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MEAM Graduate Courses

For a full listing of all University of Pennsylvania courses check the Course Register.

502. (MEAM 402) Energy Engineering.
Prerequisite(s): MEAM 203 (Thermodynamics), or equivalent and MEAM 333 or equivalent (Heat Transfer, that could be taken concurrently with MEAM 502).
Quantitative introduction to the broad area of energy engineering, from basic principles to applications. The focus is on the science and engineering, and includes environmental impact and some economics considerations. A review of energy consumption, use, and resources; sustainability, methods of energy and exergy (second law) analysis; power cycles, combined cycles, and co-generation; batteries and fuel cells; nuclear energy and wastes; fusion power; solar energy; power generation in space.

505. (MEAM 405, MSE 405, MSE 505) Mechanical Properties of Macro/Nanoscale Materials. (C)
The application of continuum and microstructural concepts to consideration of the mechanics and mechanisms of flow and fracture in metals, polymers and ceramics. The course includes a review of tensors and elasticity with special emphasis on the effects of symmetry on tensor properties. Then deformation, fracture and degradation (fatique and wear) are treated, including mapping strategies for understanding the ranges of material properties.

509. Mechanics of Human Motion.

This course considers normal human movement (especially grasping, reaching, walking, and running), pathological conditions (e.g., resulting from disease, injury, malformations), and engineering approaches such as prostheses (limb replacements) and orthoses (limb assists) that may ameliorate the conditions and promote normal movements and function. In doing so, we will also learn musculoskeletal anatomy, comparative anatomy, muscle mechanics, and neural control. An objective of the course is to bring together technical analysis and synthesis skills of students with the practical problems of persons disabled by amputation, stroke, spinal cord injury, and other causes. The potential problems of applying engineering techniques to human beings will be emphasized. Engineering design comprises that are necessary are also given emphasis.

510. (MEAM 410) Design of Mechatronic Systems.
Prerequisite(s): MEAM 310.
This course is cross-listed with an advanced level undergraduate course. It may be taken by M.S.E. students for credit. M.S.E. students will be required to do some extra work, they will be graded on a different grade scale than B.S. students, and they will be required to demonstrate a higher level of maturity in their class assignments. MEAM doctoral students will not be able to count 400/500 courses as a part of their degree requirements.
In many modern mechanical systems, mechanical elements are tightly coupled with electronics used for control or for sensing and possibly with microprocessors. Mechatronics is the study of computer-controlled electromechanical systems. This course is intended to provide an integrated introduction to the design of such systems. The course is intended for juniors and seniors in computer science and engineering, electrical engineering, mechanical engineering and systems engineering. The central focus of this course will be the completion of a team-based project, to be tested in an in-class competition during the final week of the course. Topics to be covered include: a review of mechanics; instrumentation, sensing and measurement; actuation and actuator dynamics; analog and digital interfacing; micro-processor technology and programming; basic control theory.

511. Creative Thinking & Functional Iteration In Design.

Visual Thinking is a drawing, creative thinking, and iterative prototyping course that uses a series of mechanical design projects to move students into the broad realm of unpredictable time-constrained problem solving.  Drawing and modeling are used as both tools of communication and as speculations in the development of concrete designs.

512. Design Arts Basics.   Note: For MEAM undergraduates, this course will only count as a Free Elective.

This course provides an introduction to the ideas and techniques of Industrial Design, which operates between Engineering and Marketing as the design component of Integrated Product Development.  The course is intended for students from engineering, design, or business with an interest in multi-disciplinary, needs-based product design methods.  It will follow a workshop model, combining weekly lectures on design manufacturing, with a progressive set of design exercises.

513. (ESE 406, ESE 505) Modern Feedback Control Theory.
Prerequisite(s): ESE 210.  Juniors and Seniors encouraged to enroll.

Basic methods for analysis and design of feedback control in systems. Applications to practical systems.  Methods presented include time response analysis, frequency response analysis, root locus, Nyquist and Bode plots, and the state-space approach.

514. Design for Manufacturability.

This course is aimed at providing current and future product design/development engineers, manufacturing engineers, and product development managers with an applied understanding of Design for Manufacturability (DFM) concepts and methods. The course content includes materials from multiple disciplines including: engineering design, manufacturing, marketing, finance, project management, and quality systems.

515. (MEAM415, OPIM415) Product Design.
This course provides tools and methods for creating new products. The course is intended for students with a strong career interest in new product development, entrepreneurship, and/or technology development. The course follows an overall product design methodology, including the identification of customer needs, generation of product concepts, prototyping, and design-for-manufacturing. Weekly student assignments are focused on the design of a new product and culminate in the creation of a prototype.

519. (MSE 550) Elasticity and Micromechanics of Materials.

This course is targeted to engineering students working in the areas on micro/nanomechanics of materials. The course will start with a quick review of the equations of linear elasticity and proceed to solutions of specific problems such as the Hertz contact problem, Eshelby’s problem etc. Failure mechanisms such as fracture and the fundamentals of dislocations/plasticity will also be discussed.

520. (CIS 390, MEAM420) Robotics and Automation.
Prerequisite(s): Graduate standing in engineering or permission of instructor.
Today's robots replace, assist, or entertain humans in many tasks. Recent examples of robots are planetary rovers, robot pets, medical surgical assistive devices, and semi-autonomous ground vehicles for search and rescue operations. The goal of this class is to introduce the students to the common kinematic, dynamic, and computational principles and practical examples that are representative of today's robotic systems. The three main topics are coordinate system transformations and kinematics, control of mobile robots, and motion planning of robotic systems. The laboratory component includes simulation exercises, programming and control of mobile robots, and demonstrations with robot arms.

521. Title: Introduction to Parallel Computing for Scientific Applications.
Prerequisites: Programming. Familiarity with Linux or Unix will help.
From numerical weather prediction and earthquake simulations, to quantum mechanics, and to genome sequencing and molecular dynamics, high-performance computing (HPC) is a fundamental tool for science. The basic principles on how to design, implement, and evaluate HPC techniques will be covered. Topics include parallel non-numerical and numerical algorithms, computing platforms, and message passing interface. Science applications will sample techniques applied to partial differential equations, many-body problems, and statistical physics. Practical problem-solving and hands-on examples will be a basic part of the course.

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522. Fundamentals of Sensor Technology.
Explores the principles of sensor science, develops the relationship between intensive and extensive variables, and presents the linear laws between these variables. Students will review the flux-force relations describing kinetic phenomena against the context of means for transducing temperature, stress, strain, magnetic processes and chemical concentration into electrical signals. The need for multivariate signal processing will be introduced and selected applied topics considered.

527. (ENM 427) Finite Element Analysis.
Prerequisite(s): MATH 241 and PHYS 151.
The objective of this course is to equip students with the background needed to carry out finite elements-based simulations of various engineering problems.  The first part of the course will outline the theory of finite elements.  The second part of the course will address the solution of classical equations of mathematical physics such as Laplace, Poisson, Helmholtz, the wave and the Heat equations.  The third part of the course will consist of case studies taken from various areas of engineering and the sciences on topics that require or can benefit from finite element modeling.  The students will gain hand-on experience with the multi-physics, finite element package FemLab.

528. Advanced Kinematics.
Prerequisite(s): Multivariate calculus, introductory abstract algebra, and mathematical maturity.
Differential geometry, Lie groups and rigid body kinematics; Lie algebra, quaternion and dual number algebra; geometry of curves and ruled surfaces; trajectory generation and motion planning; applications to robotics and spatial mechanisms.

529. (ESE 529) RF MEMS. (M)

Introduction to RM MEMS technologies; need for RF MEMS components in wireless communications. Review of micromachining techniques and MEMS fabrication approaches. Actuation methods in MEMS, TRF MEMS design and modeling. Examples of RF MEMS components from industry and academia. Case studies: micro-switches, tunable capacitors, inductors, resonators, filters, oscillators and micromachined antennas. Overview of RF NEMS.

530. Continuum Mechanics.
Prerequisite(s): Multivariable Calculus, Linear Algebra, Partial Differential Equations.

This course serves as a basic introduction to the Mechanics of Continuous Media and it will prepare the student for more advanced courses in Solid and Fluid Mechanics.  The topics to be covered include: Tensor Algebra and Calculus; Lagrangian and Eulerian Kinematics; Cauchy and Piola-Kirchhoff Stresses; General principles, Conservation of Mass, Conservation of Linear and Angular Momentum, Energy and the First Law of Thermodynamics, Entropy and the Second Law of Thermodynamics; Constitutive Theory, Ideal Fluids, Newtonian and non-Newtonian Fluids, Finite Elasticity, Linear Elasticity, Materials with Microstructure.

533. (MEAM 433) Advanced Heat and Mass Transfer.
Prerequisite(s): MEAM 302 and 333, or equivalent.
This course is cross-listed with an advanced level undergraduate course. It may be taken by M.S.E. students for credit. M.S.E. students will be required to do some extra work, they will be graded on a different grade scale than B.S. students, and they will be required to demonstrate a higher level of maturity in their class assignments. MEAM doctoral students will not be able to count 400/500 courses as a part of their degree requirements.
This course follows a first general course in heat transfer, to give further understanding of the basic mechanisms, the kinds of transport processes and of engineering applications, design and methodology. More generalized formulations, treatment, and results for conductive, convective, radiative and combined transport will be given. Extensive use of computers and microcomputers for numerical solutions of complex problems and computer-aided education. Several specific design applications will be considered in detail, such as the following: heat exchangers, thermal stressing, solar collectors, electronic equipment cooling, cooling towers, environmental discharges, engine cooling and structure icing.

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535. Advanced Dynamics.
Rigid body kinematics; Newtonian formulations of laws of motion; concepts of momentum, energy and inertia properties; generalized coordinates, holonomic and nonholonomic constraints.  Generalized forces, principle of virtual work, D'Alembert's principle.  Lagrange's equations of motion and Hamilton's equations.  Conservation laws and integrals of motion.  Friction, impulsive forces and impact.  Applications to systems of rigid bodies.

536. (MEAM 436) Viscous Fluid Flow.
Prerequisite(s): MEAM 302.
This course may be taken by M.S.E. students for credit. M.S.E. students will be required to do some extra work, they will be graded on a different grade scale than undergraduate students, and they will be required to demonstrate a higher level of maturity in their class assignments. MEAM doctoral students will not be permitted to count this course as a part of their degree requirements.
Review of the fundamental laws of fluid mechanics. Analysis and discussion of the theory of incompressible viscous flow. Dimensional reasoning, similarity, Stokes approximations, laminar boundary layer theory, methods for non-similar boundary layers, approximate techniques, stability and turbulence.

537. (MSE 537) Nanomechanics and Nanotribology at Interfaces
Prerequisites: Freshman physics; MEAM 354 or equivalent, or consent of instructor.
Engineering is progressing to ever smaller scales, enabling new technologies, materials, devices, and applications.  Mechanics enters a new regime where the role of surfaces, interfaces, defects, material property variations, and quantum effects play more dominant roles. This course will provide an introduction to nano-scale mechanics and tribology at interfaces, and the critical role these topics play in the developing area of nanoscience and nanotechnology. We will discuss how mechanics and tribology at interfaces become integrated with the fields of materials science, chemistry, physics, and biology at this scale. We will cover a variety of concepts and applications, drawing connections to both established and new approaches. We will discuss the limits of continuum mechanics and present newly developed theories and experiments tailored to describe micro- and nano-scale phenomena. We will emphasize specific applications throughout the course. Literature reviews, critical peer discussion, individual and team problem assignments, a laboratory project, and student presentations will be assigned as part of the course.

540. Optimal Design of Mechanical Systems.
Prerequisites: MATH 240, 312 or equivalent; MEAM 210, 453 or equivalent, or permission of the instructor; familiarity with a computer language; undergraduates need permission.
Mathematical modeling of mechanical design problems for optimization. Highlights and overview of optimization methods: unconstrained optimization, unidirectional search techniques, gradient, conjugate direction, and Newton methods.  Constrained optimization: KKT optimality conditions, penalty formulations, augmented Lagrangians, and others.  SLP and SQP and other approximate techniques for solving practical design problems.  Optimization of structural elements including shape and topology synthesis.  Variational formulation of distributed and discrete parameter structures.  Design criteria for stiffness, strength, stability, compliance, and dynamic response.  Design sensitivity analysis.  The course will emphasize computer programs to implement the algorithms discussed and solve realistic design problems.  A term project is required.

544. (BE 455, MEAM 455) Continuum Biomechanics. (I) Prerequisite(s): Statics, linear algebra, and differential equations. (L/R)
Biological and non-biological systems are both subject to several basic physical balance laws of broad engineering importance. Fundamental conservation laws are introduced and illustrated using examples from both animate as well as inanimate systems. Topics include kinematics of deformation, the concept of stress, conservation of mass, momentum, and energy. Mechanical constitutive equations for fluids, solids and intermediate types of media are described and complemented by hands-on experimental and computational laboratory experiences. Practical problem solving using numerical methods will be introduced.

545. (MEAM 435) Aerodynamics.
Prerequisite(s): MEAM 302.
This course is cross-listed with an advanced level undergraduate course. It may be taken by M.S.E. students for credit. M.S.E. students will be required to do some extra work, they will be graded on a different grade scale than undergraduate students, and they will be required to demonstrate a higher level of maturity in their class assignments. MEAM doctoral students will not be permitted to count this course as a part of their degree requirements.
Review of fluid kinematics and conservation laws; vorticity theorems; two-dimensional potential flow; airfoil theory; finite wings; oblique shocks; supersonic wing theory; laminar and turbulent boundary layers.

550. Design and Modeling of Micro-Electro-Mechanical Systems.
Prerequisites: MEAM 527 or equivalent is recommended. Undergraduates need permission.
Introduction to Micro-Electro-Mechanical Systems (MEMS). Modeling and multi-energy domain coupled simulations of MEMS devices and systems using simple analytical models as well as state-of-the-art methods and software. Designing MEMS devices for a Surface Micromachining "foundry" process: from paper designs to real devices. Nonlinear dynamics of electrostatically actuated MEMS devices. Synthesis of compliant micro structures. Review of selected papers from the literature. A term-project that includes design and fabrication (at an external "foundry" facility) of a micro device, and a term-paper on a selected topic are required.

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554. (MEAM 454) Mechanics of Materials.
Prerequisites: MEAM 210, MATH 240, 241.
This course is cross-listed with an advanced level undergraduate course. It may be taken by M.S.E. students for credit. M.S.E. students will be required to do some extra work, they will be graded on a different grade scale than B.S. students, and they will be required to demonstrate a higher level of maturity in their class assignments. MEAM doctoral students will not be able to count 400/500 courses as a part of their degree requirements.
Rods and Trusses. Stress. Principal Stresses. Strain. Compatibility. Elastic Stress-Strain Relations. Strain Energy. Plane Strain. Plane Stress. Bending of Beams. Torsion. Rotating Disks. Castigliano's Theorem. Dummy Loads. Principle of Virtual Work. The Rayleigh-Ritz Method. Introduction to the Finite Element Method. Non-Linear Material Behavior. Yielding. Failure.

555. (CBE 444/555, BE 444/555) – Nanoscale Systems Biology. (B)
Prerequisite(s): Background in Biology, Chemistry or Engineering with coursework in thermodynamics or permission of instructor. (L/L)

From single molecule studies to single cell manipulations, the broad field of cell and molecular biology is becoming increasingly quantitative and increasingly a matter of systems simplification and analysis. The elaboration of various stresses on cellular structures, influences of interaction pathways and convolutions of incessant thermal motions will be discussed via lectures and laboratory demonstration. Topic will range from, but are not limited, to protein folding/forced unfolding to biomoleculer

associations, cell and membrane mechanics, and cell motility, drawing from very recent examples in the literature. Frequent hands-on exposures to modern methods in the field will be a significant element of the course in the laboratory. Skills in analytical and professional presentations, papers and laboratory work will be developed.

561. Thermodynamics I.
Prerequisite(s): Undergraduate thermodynamics.
To introduce students to advanced classical equilibrium thermodynamics based on Callen's postulatory approach, to exergy (Second-Law) analysis, and to fundamentals of statistical and nonequilibrium thermodynamics. Applications to be discussed include advanced power and aerospace propulsion cycles, fuel cells, combustion, diffusion, transport in membranes, materials properties, superconductivity, elasticity, and biological processes.

564. (ESE 460, ESE 574) The Principles and Practice of Microfabrication Technology.
Prerequisite(s): Any of the following courses: ESE 218, MSE 321, MEAM 333, CHE 351, CHEM 321/322, Phys 250 or permission of the instructor.
A laboratory course on fabricating microelectronic and micromechanical devices using photolithographic processing and related fabrication technologies. Lectures discuss clean room procedures; microelectronic and microstructural materials; photolithography; diffusion, oxidation; materials deposition; etching and plasma processes. Basic laboratory processes are covered in the first two thirds of the course with students completing structures appropriate to their major in the final third. Students registering for ESE 574 will be expected to do extra work (including term paper and additional project).

570. (CBE 640) Transport Processes I.
The course provides a unified introduction to momentum, energy (heat), and mass transport processes.  The basic mechanisms and the constitutive laws for the various transport processes will be delineated, and the conservation equations will be derived and applied to internal and external flows featuring a few examples from mechanical, chemical, and biological systems.  Reactive flows will also be considered.

571. Advanced Topics in Transport Phenomena. (C)
Prerequisite(s): Either MEAM 570, MEAM 642, CHE 640 or equivalent, or Written permission of the Instructor.
The course deals with advanced topics in transport phenomena and is suitable for graduate students in mechanical, chemical and bioengineering who plan to pursue research in areas related to transport phenomena or work in an industrial setting that deals with transport issues. Topics include: Multi-component transport processes; Electrokinetic phenomena; Phase change at interfaces: Solidification, melting, condensation, evaporation, and combustion; Radiation heat transfer: properties of real surfaces, non-participating media, gray medium approximation, participating media transport, equation of radiative transfer, optically thin and thick limits, Monte-Carlo methods: Microscale energy transport in solids; microstructure, electrons, phonons, interactions of photons with electrons, phonons and surfaces; microscale radiation phenomena.

572. Micro/Nanoscale Energy Transport.
Prerequisite: Undergraduate thermodynamics and heat transfer (or equivalent), or permission of the instructor.  Undergraduates may enroll with permission of the instructor.
As materials and devices shrink to the micro- and nanoscale, they transmit heat, light, and electronic energy much differently than at macroscopic length scales.  This course provides a foundation for studying the transport of thermal, optical, and electronic energy from a microscopic perspective.  Concepts from solid state physics and statistical mechanics will be introduced to analyze the influence of small characteristic dimensions on the propagation of crystal vibrations, electrons, photons, and molecules.  Applications to modern microdevices and thermometry techniques will be discussed.  Topics to be covered include natural and fabricated microstructures, transport and scattering of phonons and electrons in solids, photonphonon and photon-electron interactions, radiative recombinations, elementary kinetic theory, and the Boltzmann transport equation.

575. Physicochemical Hydrodynamics and Interfacial Phenomena.
The course will focus on a few topics relevant to micro-fluidics and nano-technology. In particular, we will learn how the solid liquid interface acquires charge and the role that this charge plays in colloid stability, electroosmosis, and electrophoresis. Other topics will include controlled nano-assembly with dielectrophoresis, and stirring at very low Reynolds numbers (Lagrangian Chaos). The focus of the course will be on the physical phenomena from the continuum point of view. The mathematical complexity will be kept to a minimum. Software tools such as Maple and Femlab will be used throughout the course. The course will be reasonably self-contained and necessary background material will be provided consistent with the students’ level of preparation.

613. (CBE 617, CIS 613, ESE 617) Nonlinear Control Theory.
Prerequisite(s): Undergraduate Controls course.
This course focuses on nonlinear systems, planar dynamical systems, Poincare Bendixson Theory, index theory, bifurcations, Lyapunov stability, small-gain theorems, passivity, the Poincar map, the center manifold theorem, geometric control theory, and feedback linearization.

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620. Robotics.

Prerequisite(s): Graduate standing in engineering and MEAM 535 or ESE  500 or CIS 580 or equivalent.
Geometry of rigid body displacements, coordinate systems and transformations; Kinematics of spatial mechanisms, direct and inverse kinematics for serial chain linkages, velocity and acceleration analysis; Dynamics, trajectory generation and control of manipulators; Motion planning and control of robotic systems.

625. Haptic Interfaces for Virtual Environments and Teleoperation
Prerequisite(s): Graduate standing in engineering and MEAM 535 (Advanced Dynamics) or ESE 500 (Linear Systems Theory) or CIS 580 (Machine Perception) or equivalent. Undergraduates require permission.
This class provides a graduate-level introduction to the field of haptics, which involves human interaction with real, remote, and virtual objects through the sense of touch. Haptic interfaces employ specialized robotic hardware and unique computer algorithms to enable users to explore and manipulate simulated and distant environments. Primary class topics include human haptic sensing and control, haptic interface design, virtual environment rendering methods, teleoperation control algorithms, and system evaluation; current applications for these technologies will be highlighted, and important techniques will be demonstrated in a laboratory setting. Coursework includes problem sets, programming assignments, reading and discussion of research papers, and a final project. Appropriate for students in any engineering discipline with interest in robotics, dynamic systems, controls, or human-computer interaction.

631. Advanced Elasticity.
Prerequisite(s): MEAM 519 or permission of instructor.
Reciprocal theorem. Uniqueness. Variational theorems. Rayleigh-Ritz, Galerkin, and weighted residue methods. Three-dimensional solutions and potentials. Papkovitch-Neuber formulation. Problems of Boussinesq and Mindlin. Hertz theory of contact stress.

632. Plasticity.
Prerequisite(s): MEAM 519 or permission of instructor.
Plastic yield conditions and associated flow rules. Phenomenological theories for strain-hardening plasticity. Large strain theory. Physical theories of single crystal and polycrystal plasticity. Boundary value problems and plane strain slipline fields. Variational principles and limit analysis. Creep. Applications to structures, metal forming, friction and wear, contact, and fracture.

633. Fracture Mechanics.
Prerequisite(s): Background equivalent to MEAM 519 and ENM 510.
Linear elastic analysis of bodies with cracks. Energy balance criterion for crack growth and stability. Analysis of cracks in elastic-plastic and rate-dependent materials. J integral and applications to crack growth and stability. Large-scale yielding and dynamic fracture. Interface fracture.

634. Rods and Shells
Prerequisites: First-year graduate-level applied mathematics for engineers (ENM 510 and 511) and a first course in continuum mechanics or elasticity or permission of instructor.
This course is intended for 2nd year graduate students and introduces continuum mechanics theory of rods and shells with applications to structures and to biological systems as well as stability and buckling. The course begins with topics from differential geometry of curves and surfaces and the associated tensor analysis on Riemannian spaces. A brief introduction to variational calculus is included since variational methods are a powerful tool for formulating approximate structural mechanics theories and for numerical analysis. The structural mechanics theories of rods, plates and shells are introduced including both linear and nonlinear theories.

635. Composite Materials.
Prerequisite(s): ENM 510.  Corequisite(s): ENM 511.
This course deals with the prediction of the average, or effective properties of composite materials. The emphasis will be on methods for determining effective behavior. The course will be concerned mostly with linear mechanical and physical properties, with particular emphasis on the effective conductivity and elastic moduli of multi-phase composites and polycrystals. However, time-dependent and non-linear properties will also be discussed.

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642. Fluid Mechanics I.
Fluid mechanics as a vector field theory; basic conservation laws, constitutive relations, boundary conditions, Bernoulli theorems, vorticity theorems, potential flow. Viscous flow; large Reynolds number limit; boundary layers.

643. Fluid Mechanics II.
Waves, one-dimensional gas dynamics. Transition, turbulence. Small Reynolds number limit: Stokes' flow. Compressible potential flow. Method of characteristics. Rotating flows. Stratified flows. Jets.

644. Fluid Mechanics III.
Theory of hydrodynamic discontinuities: contact and gas dynamic. Shock structure. Higher order boundary layer theory. Stability theory. Compressible boundary layers or introduction to kinetic theory.

645. Fluid Mechanics IV.
Gas kinetic theory: Boltzmann equation. H-theorem, equilibrium solutions; transport coefficients. Rarified gas dynamics; methods of approximate solution to Boltzmann equation. Continuum limit: Navier-Stokes equations.

646. Computation Mechanics.
Prerequisite(s): ENM 510, ENM 511, and one graduate level introductory course in mechanics. FORTRAN or C programming experience is necessary.
The course is divided into two parts. The first introduces general numerical techniques for elliptical partial differential equations - finite difference method, finite element method and spectral method. The second part of the course introduces finite volume method. SIMPLER formulation for the NAVIER-Stokes equations will be fully described in the class. Students will be given chances to modify a program specially written for this course to solve some practical problems in heat transfer and fluid flow.

647. Non-Newtonian Fluid Dynamics.
Prerequisite(s): ENM 510 and MEAM 642 or 630.
This in an introductory course in rheology - study of flow and deformation of matter. The course will concentrate on modeling of mechanical behavior of fluids of high molecular weight under different flow conditions. The material covered in the course will be of interest to students in mechanical engineering, chemical engineering, materials science and bioengineering.

660. (MSE 660) Atomistic Modeling in Materials Science

Why and what to model: Complex lattice structures, structures of lattice defects, crystal surfaces, interfaces, liquids, linking structural studies with experimential observations, computer experiments.  Methods: Molecular statics, molecular dynamics, Monte Carlo.  Evaluation of physical quantities employing averages, fluctuations, correlations, autocorrelations, radial distribution function, etc.  Total energy and interatomic forces: Local density functional theory and abinitio electronic structure calculations, tight-binding methods, empirical potentials for metals, semiconductors and ionic crystals.

661. Advanced Thermodynamics Seminar.

Upon demand.

Classical statistical mechanics as developed by Gibbs and Boltzmann. The H-theoremand approach to equilibrium. Fluctuations, application to ideal and real gases and to chemical equilibrium, quantized systems, theory of specific heats, Maxwell Boltzmann, Bose-Einstein and Fermi-Dirac Statistics, mean-free path phenomena diffusion, the Botzmann equation and transport phenomena.

662. (BE 662, CBE 618) Advanced Molecular Thermodynamics.
Review of classical thermodynamics. Phase and chemical equilibrium for multicomponent systems. Prediction of thermodynamic functions from molecular properties. Concepts in applied statistical mechanics. Modern theories of liquid mixtures.

663. Entropic Forces in Biomechanics.

This course is targeted to engineering/physics students working in the areas of nano/bio technology. The course will start with a quick review of statistical mechanics and proceed to topics such as Langevin dynamics, solution biochemistry (Poisson-Boltzmann and Debye-Huckel theory), entropic elasticity of bio-polymers and networks, reaction rate kinetics, solid state physics and other areas of current technological relevance. Students will be expected to have knowledge of undergraduate mechanics, physics and thermodynamics.

664. Heat Conduction and Mass Diffusion.
Prerequisite(s): ENM 510, and undergraduate level heat and/or mass transfer.
Advanced modeling and solutions of heat conduction and mass diffusion, with emphasis on the similarities and analogies between these phenomena. Analytical and numerical solutions include the use of available general and specific software for the solution of the associated differential equations. Inverse problem solution techniques. Applications including basic and combined problems as well as moving interfaces, effects of energy sources and chemical reactions, interfacial contact resistance advanced insulation, thermal stresses, composite materials, and microscale and non-continuum systems.

665. Heat Transfer II: Convection.
Prerequisite(s): Undergraduate level heat transfer and MEAM 642 or permission of instructor.
Development of formulations governing forced, buoyancy induced, and phase change transport and convective motions with emphasis on the underlying conservation principles. Following the delineation of the different kinds of transport, the principal models, and methods applicable for each kind are discussed.

666. Heat Transfer III: Radiation.
Prerequisite(s): MEAM 664 and 665.
Introduction, black body radiation, radiation to and from a surface element, radiative heat exchange among surfaces separated by a non-participating medium, radiation and conduction in non-participating media, radiation and convection in non-participating media, introduction to radiative heat transfer in participating media.

690. Advanced topics in solid mechanics, dynamics, thermal-fluid science, or energy disciplines.
This course will be offered when demand permits. The topics will change due to the interest and specialties of the instructor(s). Some topics could include: Computational Fluid Mechanics, Visualization of Computational Results, Free Surface Flows, Fluid Mechanics of the Respiratory System, and transport in Reacting Systems.

691. Special Topics in Mechanics of Materials.
This course will be offered when demand permits. The topics will change due to the interests and specialties of the instructor(s). Some topics could include: Compliant Mechanisms, Optimal Control, and Fluid-Structure interaction.

692. Topics in Mechanical Systems.
This course will be offered when demand permits. The topics will change due to the interests and specialties of the instructor(s). Some topics could include: Electromagnetics, Control Theory, and Micro-Electro-Mechanical Systems.

699. MEAM Seminar.
The seminar course has been established so that students get recognition for their seminar attendance as well as to encourage students to attend. Students registered for this course are required to attend weekly departmental seminars given by distinguished speakers from around the world. There will be no quizzes, tests, or homeworks. The course will be graded S/U. In order to obtain a satisfactory (S) grade, the student will need to attend more than 70% of the departmental seminars. Participation in the seminar course will be documented and recorded on the students transcript. In order to obtain their degree, doctoral students will be required to accumulate six seminar courses and MS candidates (beginning in the Fall 2001) two courses. Under special circumstances, i.e. in case of conflict with a course, the student may waive the seminar requirement for a particular semester by petition to the Graduate Group Chair.

895. Teaching Practicum.
This course provides training in the practical aspects of teaching. The students will attend seminars emphasizing teaching and communication skills, deliver demonstration lectures, lead recitations, lead tutorials, supervise laboratory experiments, develop instructional laboratories, develop instructional material, prepare and grade homework; grade laboratory reports, and prepare and grade examinations. Some of the recitations will be supervised and feedback and comments will be provided to the student by the faculty responsible for the course. At the completion of the 0.5 c.u. of teaching practicum, the student will receive a Satisfactory/Unsatisfactory grade and a written evaluation signed by the faculty member responsible for the course. The evaluation will be based on comments of the students taking the course and the impressions of the faculty in charge.

899. Independent Study.
For students who are studying specific advanced subject areas in mechanical engineering and applied mechanics. Before the beginning of the term, the student must submit a proposal outlining and detailing the study area, along with the faculty supervisor's consent, to the graduate group chair for approval. At the conclusion of the independent study, the student should prepare a brief report.

990. Masters Thesis.
Master's Thesis

995. Dissertation.

999. Thesis/Dissertation Research.
Ph.D Thesis; Both terms.

Engineering and Applied Science (EAS)

EAS 501. (EAS 401) ENERGY AND ITS IMPACTS: TECHNOLOGY, ECOLOGY, ECONOMICS, SUSTAINABILITY.
(C) No prerequisites.  Any university student interested in energy and its impacts, preferably at the upper level undergraduate and non-engineering graduate level of maturity.  Students taking the course as EAS 501 will be given assignments commensurate with graduate standing.

The objective is to introduce students to one of the most dominating and compelling areas of human existence and endeavor: energy, with its foundations in technology, association to economics, and impacts on ecology and society. This introduction is intended both for general education and awareness and for preparation for careers related to this field. The course spans from basic principles to applications.  A review of energy consumption, use, and resources; ecological impacts, sustainability and design of sustainable energy systems; methods of energy analysis; forecasting; electricity generation systems (steam and gas turbine based power plants, fuel cells), energy for transportation (cars, aircraft, and ships); nuclear energy and wastes; renewable energy use: solar, wind, hydroelectric, geothermal, biomass; prospects for future energy systems: fusion power, power generation in space.

EAS 545. (EAS 445) Engineering Entrepreneurship I. (C)
Engineers and scientists create and lead great companies, hiring managers when and where needed to help execute their vision.  Designed expressly for students having a keen interest in technological innovation, this course investigates the roles of inventors and founders in successful technology ventures.  Through case studies and guest speakers, we introduce the knowledge and skills needed to recognize and seize a high-tech entrepreneurial opportunity - be it a product or service - and then successfully launch a startup or spin-off company.  The course studies key areas of intellectural property, its protection and strategic value; opportunity analysis and concept testing; shaping technology driven inventions into customer-driven products; constructing defensible competitive strategies; acquiring resources in the form of capital, people and strategic partners; and the founder's leadership role in an emerging high-tech company.  Throughout the course emphasis is placed on decisions faced by founders, and on the sequential risks and determinants of success in the early growth phase of a technology venture. The course is designed for, but not restricted to, students of engineering and applied science and assumes no prior business education.

EAS 546. (EAS 446) Engineering Entrpreneurship II. (C)
This course is the sequel to EAS 545 and focuses on the planning process for a new technology venture.  Like its prerequisite, the course is designed expressly for students of engineering and applied science having a keen interest in technological innovation.  Whereas EAS 545 investigates the sequential stages of engineering entrepreneurship from the initial idea through the early growth phase of a startup company, EAS 546 provides hands-on experience in developing a business plan for such a venture.  Working in teams, students prepare and present a comprehensive business plan for a high-tech opportunity.  The course expands on topics from EAS 545 with more in-depth attention to: industry and marketplace analysis; competitive strategies related to high-tech product/service positioning, marketing, development and operations; and preparation of sound financial plans. Effective written and verbal presentation skills are emphasized throughout the course.  Ultimately, each team presents its plan to a distinguished panel of recognized enterepreneurs, investors and advisors from the high-tech industry.

Engineering Mathmatics (ENM)

ENM 502. (ENM 402) Numerical Methods and Modeling.
Prerequisite(s): Knowledge of a computer language, Math 240 and 241; ENM 510 is highly recommended; or their equivalents. 
Numerical modeling using effective algorithms with applications to problems in engineering, science, and mathematics, and is intended for graduate and advanced undergraduate students in these areas.  Interpolation and curve fitting, numerical integration, solution of ordinary and partial (the course emhasis) differential equations by finite difference, and, more limitedly, finite element methods.  Optimization; Monte Carlo simulation.  Includes use of representative numerical software packages such as MATLAB PDE Toolbox and ALGOR.

ENM 510. Foundations of Engineering Mathematics - I.
Prerequisite(s): MATH 240, MATH 241 or equivalent.
This is the first course of a two semester sequence, but each course is self contained. Over the two semesters topics are drawn from various branches of applied mathematics that are relevant to engineering and applied science. These include: Linear Algebra and Vector Spaces, Hilbert spaces, Higher-Dimensional Calculus, Vector Analysis, Differential Geometry, Tensor Analysis, Optimization and Variational Calculus, Ordinary and Partial Differential Equations, Initial-Value and Boundary-Value Problems, Green’s Functions, Special Functions, Fourier Analysis, Integral Transforms, and Numerical Methods. For the 2006-07 Academic Year, the fall course will emphasize the study of Hilbert spaces, ordinary and partial differential equations, the initial-value, boundary value problem, and related topics.

ENM 511. Foundations of Engineering Mathematics - II.
Prerequisite(s): ENM 510 or equivalent.
Vector Analysis: space curves, Frenet – Serret formulae, vector theorems, reciprocal systems, co and contra variant components, orthogonal curvilinear systems. Matrix theory: Gauss-Jordan elimination, eigen values and eigen vectors, quadratic and canonical forms, vector spaces, linear independence, Triangle and Schwarz inequalities, n-tuple space.Variational calculus: Euler-Lagrange equation, Finite elements, Weak formulation , Galerkin technique, FEMLAB. Tensors: Einstein summation, tensors of arbitrary order, dyads and polyads, outer and inner products, quotient law, metric tensor, Euclidean and Riemannian spaces, physical components, covariant differentiation, detailed evaluation of Christoffel symbols, Ricci’s theorem, intrinsic differentiation, generalized acceleration, Geodesics.

ENM 520. Computational methods for ODE/PDE-constrained optimization
Prerequisites: Basic theory of ordinary and partial differential equations.
This course introduces the basic theory and algorithms for nonlinear optimization of continuum systems. Emphasis will be given on numerical algorithms that are applicable to problems in which the constraints are ordinary or partial differential equations. Such problems have numerous applications in science and engineering. Lectures and homework will examine examples related to control, design, and inverse problems in vision, robotics, computer graphics, bioengineering, fluid and solid mechanics, molecular dynamics, and geophysics.

ENM 540. Topics in Computational Science and Engineering.
Prerequisites: Background in ordinary and partial differential equations; proficiency in a programming language such as MATLAB, C, or Fortran.
This course focused on techniques for numerical solutions of ordinary and partial differential equations. The content will include: algorithms and their analysis for ODEs; finite element analysis for elliptic, parabolic and hyperbolic PDEs; approximation theory and error estimates for FEM.

ENM 600. Functional Analysis.
Prerequisite(s): ENM 500, ENM 501 or ENM 510, ENM 511 or equivalent.
This course teaches the fundamental concepts underlying metric spaces, normed spaces, vector spaces, and inner-product spaces. It begins with a discussion of the ideals of convergence and completeness in metric spaces and then uses these ideas to develop the Banach fixed-point theorem and its applications to linear equations, differential equations and integral equations. The course moves on to a study of normed spaces, vector spaces, and Banach spaces and operators defined on vector spaces, as well as functional defined between vector spaces and fields. The course then moves to the study of inner product spaces, Hilbert spaces, orthogonal complements, direct sums, and orthonormal sets. Applications include the study of Legendre, Hermite, Laguerre, and Chebyshev polynomials, and approximation methods in normed spaces. The course then concludes with a study of eigenvalues and eigenspaces of linear operators and spectral theory in finite-dimensional vector spaces.

ENM 601. Special Topics in Engineering Mathematics - Nonlinear Dynamics and Chaos.
Prerequisite(s): Permission of Instructor.
Continuous Dynamical Systems:  Nonlinear Equations versus Linear Equations, One-Dimensional Flows: Flows on a Line, Fixed Points and Stability, Linear Stability Analysis, Potentials, Bifurcations, and Flows on the Circle. Two-Dimensional Flows: Linear Systems, Eigenvalues and Eigenvectors, Classification of Fixed Points, Phase Portraits, Conservative Systems, Reversible Systems, Index Theory, Limit Cycles, Gradient Systems, Liaponov Functions, Poincare-Bendixson Theorem, Lienard Systems, Relaxation Oscillations, Weakly Nonlinear Oscillators, Perturbation Theory, Saddle-Node, Transcritical and Pitchfork Bifurcations, Hopf Bifurcations, Global Bifurcations of Cycles, Hysteresis, and Poincare Maps. Three-Dimensional Flows: The Lorenz Equations, Strange Attractors and Chaos, The Lorenz Map.

Discrete Dynamical Systems: One-Dimensional Maps, Chaos, Fixed Points and Cobwebs, The Liapunov Exponent, Universality and Feigenbaum's Number, Renormalization Theory, Fractals, Countable and Uncountable Sets, The Cantor Middle-Thirds Set, Self-Similar Fractals and Their Dimensions, The von Koch Curve, Box Dimension and Multifractals.