementary perturbation methods. Description of basic wave motion. Examples from areas including biology, elasticity, fluid dynamics, particle mechanics, chemistry, geophysics, and finance.
Prerequisites/Corequisites: Prerequisite: MATH 2400 is required, and MATH 2010 is recommended.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4720 - Mathematics in Medicine and Biology
An introduction to mathematics used in biology, biophysics, biomedical engineering, and medicine. The mathematical topics covered are selected from calculus, linear algebra, differential equations, numerical methods, and Fourier analysis. The biological applications covered are selected from human physiology (heart, lung, brain), population models (microorganisms, cells, animals), and the diagnosis and treatment of disease (heart, cancer).
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4740 - Introduction to Financial Mathematics and Engineering
This course is designed to introduce students to mathematical and computational finance. Topics include a mathematical approach to risk analysis, portfolio selection theory, futures, options, and other derivative investment instruments. Finite difference and finite element methods for computing American option prices are discussed. A working knowledge of MAPLE or MATLAB is required to compute optimal portfolios.
Prerequisites/Corequisites: Prerequisite: MATH 1020.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4800 - Numerical Computing
A survey of numerical methods for scientific and engineering problems. Topics include numerical solution of linear and nonlinear algebraic equations, interpolation and least squares approximations, numerical integration and differentiation, eigenvalue problems, and an introduction to the numerical solution of ordinary differential equations. Emphasis placed on efficient computational procedures including the use of library and student written procedures using high-level software such as MATLAB.
Prerequisites/Corequisites: Prerequisites: MATH 2010 and MATH 2400.
When Offered: Fall and spring terms annually.
Cross Listed: Cross listed as CSCI 4800. Students cannot obtain credit for both this course and CSCI 4800.
Credit Hours: 4
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MATH 4820 - Introduction to Numerical Methods for Differential Equations
Derivation, analysis, and use of computational procedures for solving differential equations. Topics covered include ordinary differential equations (both initial value and boundary value problems) and partial differential equations. Runge-Kutta and multistep methods for initial value problems. Finite difference methods for partial differential equations including techniques for heat conduction, wave propagation, and potential problems. Basic convergence and stability theory.
Prerequisites/Corequisites: Prerequisite: MATH 4800 or CSCI 4800.
When Offered: Spring term even-numbered years.
Cross Listed: Cross listed as CSCI 4820. Students cannot obtain credit for both this course and CSCI 4820.
Credit Hours: 4
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MATH 4840 - Numerical Linear Algebra with Applications
The focus of the course is on fundamental algorithms in computational linear algebra and their applications in science and engineering. These algorithms involve QR and SVD factorizations, the computation of eigenvalues and eigenvectors, basic optimization methods, and iterative methods for sparse systems. Applications will be considered in areas such as data analysis and compression, principal component and spectral analysis, solutions of large sparse systems, among others.
Prerequisites/Corequisites: MATH 4800.
When Offered: Spring term odd-numbered years.
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MATH 4940 - Readings in Mathematics
Credit Hours: 1 to 4
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MATH 4950 - Senior Research
Undergraduate mathematics projects that utilize students’ mathematical knowledge will result in formal reports and final presentations. Examples are research projects or critical in-depth mathematical literature reviews. Information about projects will be exchanged in weekly meetings. Students wishing to work on research should make arrangements with faculty in advance. Students already engaged in research may extend and present their results. This is a communication-intensive course. To be graded S/U.
Prerequisites/Corequisites: Prerequisite: open to mathematics seniors only.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 4960 - Topics in Mathematics
Credit Hours: 1 to 4
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MATH 4980 - Undergraduate Project in Mathematics
Credit Hours: 1 to 4
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MATH 6190 - Topics in Mathematics
The course is intended to provide a mathematical perspective on one or more topics chosen from algebra, geometry, and/or topology. Topics may include combinatorial matrix theory, classification of surfaces, Lie groups, Galois theory, geometric analysis, computational geometry, homology, and/or fixed point theorems.
Prerequisites/Corequisites: Prerequisites: vary with topic.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 6200 - Real Analysis
A careful study of measure theory, including abstract and Lebesgue measures and integration, absolute continuity and differentiation, L^p spaces, Fourier transforms and Fourier series, Hilbert spaces and normed linear spaces.
Prerequisites/Corequisites: Prerequisite: MATH 4210 or equivalent or permission of instructor.
When Offered: Fall term even-numbered years.
Credit Hours: 4
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MATH 6220 - Applied Functional Analysis
A basic course in the concepts of linear functional analysis, including such topics as Banach and Hilbert spaces, L^p and l^p (sequence) spaces; weak, strong and weak* convergence; linear functionals; linear bounded, unbounded, closed, and compact operators; spectrum, resolvent, the spectral theorem for compact operators, Fredholm alternative; applications are to differential equations, integral equations and optimization.
Prerequisites/Corequisites: Prerequisites: MATH 4210 and MATH 4300, or equivalent or permission of instructor.
When Offered: Fall term odd-numbered years.
Credit Hours: 4
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MATH 6400 - Ordinary Differential Equations
Analytical and computational methods for ordinary differential equations: existence and uniqueness of solutions, similarity methods, linear equations, regular singular points, hypergeometric equations, asymptotic expansions near irregular singular points, WKB theory, turning points, stability theory, stable and unstable manifolds, periodic solutions and Poincare maps, Floquet theory, stabilization and destabilization by periodic forcing, calculus of variations, Lagrangian and Hamiltonian systems, Poincare invariants, symplectic integrators, basic bifurcation theory, examples of chaotic dynamics, applications to physics, chemistry, and biology.
Prerequisites/Corequisites: Prerequisite: MATH 4300 and MATH 4400 or equivalent or permission of instructor.
When Offered: Spring term odd-numbered years.
Credit Hours: 4
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MATH 6490 - Topics in Ordinary Differential Equations
Mathematical foundations and/or applications of ordinary differential equations. Possible topics include: stability and chaos in dynamics, mathematical methods of classical mechanics, stochastic differential equations, and soliton equations.
Prerequisites/Corequisites: Prerequisites: vary with topic.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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MATH 6500 - Partial Differential Equations
A course dealing with the basic theory of partial differential equations. It includes such topics as properties of solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables; linear and nonlinear first order equations; existence and uniqueness theory for general higher order equations; potential theory and integral equations.
Prerequisites/Corequisites: Prerequisite: MATH 4210 or equivalent or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 6590 - Topics in Partial Differential Equations
Mathematical foundation and/or applications of partial differential equations. Possible topics include soliton theory and applications, wavelets and PDEs, scattering theory, hyperbolic conservation laws.
Prerequisites/Corequisites: Prerequisites: vary with topic.
When Offered: Spring term annually.
Credit Hours: 4
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MATH 6600 - Methods of Applied Mathematics
Linear vector spaces; eigenvalues and eigenvectors in discrete systems; eigenvalues and eigenvectors in continuous systems including Sturm-Liouville theory, orthogonal expansions and Fourier series, Green’s functions; elementary theory of nonlinear ODEs including phase plane, stability and bifurcation; calculus of variations. Applications will be drawn from equilibrium and dynamic phenomena in science and engineering.
Prerequisites/Corequisites: Prerequisites: MATH 2400 and MATH 4600 or equivalent or permission of instructor.
When Offered: Fall term annually.
Credit Hours: 4
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MATH 6620 - Perturbation Methods
This course is devoted to advanced methods rather than theory. Content includes such topics as matched asymptotic expansions, multiple scales, WKB, and homogenization. Applications are made to ODEs, PDEs, difference equations, and integral equations. The methods are illustrated using currently interesting scientific and engineering problems that involve such phenomena as boundary or shock layers, nonlinear wave propagation, bifurcation and stability, and resonance.
Prerequisites/Corequisites: Prerequisites: MATH 2400 and MATH 4600 or equivalent or permission of instructor.
When Offered: Spring term even-numbered years.
Credit Hours: 4
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