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.
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.
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
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.
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
pertinent to Convective
(1)
Heat Transfer (2)
UNDERGRADUATE, AND DUAL
400-500 RELEVANT COURSES
These courses are mentioned to help in
Preparation for columns (1) and (2)
(3)
-615
Conduction Heat
Transfer
-616
Convection Heat
Transfer
-617
Radiation Heat
Transfer
-618
Boiling Heat Transfer
And Two-Phase Flow
-608 Thermodynamics
-600
Gas Dynamics
-300
Thermodynamics I
610
-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
-650 Tribology
-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
Dynamics Of Viscous
Flow I
-611
Computational Fluid
Dynamics I
-655
Micro- And Nano-Fluid
Dynamics
-710
Dynamics Of Viscous
Flow II
-711
Computational Fluid
Dynamics II
-715
Hydrodynamic Stability
- 550
Introduction To Computational Fluid Flow
And Convection
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.
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
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)
Undergraduate and
(400-500) 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)
New Rules of ME Ph.D. Qualifying Exams
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)
8/8
New Rules of ME Ph.D. Qualifying Exams
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
9/8