New Rules of ME Ph.D. Qualifying Exams 1/8

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1 New Rules of ME Ph.D. Qualifying Exams 1/8 Qualifying Examination The student must pass a Qualifying Examination before the Dissertation Director, the Interdisciplinary Committee, and the courses for the Plan of Study are selected. The objective of the Qualifying Examination is to determine if the student has sufficient engineering background to qualify for doctoral studies. To ensure an equitable basis for evaluation, the Qualifying Examination shall be taken by all first year graduate students and must be a common written departmental examination. For ME students, the Qualifying Examination includes a mathematic portion and an Engineering portion. For the mathematic portion, each student takes one of three different exams (see Appendix I). For the Engineering portion, each student first needs to choose a primary area of exam among the following seven major areas in the Department: Thermal Sciences, Solid Mechanics, Fluids, Dynamics and Vibration, Controls and Manufacturing, and Materials, and Systems and Industrial Engineering. The student then needs to choose a secondary area from the rest of six areas. Student is required to take exams in both areas, with the primary exams more substantial than the secondary ones. The specific format in each area is listed in the Appendix II. Qualifying examination takes place each year on the dates determined by the coordinator of qualifying exam, usually at the end of September. Pass/Fail Criterion: Student must PASS all exams as required. The Pass/Fail criterion in each exam is determined by the faculty making up the exam. If a student fails any exam, the faculty grading the exam shall recommend to the ME Department whether he/she should (a) take the appropriate remedial course and score a B or higher grade in it or (b) re-take the exam. The student is only allowed to take the remedial course once and only one repeat test of an area exam is permitted. The repeat exam may be an Oral Exam if the responsible faculty so chooses.

2 New Rules of ME Ph.D. Qualifying Exams 2/8 Appendix I: Rules for the Math Part of ME Ph.D. Qualify Exams: Each student can take one of three different exams. Each exam would have 5 problems, and the student would be required to solve 3 of the 5 problems in two hours. The exams would be closed no notes or formula sheets (except those provided with the exam) would be permitted, although calculators would be required. Examination in Differential Equations. This exam will cover Ordinary Differential Equations (ODEs) and Partial Differential Equations (PDEs), two topics that are currently offered as separate exams. Five computational questions will be offered, 3 in ODEs and 2 in PDEs. A formula sheet containing Laplace Transform identities and formulas will be provided. The student must solve at least 1 problem from each subset as well as a third problem from either subset. Topics in ODEs include first order equations, second order constant coefficient inhomogeneous equations, Laplace transforms, systems of first order equations, and regular power series solutions. Topics in PDEs include separation of variables for second order hyperbolic or parabolic equations (which may include sources or inhomogeneous boundary conditions), and Laplace transform methods. The topics on this exam are covered in the courses 3450:335 Ordinary Differential Equations and 3450:439/539 Advanced Engineering Mathematics II. A calculator will probably not be useful on this exam. Students may use standard textbooks in ODEs and PDEs to prepare for the exam. Examination in Numerical Methods. This exam will cover basic numerical techniques covered in 3450:427/527 Applied Numerical Methods I. Five computational questions will be offered, and the student must solve 3 of the 5. Topics include root finding for nonlinear equations (Newton s Method, Secant Method, Bisection Method), polynomial interpolation (divided differences and using the error theorem), numerical integration (Newton-Cotes and Gaussian rules and their error formulas), and numerical linear algebra (Gauss Elimination with partial pivoting, Jacobi and Gauss-Seidel iteration). A calculator is necessary for this exam. Students may use standard textbooks in numerical analysis or numerical methods to prepare for the exam. Examination in Analysis. This exam will cover a range of topics (currently offered in the existing exams) that broadly fit under the title of analysis, although the problems will be mainly computational in nature. There will be three subtopics: Matrix Analysis (eigenvalues/eigenvectors, diagonalization, solvability of systems), Vector Calculus (vector fields, divergence and curl, line integrals, Green s Theorem, Divergence Theorem, Stokes Theorem), and Operational Methods (Bessel functions, Fourier series, Sturm-Liouville problems). Five computational questions will be offered, and the student must solve 3 of the 5. The exam will include two problems from Matrix Analysis, two problems from Vector Calculus and one problem from Operational Methods. The student must solve one problem from Matrix Analysis, one problem from Vector Calculus and one of the remaining problems from any of the subtopics. The topics Matrix Analysis and Vector Calculus are covered in 3450:438/538 Advanced Engineering Mathematics I. A calculator will be useful on this exam. Students may use any text on Advanced Engineering Mathematics to prepare for the exam all three subtopics can be found in these texts.

3 New Rules of ME Ph.D. Qualifying Exams 3/8 Appendix II: Rules for the Engineering Part of ME Ph.D. Qualify Exams (Draft): II-1. Solid Mechanics: Students who designate Solid Mechanics as a Primary or Core Qualifying Exam choose THREE exams in any of the topics listed below. Students who designate Solid Mechanics as a Secondary Qualifying Exam choose ONE exam in any of the topics listed below. The appropriate course which should prepare the student for each area exam is listed in brackets. The format of each test (written, open-book, closed-book, etc ) is determined by the faculty making up the exam. Note that only taking the recommended preparation courses does not guarantee a student will successfully pass any of these exams. Successful completion of doctoral qualifying exams is also a result of thorough and effective exam preparation. Complete preparation for taking any doctoral qualifying exam, including the collection of allowable formulas, graphs and tables for open-book exams, is the student s responsibility. Students are encouraged to speak to the relevant faculty about what is expected or required of them before taking any of the Qualifying Exams. Topics (and Recommended Preparation Courses) Advanced Mechanics of Solids (4600:625) Applied Stress Analysis (4600: 623) Applied Failure Analysis (4600:661) Continuum Mechanics (4600:622) Finite Element Analysis (4600:609) Composite Structures (4300:610) Theory of Elasticity (4300:682) Theory of Plasticity (4300:683) Pressure Vessel Analysis (4600:562) Experimental Stress Analysis (4600:522) II-2. Controls and Manufacturing Students who designate Controls and Manufacturing as a Primary Exam choose three exams in any of the topics listed below. Students who designate Controls and Manufacturing as a Secondary Qualifying Exam topic choose one exam in any of the topics listed below. The format of each test is determined by the faculty making up the exam. Control Sys Design 441/541 CAD/CAM 463/563 Robot Design Control & Applications 444/544 Exp. Sys: Controls & Manufacturing 646 Vehicle Dynamics 432/532 Neural/Fuzzy Control Systems 647 Process Identification and Computer Control 645 Integrated Flexible Manufacturing Systems 670

4 New Rules of ME Ph.D. Qualifying Exams 4/8 Fundamental and Applications of MEMS 671 Design of Micro and Nano Devices 672 Analysis of Manufacturing Systems II-3. Dynamics and Vibration A student whose primary area is Dynamics and Vibrations would be required to take an exam which covers 4600:203 and 4600:431 (both are undergraduate courses). The exam would cover advanced topics. A student taking Dynamics and Vibrations as a secondary area would only be required to take one exam (either Dynamics or Vibrations). The content in Dynamics would be at the advanced undergraduate level. The student should be able to take the principles of Dynamics and formulate advanced solutions form them (more than is seen in 4600:203). The Vibrations exam covers one and multi-degree-of-freedom systems from problem formulation through vibration isolation and vibration absorbers. II-4. Heat Transfer Exam Format: o Students who designate Heat Transfer as a Primary or Core Qualifying Exam will first choose TWO exams in any of the topics listed below in column (1). o Students who designate Heat Transfer as a Primary or Core Qualifying Exam may choose the THIRD exam also from column (1) or (2). o Students who designate Heat Transfer as a Primary or Core Qualifying Exam may choose a FOURTH engineering exam from any of the other disciplines available in the department. Alternately, the FOURTH exam may also be chosen from columns (1) or (2) o Students who designate Heat Transfer as a Secondary Qualifying Exam will choose ONE exam in any of the topics listed below in the Primary Qualifying Exam column (1). The format of each test (written, open-book, closed-book, etc ) is determined by the faculty making up the exam. There will be no oral examination. There is an underlying core of topics relevant to heat transfer and fluid flow that are covered in undergraduate courses. In preparation for the exams listed in columns (1) and (2) the students are advised to review and be familiar with material covered by the courses listed in column (3). Students are expected to demonstrate both basic understanding of the theoretical topics as well as the capability of applying theoretical knowledge to problem solving.

5 New Rules of ME Ph.D. Qualifying Exams 5/8 Students are highly advised to contact the faculty responsible in preparing the exam to find out the format of the exam as well as determine overall the areas they need to cover for proper preparation in anticipation of the exam. Primary Exams and Course List for Heat Transfer (Columns 1&2 and Recommended Courses of Study for General Preparation and Underlying Knowledge (Column 3) GRADUATE COURSES (4600)-XXX Primary, or Core Heat Transfer Thermo-Fluid Courses (1) pertinent to Convective Heat Transfer (2) -615 Conduction Heat Transfer -616 Convection Heat Transfer -617 Radiation Heat Transfer -618 Boiling Heat Transfer And Two-Phase Flow -600 Gas Dynamics 610 Dynamics Of Viscous Flow I -611 Computational Fluid Dynamics I -655 Micro- And Nano-Fluid Dynamics -608 Thermodynamics -710 Dynamics Of Viscous Flow II -650 Tribology -711 Computational Fluid Dynamics II -662 Microscale Heat And Mass Transfer -664 Fundamentals Of Crystallization And Solidification -693 Measurements Methods And Experimental Error in Thermofluid Sciences -719 Advanced Heat Transfer -715 Hydrodynamic Stability UNDERGRADUATE, AND DUAL RELEVANT COURSES These courses are mentioned to help in Preparation for columns (1) and (2) (3) -300 Thermodynamics I -301 Thermodynamics II -310 Fluid Mechanics I -311 Fluid Mechanics II -315 Heat Transfer -411 Compressible Fluid Mechanics -511 Compressible Fluid Mechanics -516 Heat Transfer Processes Introduction To Computational Fluid Flow And Convection

6 New Rules of ME Ph.D. Qualifying Exams 6/8 II-5. Materials Examination Format: 1. Students who designate Materials Science and Engineering as a Primary or Core Qualifying Examination will choose THREE exams in any of the topics delineated below. 2. Students who designate Materials Science and Engineering as the Primary Qualifying Exam will choose ONE Exam as Secondary Qualifying Exam from the subject topics delineated in the Column below. 3. Students who designate Materials Science and Engineering as a Secondary Qualifying Exam will choose ONE Exam in any of the topics listed in the table. The format of each written test or examination (written, open-book, closed book, etc) will be determined by the concerned faculty making up the examination. There will be NO oral examination. There is an underlying topic relevant to Materials Science and Engineering and is covered in the undergraduate curriculum. The students are expected to have a thorough knowledge of this topic as well, even though the course of choice for the examination is listed in Column 1 of the table. The students are expected to demonstrate both a basic understanding of the fundamental aspects of Materials Science and Materials Engineering as well as the synergism between the two and its applicability to solving problems in engineering and technological advances and innovation. Students are urged, advised and encouraged to contact the faculty responsible in preparing the examination to ascertain for themselves (a) the format of the examination, and (b) to determine the areas they need to concentrate for proper preparation in anticipation of the exam. The PASS-FAIL Criterion Students must pass all of the three examinations designated as a Core Qualifying Exam and ONE exam designated as Secondary Qualifying Exam. The pass/fail criterion in each exam is determined primarily by the faculty making up the examination. If a student fails in any of the examination, the faculty grading the exam shall recommend to the Mechanical Engineering department whether he/she should: (a) Take the appropriate remedial course and score an A- or higher grade in it (b) Re-take the examination. The student is only allowed to take the remedial course once and only one repeat test in an area examination is permitted. The repeat examination maybe an ORAL exam if the responsible faculty so chooses. The overall guidelines regarding to Doctoral (PhD) degree program, as well as the qualifying examination the student is encouraged to consult the Graduate Bulletin.

7 New Rules of ME Ph.D. Qualifying Exams 7/8 TABLE II-5.1 Graduate Courses and Related Under-graduate Course in the area crosspollinating Materials Science and Engineering Graduate Courses (4600:) 624: Fundamentals of Fracture Mechanics (Dr. Srivatsan) 626: Fatigue Behavior of Engineering Materials (Dr. Srivatsan) 627: Advanced Materials and Manufacturing Processes (Dr. Srivatsan) 628: Mechanical Behavior of Materials (Dr. Srivatsan 664: Crystallization and Solidification (Dr. G.X Wang) 694: Deform & Fail-Poly &Soft Materials (Dr. S-C. Wong) Fundamental and Applications of MEMS 671 Design of Micro and Nano Devices 672 Undergraduate and ( ) courses 380: Mechanical Metallurgy (i.e: Introduction to Materials Science and Engineering) (Dr. Srivatsan) 486: Corrosion in Engineering (Dr. R. Shemenski) New Course by Course by (Dr. Greg Morscher) Corrosion in Engineering ( Dr. R. Shemenski) 696: Mechanical Behavior of Nanomaterials and Composites (Dr. S. C. Wong) New Course by (Dr. Greg Morscher) Multi-scale and multi-physics modeling (Dr. Z. Xia)

8 New Rules of ME Ph.D. Qualifying Exams 8/8 II-6. Fluid Mechanics Exam Format Written examination all students answer compulsory questions students choose a number of optional questions Oral examination (immediately following primary exam) Exam topics Fluid statics Control volume theory Reynolds transport theorem application of conservation equations Fluid kinematics material derivative deformation of a fluid element (primary exam only) Differential fluid mechanics Navier-Stokes equations boundary layer theory Reynolds averaging turbulence modeling (primary exam only) potential theory (primary exam only) Computational Fluid Mechanics Gas dynamics stagnation properties for ideal gases isentropic flow with area change normal shock waves compressible flow with heat transfer (primary exam only) compressible flow with friction(primary exam only)

9 New Rules of ME Ph.D. Qualifying Exams 9/8 II-7. Systems and Industrial Engineering Students who designate Systems and Industrial Engineering as a Primary Exam take (1) a comprehensive written exam covering three of the topics listed below, and (2) an oral exam immediately following the written exam. Students who designate Systems and Industrial Engineering as a Secondary Qualifying Exam topic take a written exam covering one of the topics listed below. Introduction to Systems Engineering Enterprise Systems Engineering Lean Six Sigma Systems Simulation Neural Networks Operations Management of Supply Chain Stochastic Process Reliability