Objectives of the Engineering Mechanics Program
Honors in Undergraduate Research Program
Engineering Mechanics Curriculum
Astronautics Option in Engineering Mechanics
Astronautics Curriculum
Facilities
Courses
153 Engineering Research Building, 1500 Engineering Drive, Madison, WI 53706; 608/263-7038; www.engr.wisc.edu/ep/ema
Professors Corradini (chair) (also Mechanical Engineering), Bier (also Industrial Engineering), Blanchard, Deluca (also Medical Physics), Drugan, Fonck, Hegna, Henderson, Hershkowitz, Kammer, Kulcinski, Lakes, Moses, Pfotenhauer (also Mechanical Engineering), Plesha, Smith (also Mathematics), Waleffe (also Mathematics); Associate Professors Bonazza, Crone, Sovinec, Thomadsen (also Medical Physics), Witt; Assistant Professors M. Allen, T. Allen, WilsonThe Department of Engineering Physics administers the B.S., M.S., and Ph.D. degrees in engineering mechanics. The B.S. degree in engineering mechanics may be accompanied by an option in astronautics.
Engineering mechanics provides a broad basic scientific background which enables its graduates to explore fundamental questions in most fields of engineering. The curriculum emphasizes the basic sciences—mathematics, computer science, physics, and chemistry, and the engineering sciences—fluid dynamics, thermodynamics, mechanics, materials science, and electrical engineering. Although entitled engineering mechanics here, similar programs are offered at many other major universities under such titles as engineering science, or theoretical and applied mechanics.
The objective of the program is to provide the student with a broad background in the fundamental physical sciences and applied mathematics, coordinated with both theoretical and applied engineering methods and experimental techniques. This type of educational background will give the student the degree of versatility necessary for dealing with the variety and complexity of modern technological problems as well as the ability to adapt to the rapidly changing needs and interests of industry, government, and society.
The values of an education in engineering mechanics are many. First, engineers frequently work on interdisciplinary teams with chemists, physicists, and mathematicians and must be able to interact with them. Second, many industrial organizations prefer that their engineers have a broad, fundamental scientific background. Third, and probably most important, great changes have taken place in science and engineering during recent years. Among the most important of these have been the rapid diffusion of scientific knowledge and disciplines into engineering, the increasing use of analytical and computer methods for the solution of practical problems, the need for a better understanding of the properties and behavior of materials, and the increasing need for engineers who can adapt known methods to new situations and develop new experimental and analytical methods.
The required courses taken early in the curriculum are intended to give the student a fundamental background in mathematics, science, and engineering. In addition to developing versatility through exposure to important concepts in various scientific fields, the required courses allow the students to identify areas of interest. With the relatively large number of elective credits available in the latter part of the program, the student may either continue to follow a general program or may prefer to concentrate elective courses in such areas as stress analysis and structural mechanics, dynamics and vibrations, experimental mechanics, applied mathematics, materials science, geological engineering, biomechanics, aerospace mechanics, mechanical systems analysis, etc.
Engineering mechanics graduates are sought by most industries and governmental agencies including in particular those participating in the newly developing areas of engineering such as space technology, performance of new structural materials, and so on. Their work often involves participation in design, research and development projects where the problems are sufficiently complex or unusual that their solutions require engineers with (1) a thorough understanding of the fundamentals of engineering, (2) advanced training in the established experimental and analytical methods, and (3) the ability to develop new experimental and analytical methods to attack problems for which standard methods, formulas, and materials have not yet been developed. The program also provides excellent preparation for graduate study in a variety of related disciplines.
The objectives of the engineering mechanics program are to:
Qualified undergraduates may earn a Honors in Research designation on their transcript and diploma by completing 8 credits of undergraduate honors research, including a senior thesis. Further information is available in the department office.
The following curriculum applies to students who entered the College of Engineering after May 2001.
Mathematics/Statistics Requirement, 22 cr
Science Requirement, 13 cr
Engineering Science Requirement, 26 cr
Engineering Mechanics Core Requirement, 31 cr
EMA Electives, 9 cr
Communications Skills Requirement, 7 cr Liberal Studies Requirement, 16 cr
Technical Electives Requirement, 3 cr
Total Credits: 127
Math 221 Calculus and Analytic Geometry, 5 cr
Math 222 Calculus and Analytic Geometry, 5 cr
Math 234 Calculus-Function of Several Variables, 3 cr
Math 319 Techniques in Ordinary Differential Equations, 3 cr
Math 340 Elementary Matrix and Linear Algebra, 3 cr
Stat 224 Introductory Statistics for Engineers, 3 cr
Chem 109 General Chemistry, 5 cr
Physics 202 General Physics, 5 cr
Physics 241 or 244 Modern Physics, 3 cr
EPD 160 Introduction to Engineering, 3 cr
ME 231 Introductory Engineering Graphics, 2 cr
NE 271 Engineering Problem Solving I, 3 cr
MS&E 350 Introduction to Materials Science, 3 cr
ME 361 Engineering Thermodynamics, 3 cr
ME 363 or CEE 310 Fluid Mechanics, 3 cr
ME 364 Elementary Heat Transfer, 3 cr
ECE 376 Electrical and Electronic Circuits, 3 cr
Computing Elective, 3 cr (must be selected from an approved list available in the department office)
EMA 201 Statics, 3 cr
EMA 202 Dynamics, 3 cr
EMA 303 Mechanics of Materials, 3 cr
EMA 307 Mechanics of Materials Lab, 1 cr
EMA 405 Practicum in Finite Elements, 3 cr
EMA 469 Design Problems in Engineering, 3 cr
EMA 506 Advanced Mechanics of Materials I, 3 cr
EMA 570 or EMA 540 or EMA 611 Exp. Mechanics or EMA 601 Exp. Mechanics Labs, 3 cr
EMA 521 Aerodynamics or ME 563 Intermediate Fluid Mechanics, 3 cr
EMA 542 Advanced Dynamics or EMA 545 Mechanical Vibrations, 3 cr
EMA 569 Senior Design Project, 3 cr
Any EMA course numbered 500 and above.
Communications "A" Elective, 2 (must be selected from an approved list available in the department office)
EPD 275 Technical Presentations or Com Arts 105 Public Speaking, 2 cr
EPD 397 Technical Writing, 3 cr
The College Liberal Studies Requirement is followed.
Three credits at a level that requires 2 semesters of calculus or 2 semesters of physics.
Chem 109 General Chemistry, 5 cr
Math 221 Calculus and Analytic Geometry, 5 cr
Communications "A" Elective, 2 cr
InterEgr (EPD) 160 Introduction to Engineering, 3 cr
EMA 201 Statics, 3 cr
Math 222 Calculus and Analytic Geometry, 5 cr
Stat 224 Statistics for Engineers, 3 cr
ME 231 Introductory Engineering Graphics, 2 cr
Liberal Studies Electives, 3 cr
Math 234 Calculus-Fn of Several Variables, 3 cr
Physics 202 General Physics, 5 cr
EMA 202 Dynamics, 3 cr
NE 271 Engineering Problem Solving I, 3 cr
EPD 275 or Com Arts 105 Public Speaking, 2 cr
Math 319 Techniques in Ordinary Differential Equations, 3 cr
Physics 241 or 244 Modern Physics, 3 cr
ME 361 Engineering Thermodynamics, 3 cr
EMA 303 Mechanics of Materials, 3 cr
EMA 307 Mechanics of Materials Lab, 1 cr
Liberal Studies Electives, 3 cr
EMA 506 Advanced Mechanics of Materials I, 3 cr
EMA 542 Advanced Dynamics or
EMA 545 Mechanical Vibrations, 3 cr
Math 340 Elementary Matrix and Linear Algebra, 3 cr
MS&E 350 Introduction to Materials Science, 3 cr
EPD 397 Technical Writing, 3 cr
Liberal Studies Electives, 3 cr
EMA 405 Practicum in Finite Elements, 3 cr
ME 363 or CEE 310 Fluid Mechanics, 3 cr
Computing Elective, 3 cr
Technical Electives, 3 cr
EMA 611 or EMA 540 or EMA 570, 3 cr
EMA 469 Design Problems in Engineering, 3 cr
EMA 521 Aerodynamics, 3 cr
EMA Electives, 3 cr
Liberal Studies Electives, 4 cr
ECE 376 Electrical Circuits, 3 cr
EMA 569 Senior Design Project, 3 cr
ME 364 Elementary Heat Transfer, 3 cr
EMA Electives, 6 cr Liberal Studies Electives, 3 cr
The astronautics option in engineering mechanics prepares students for design, development, and research, with an emphasis on applied mathematics and astronautics. Its purpose is to improve and expand the educational opportunities of students at the university who wish to pursue careers in astronautics and space-related areas. This is accomplished by providing in depth exposure to course sequences in astrodynamics, orbital mechanics, and flight dynamics, as well as a core curriculum of structural and material analysis, advanced dynamics, and vibrations. The program requires a minimum of 127 credits; students selecting this option must submit an option declaration form to the department office.
The following curriculum applies to students who entered the College of Engineering after May 2001.
Mathematics/Statistics Requirement, 22 cr
Science Requirement, 13 cr
Engineering Science Requirement, 26 cr
Engineering Mechanics/Astronautics Core Requirement, 40 cr
EMA Electives, 3 cr
Communications Skills Requirement, 7 cr
Liberal Studies Requirement, 16 cr
Total Credits: 127
Math 221 Calculus and Analytic Geometry, 5 cr
Math 222 Calculus and Analytic Geometry, 5 cr
Math 234 Calculus-Fn of Several Variables, 3 cr
Math 319 Techniques in Ordinary Differential Equations, 3 cr
Math 340 Elementary Matrix and Linear Algebra, 3 cr
Stat 224 Introductory Statistics for Engineers, 3 cr
Chem 109 General Chemistry, 5 cr
Physics 202 General Physics, 5 cr
Physics 241 or 244 Modern Physics, 3 cr
EPD 160 Introduction to Engineering, 3 cr
ME 231 Intro. Engineering Graphics, 2 cr
NE 271 Engineering Problem Solving I, 3 cr
ME 361 Engineering Thermodynamics, 3 cr
ME 363 or CEE 310 Fluid Mechanics, 3 cr
ECE 376 Electrical and Electronic Circuits, 3 cr
ME 364 Elementary Heat Transfer, 3 cr
ECE 332 or ME 446 Control Systems, 3 cr
Computing Elective, 3 cr (must be selected from an approved list available in the department office)
EMA 201 Statics, 3 cr
EMA 202 Dynamics, 3 cr
EMA 303 Mechanics of Materials, 3 cr
EMA 307 Mechanics of Materials Lab, 1 cr
EMA 405 Practicum in Finite Elements, 3 cr
EMA 469 Design Problems in Engineering, 3 cr
EMA 506 Advanced Mechanics of Materials I, 3 cr
EMA 540 or EMA 570 or EMA 611 Exp. Mechanics or EMA 601 Exp. Mechanics Labs, 3 cr
EMA 521 Aerodynamics or ME 563 Intermediate Fluid Dynamics, 3 cr
EMA 542 Adv. Dynamics, 3 cr
EMA 545 Mech. Vibrations, 3 cr
EMA 550 Astrodynamics, 3 cr
EMA 569 Senior Design Project, 3 cr
EMA 642 Satellite Dynamics, 3 cr
Any EMA course numbered 500 and above.
Communications "A" Elective, 2 cr (must be selected from an approved list available in the department office)
EPD 275 Technical Presentations or Com Arts 105 Public Speaking, 2 cr
EPD 397 Technical Writing, 3 cr
The College Liberal Studies Requirement is followed.
Chem 109 General Chemistry, 5 cr
Math 221 Calculus and Analytic Geometry, 5 cr
Communications "A" Elective, 2 cr
InterEgr (EPD) 160 Introduction to Engineering, 3 cr
EMA 201 Statics, 3 cr
Math 222 Calculus and Analytic Geometry, 5 cr
Stat 224 Statistics for Engineers, 3 cr
ME 231 Introductory Engineering Graphics, 2 cr
Liberal Studies Electives, 3 cr
Math 234 Calculus-Functions of Several Variables, 3 cr
Physics 202 General Physics, 5 cr
EMA 202 Dynamics, 3 cr
NE 271 Engineering Problem Solving I, 3 cr
EPD 275 Technical Presentations or Com Arts 105 Public Speaking, 2 cr
Math 319 Techniques in Ordinary Differential Equations, 3 cr
Physics 241 or 244 Modern Physics, 3 cr
ME 361 Thermodynamics, 3 cr
EMA 303 Mechanics of Materials, 3 cr
EMA 307 Mechanics of Materials Lab, 1 cr
Liberal Studies Electives, 3 cr
EMA 506 Adv. Mechanics of Materials I, 3 cr
EMA 405 Practicum in Finite Elements, 3 cr
ME 363 or CEE 310 Fluid Mechanics, 3 cr
Math 340 Elementary Matrix and Linear Algebra, 3 cr
EPD 397 Technical Writing, 3 cr
Liberal Studies Elective, 3 cr
EMA 550 Astrodynamics, 3 cr
EMA 545 Mechanical Vibrations, 3 cr
ME 364 Elementary Heat Transfer, 3 cr
Computing Elective, 3 cr
EMA 611 or EMA 540 or EMA 570, 3 cr
EMA 469 Design Problems in Engineering, 3 cr
EMA 521 Aerodynamics, 3 cr
EMA 542 Advanced Dynamics, 3 cr
Liberal Studies Electives, 4 cr
ECE 376 Electrical Circuits, 3 cr
EMA 569 Senior Design Project, 3 cr
EMA 642 Satellite Dynamics, 3 cr
ECE 332 or ME 446 Control Systems, 3 cr
Technical Electives, 3 cr
Liberal Studies Electives, 3 cr
Facilities available for instruction and research include:
Mechanics Holographic Lab
Viscoelasticity and Composites Lab
Wisconsin Laboratory for Structures and Materials Testing: Materials Testing Lab
Structural Mechanics Lab
Structural Dynamics and Vibrations Lab
Fatigue/Fracture Lab
Instructional Computing Lab (in Computer Aided Engineering)
Research Computing Lab
1 Cooperative Education Program. I, II, SS; 1 cr. Work experience which combines classroom theory with practical knowledge of operations to provide students with a background upon which to base a professional career in industry. P: So st.
201 Statics. I, II, SS; 3 cr (P-I). Principles of mechanics, force systems, equilibrium, structures, distributed forces, moments of inertia of areas, and friction. P: Math 222 or con reg. Open to Fr.
202 Dynamics. I, II, SS; 3 cr (P-I). Kinematics, force-mass-acceleration relations, work and energy, impulse and momentum, moments of inertia and mass. P: EMA 201 or 214; and Math 222; or cons inst.
303 Mechanics of Materials. I, II, SS; 3 cr (P-I). Stress and strain, torsion, bending of beams, shearing stresses in beams, compound stresses, principal stresses, deflections of beams, statically indeterminate members, columns. For civil engineers. P: EMA 201 & Math 222.
304 Mechanics of Materials. Irr.; 3 cr. Stress and strain, torsion, bending of beams, shearing stress in beams, compound stresses, principal stresses, deflections of beams, statically indeterminate members, columns. Includes six lab demonstrations on basic strength of materials properties of metal per semester. P: EMA 201 & Math 222.
306 Mechanics of Materials. I, II, SS; 4 cr. Stress and strain, bending of beams, shearing stresses in beams, compound stresses, principal stresses, deflection of beams, statically indeterminate members, columns, connections, energy methods. P: EMA 201 & Math 222.
307 Mechanics of Materials Lab. (Crosslisted with ME) I, II, SS; 1 cr. Data processing, tension/compression tests, creep stress concentrations, fatigue, fracture, composite materials, combined stress, beam flexure, dynamic loads, buckling. P: ME 306 or con reg, or EMA 306 or con reg, or EMA 304 or con reg.
395 Materials for Constructed Facilities. (Crosslisted with Civ Engr) II; 3 cr. Properties and tests of materials used in the initial construction or repair of facilities (including buildings, transportation systems, utility systems, and reinforced earth). Introduction to laboratory and field measurement techniques to assess material performance capabilities. Technical report preparation. P: EMA 304 or con reg.
405 Practicum in Finite Elements. I, II; 3 cr. Use of finite elements (FE) for solving practical problems in mechanics. Elementary theory of FE is discussed. A commercial computer program is used for applications. Major emphasis is on behavior of FE, modeling, and evaluation of results for correctness. P: EMA 214, 303, 304, or 306; EMA 202 or 221; knowledge of elementary matrix algebra or cons inst.
425 Undergraduate Rheology Seminar. (Crosslisted with CBE, Chem, ME) I, II; 0-1 cr (A). Rheology seminar course encouraged for all interested in professions related to polymers, suspensions or rheology; will not count toward credit requirement of the major. P: Cons inst or Jr st.
469 Design Problems in Engineering. I; 3 cr. The design philosophy is presented. Students will be required to apply their knowledge of elementary mechanics, engineering and basic science to arrive at acceptable solutions to a variety of design problems. P: EMA 221, 307; ECE 376; ME 363, 361; MS&E 350; or cons inst.
471 Intermediate Problem Solving for Engineers. (Crosslisted with E P) II; 3 cr. Use of computational tools for the solution of problems encountered in engineering physics applications. Topics covered include orbital mechanics, structural vibrations, beam and plate deformations, heat transfer, neutron diffusion, and criticality. Emphasis will be on modeling, choice of appropriate algorithms, and model validation. P: Math 319 & NEEP 271 or Comp Sci 310.
476 Introduction to Scientific Computing for Engineering Physics. (Crosslisted with E P, N E) Even yrs.; II; 3 cr. Basic tools of professional scientific computation for Unix environments are taught. Programming skills in a compiled language are developed through engineering examples. Applications reinforce engineering problem-solving skills first examined in introductory courses, while motivating progressively more advanced computational methods. P: NEEP 271 or Comp Sci 310; Comp Sci 412 or equiv; Math 319; or cons inst.
489 Honors in Research. I, II, SS; 1-3 cr. Undergraduate research and senior honors thesis in engineering mechanics and astronautics. P: Honors candidacy in engineering mechanics.
506 Advanced Mechanics of Materials I. I; 3 cr. Analysis and design of load-carrying members, shear center, unsymmetrical bending, curved beams, beams on elastic foundations, energy methods, theories of failure, thick-walled cylinders, stress concentrations, design to prevent failure by excessive elastic deformation, plastic deformation and fracture. P: EMA 214, 304, or 306/307.
508 Composite Materials. (Crosslisted with ME) II; 3 cr. Physical properties and mechanical behavior of polymer, metal, ceramic, cementitious, cellulosic and biological composite systems; micro- and macro-mechanics; lamination and strength analyses; static and transient loading; fabrication; recycling; design; analytical-experimental correlation; applications. P: ME 342 or ME 444 or ME/EMA 570 or EMA 506 or cons inst.
518 Fatigue of Engineering Materials. Irr.; 3 cr. Influence of repeated stress in engineering design, fatigue testing machines and procedures, factors influencing fatigue properties, theory of fatigue failure. P: EMA 214, 304, or 306/307.
519 Fracture Mechanics. Even yrs.; II; 3 cr. Introduction to the mechanics of fracture of linear and nonlinear materials. Crack stress and deformation fields; stress intensity factors; crack tip plastic zone; fracture toughness testing; energy release rate; J-integral. Criteria for crack growth initiation/stability; application to design. P: EMA 214, 304, or 306/307.
521 Aerodynamics. I; 3 cr (P-A). Fluid dynamics, stream functions and flow patterns, vortex filaments and sheets, two- and three-dimensional airfoil theory, compressibility effects, performance characteristics, Ackeret supersonic airfoil theory. P: EMA 202 or 221; Civ Engr 310 or ME 363; Math 223; or cons inst.
540 Experimental Vibration and Dynamic System Analysis. (Crosslisted with ME) II; 3 cr. Application of digital data acquisition to the investigation of mechanical components, structures and systems using time histories, transforms and response functions to characterize free, forced and transient inputs. Introduction to sensors, instrumentation and methods appropriate for dynamic system response. P: ME 340 or ME 440 or EMA 545 or cons inst.
542 Advanced Dynamics. I; 3 cr (P-A). Kinematics and kinetics of plane and three-dimensional motion, Coriolis acceleration, general methods of linear and angular momentum, central force motion, gyrodynamics, generalized coordinates. Lagrange's equations. P: EMA 202 or 221; EMA 304 or 306/307; Math 223; or cons inst.
545 Mechanical Vibrations. Even yrs.; II; 3 cr. General theory of free, forced, and transient vibrations; vibration transmission, isolation, and measurement; normal modes and generalized coordinates; method of matrix equation formulation and solution. The application of theory and methods to the analysis, measurement and design of dynamic systems. P: EMA 202 or 221; EMA 304 or 306/307; Math 223; or cons inst.
547 Engineering Analysis I. (Crosslisted with N E) I; 3 cr (P-I). Methods of higher mathematics; stress on problem solving rather than rigorous proofs; linear algebra, calculus of variations, Green's function. P: Yr adv calc such as Math 321 & 322.
548 Engineering Analysis II. (Crosslisted with N E) II; 3 cr (P-I). Function of complex variable, series solution of different equations, partial differential equations. P: A yr of math beyond calculus.
550 Astrodynamics. (Crosslisted with Astron) II; 3 cr (P-A). Coordinate system transformations, central force motion, two body problem, three and n-body problem, theory of orbital perturbations, artificial satellites, elementary transfer orbits, and elementary rocket dynamics. P: EMA 202 or 221; or Physics 311 or con reg; or cons inst.
552 Energy Methods in Mechanics. (Crosslisted with ME) Irr.; 3 cr (P-A). Variational principles of mechanics, virtual displacements, minimum potential energy; Hamilton's principle and Lagrange equations. Applications include stress analysis, elastic stability, dynamics and vibrations of rigid and elastic systems. P: Sr st or cons inst.
569 Senior Design Project. II; 3 cr. Students will select specific engineering design projects. These projects will be student team efforts supervised by individual faculty members. P: EMA 469, & any two of EMA 510, 545, 506 (606); or cons inst.
570 Experimental Mechanics. (Crosslisted with ME) I; 3 cr. Experimental methods for design and analysis of mechanical components, structures and materials. Electrically and optically recorded stress, strain and deformation data; computer acquisition/reduction/presentat techniques; applications to static and transient events, sensors, transducer design, NDT, fracture and residual stresses. P: ME 306 or EMA 214 or 303 or 304 or cons inst.
599 Independent Study. I, II; 1-3 cr (A). P: Cons inst.
601 Special Topics in Engineering Mechanics. I, II; 1-3 cr. Selected topics in such areas as structural mechanics, dynamics, experimental mechanics, vibrations, engineering materials, soil mechanics, engineering analysis, rheology, etc. P: Cons inst.
605 Introduction to Finite Elements. I; 3 cr. A first course in finite elements, with theory and applications in stress analysis and in areas related to structural mechanics. Practice in the use and/or development of computer programs. P: EMA 304 or 306/307; Math 340; Comp Sci 302; or cons inst.
611 Advanced Mechanical Testing of Materials. II; 3 cr. Theory and use of servo-controlled, electro-hydraulic equipment for research of mechanical properties of engineering materials. Measurement of stress, strain, hysteresis energy, and material properties during deformation and at fracture. Analysis of four significant components of total strain. P: EMA 307 & either EMA 506 or con reg in EMA 506.
615 Micro- and Nanoscale Mechanics. (Crosslisted with E P) Odd yrs.; II; 3 cr. An introduction to micro- and nanoscale science and engineering with a focus on the role of mechanics. A variety of micro- and nanoscale phenomena and applications covered, drawing connections to both established and new mechanics approaches. P: EMA 303 or ME 306 or cons inst.
622 Mechanics of Continua. II; 3 cr (P-A). Tensor analysis; analysis of stress, strain and rate of strain; application of Newtonian mechanics to deformable media; mechanical constitutive equations; field equations of fluid mechanics and elasticity. P: Math 340 & Math 321 or cons inst.
630 Viscoelastic Solids. I; Odd yrs.; 3 cr. Linear theory of viscoelasticity; non-aging materials; Boltzmann superposition principle; time-temperature superposition boundary value problems. Applications: vibration damping, relaxation of stress, creep, droop, and sag in structural members, sound absorption, creep buckling, settlement of foundations, tire mechanics, and shock attenuation. P: EMA 506 or equiv; or EMA 303 & cons inst.
642 Satellite Dynamics. II; 3 cr. Review of Euler's equations, torque-free motion, stability of rotation, energy dissipation effects, gyroscopic instruments, gyrodynamics of the Earth, gravity gradient stabilized satellites, spin stabilized satellites, dual spin satellites, tethered satellites, mass movement techniques, space vehicle motion and rocket dynamics. P: EMA 542.
690 Master's Research. 1-9 cr. P: Grad st.
697 VKI Aeronautical/Astronautical Research Practicum. 2 cr. Students perform research in the areas of fluid dynamics or aerospace plasma applications at the Von Karman Institute for Fluid Dynamics, under direct supervision of the VKI faculty and the UW faculty advisor. P: Any 4 of the following: EMA 521, 547, 548, NEEP 525, 526, 527, 528, ME 563, 572, 573, 773, 775.